UTTARANCHAL
UNIVERSITY
UTTARANCHAL UNIVERSITY Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun,
Uttarakhand-248007, INDIA
Detailed Course Structure & Syllabus
of
B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
Under Choice Based Credit System (CBCS)
Course Structure & Syllabus of B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
EVALUATION SCHEME
B.Sc. (Hons.) Mathematics- 3 Years
Under Choice Based Credit System (CBCS)
Course Structure & Syllabus of B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
Semester – I
S.No Code Paper Title Period
L -T -P
Credit
L -T -P
Theory Practical
Total Total
Credit End
sem Sess
End
sem Sess
1.
TBHM/
PBHM
- 101
Calculus 4-0-2 4-0-1 60 40 25 25 150 5
2. TBHM-
102 Algebra 4-1-0 4-1-0 60 40 ----- ------ 100 5
3.
TBHG/
PBHG-
103
Generic
Elective-1
(GE-1)
4-0-4 4-0-2 60 40 25 25 150 6
4.
TBEC -
104
or
TBES -
104
English
Communicati
on/
Environmenta
l Science
2-0-0 2-0-0 60 40 ---- ------ 100 2
5. PBHA-
105
Educational
Visit/Activiti
es*
0-0-2 0-0-1 ----- ------ 25 25 50 1
Total 14-1-8 14-1-4 550 19
*Eco-Club/ Mathematics Club/ NSS activities etc.
Course Structure & Syllabus of B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
Semester – II
S.
No
Code Paper Title Period
L-T-P
Credit
L-T-P
Theory Practical Total Total
Credit End
sem.
Sess. End
sem
Sess.
1. TBHM-
201 Real Analysis 4-1-0 4-1-0 60 40 ----- ------ 100 5
2.
TBHM/P
BHM-
202
Differential
Equations 4-0-2 4-0-1 60 40 25 25 150 5
3.
TBHG/
PBHG-
203
Generic Elective-
2
(GE-2)
4-0-4 4-0-2 60 40 25 25 150 6
4.
TBEC -
204
or
TBES -
204
English
Communication/
Environmental
Science
2-0-0 2-0-0 60 40 ----- ------ 100 2
5. TBHE-
205
Human Ethics
and Professional
Values
2-0-0 2-0-0 60 40 ----- ------ 100 2
Total 16-1-6 16-1-3 600 20
Total for 1 & 2
Sem. 30-2-14 30-2-7 1150 39
Course Structure & Syllabus of B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
Semester – III S.
No
Code Paper Title Period
L-T-P
Credit
L-T-P
Theory Practical Total Total
Credit End
sem
Sess End
sem
Sess
1. TBHM-
301
Theory of
Real
Functions
4-1-0 4-1-0 60 40 ------ ----- 100 5
2. TBHM-
302
Group Theory
- I 4-1-0 4-1-0 60 40 ------ ----- 100 5
3.
TBHM/
PBHM -
303
PDE and
Systems Of
ODE
4-0-2 4-0-1 60 40 25 25 150 5
4. TBHG-
304
Generic
Elective-3
(GE-3)
4-1-0 4-1-0 60 40 ------ ----- 100 5
5.
TBHM-
305
Skill
Enhancement
Course – 1
(SEC-1)
2-0-0 2-0-0 60 40 ------ ----- 100 2
6 PBHS-
306 Seminar* 0-0-2 0-0-1 ----- ------ 25 25 50 1
Total 18-3-4 18-3-2 600 23
Total for 1, 2
& 3 Sem. 48-5-18 48-5-9 1750 62
* Seminar will be based on topic allotted by the Coordinator/HOD.
Course Structure & Syllabus of B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
Semester – IV
S.
No
Code Paper Title Period
L-T-P
Credit
L-T-P
Theory Practical Total Total
Credit End
sem.
Sess. End
sem.
Sess.
1. TBHM/
PBHM-
401
Numerical
Methods
4-0-2 4-0-1 60 40 25 25 150 5
2. TBHM-
402
Riemann
Integration
and Series of
Functions
4-1-0 4-1-0 60 40 ----- ------ 100 5
3. TBHM-
403
Ring Theory
& Linear
Algebra - I
4-1-0 4-1-0 60 40 ----- ------ 100 5
4. TBHG-
404
Generic
Elective-4
(GE-4)
4-1-0 4-1-0 60 40 ----- ------ 100 5
5. TBHM-
405
Skill
Enhancement
Course – 2
(SEC-2)
2-0-0 2-0-0 60 40 ----- ------ 100 2
6. PBHW-
406
Workshop/
Activity*
0-0-2 0-0-1 ----- ------ 25 25 50 1
Total 18-3-4 18-3-2 600 23
Total for
1,2,3 & 4
Sem.
66-8-22 66-8-11 2350 85
*Participation in activities like workshop/ model making/ poster making or any other assigned activity.
Course Structure & Syllabus of B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
Semester – V
S.
No
Code Paper Title Period
L-T-P
Credit
L-T-P
Theory Practical Total Total
Credit End
sem.
Sess End
sem.
Sess
1. TBHM
-501
Multivariate
Calculus 4-1-0 4-1-0 60 40 ------ ----- 100 5
2. TBHM
-502
Group
Theory – II 4-1-0 4-1-0 60 40 ------ ----- 100 5
3. TBHM
-503
Discipline
Specific
Elective – 1
(DSE-1)
4-1-0 4-1-0 60 40 ------ ----- 100 5
4. TBHM
-504
Discipline
Specific
Elective – 2
(DSE-2)
4-1-0 4-1-0 60 40 ------ ----- 100 5
5. PBSM
-505 Seminar* 0-0-3 0-0-2 ----- ----- 50 50 100 2
Total 16-4-3 16-4-2 500 22
Total for
1,2,3,4 & 5
Sem.
82-12-
25 82-12-13 2850 107
* Seminar will be based on SWYAM/ MOOC Courses/ UGC Open Courses or any other.
Course Structure & Syllabus of B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
Semester – VI
S.
No Code Paper Title
Period
L-T-P
Credit
L-T-P
Theory Practical
Total Total
Credit End
sem. Sess
End
sem. Sess.
1. TBHM-
601
Metric
Spaces and
Complex
Analysis
4-1-0 4-1-0 60 40 ----- ------ 100 5
2. TBHM-
602
Ring Theory
and Linear
Algebra - II
4-1-0 4-1-0 60 40 ----- ------ 100 5
3. TBHM-
603
Discipline
Specific
Elective – 3
(DSE-3)
4-1-0 4-1-0 60 40 ----- ------ 100 5
4. TBHM-
604
Discipline
Specific
Elective – 4
(DSE-4)
(Viva/
Dissertation)
4-1-0 4-1-0 60 40 ----- ------ 100 5
5. ADP-
605
Aptitude &
Reasoning
Skills
0-0-2 0-0-1 ------ ----- 25 25 50 1
Total 16-4-2 16-4-1 450 21
Total for
1,2,3,4,5 &
6 Sem.
98-16-27 98-16-14 3300 128
* Wherever there is a practical there will be no tutorial and vice-versa
Course Structure & Syllabus of B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
1. Evaluation Scheme for Internal Practical:
Practical Performance & Viva
During the Semester (10 Marks)
Attendance
Viva
Total
Internal Experiment File work
(5 Marks) (5 Marks) (5 Marks) (10 Marks) (25 Marks)
2. Evaluation Scheme for External Practical:
Experiment File Work Viva Total External
(10 Marks) (5 Marks) (10 Marks) (25 Marks)
3. Evaluation Scheme for Dissertation:
Dissertation Performance &
Presentation During the Semester Attendance Total Internal
(30 Marks) (10 Marks)
(40 arks)
4. External Evaluation (100 marks)
Thesis
Evaluation
Papers presented/Published in
conferences/Journals
Presentation &
Viva Total External
(15 Marks) (15 Marks) (30 Marks)
(60 Marks)
Course Structure & Syllabus of B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
LIST OF CORE COURSES (CC) (All 14 courses are compulsory)
S.
No. Course Code Course Name Credits Remarks
1 TBHM/ PBHM – 101 Calculus 5
2 TBHM-102 Algebra 5
3 TBHM-201 Real Analysis 5
4 TBHM/ PBHM-202 Differential Equations 5
5 TBHM-301 Theory of Real Functions 5
6 TBHM-302 Group Theory – I 5
7 TBHM/PBHM -303 PDE and Systems Of ODE 5
8 TBHM/PBHM-401 Numerical Methods 5
9 TBHM-402 Riemann Integration and Series of
Functions 5
10 TBHM-403 Ring Theory & Linear Algebra – I 5
11 TBHM-501 Multivariate Calculus 5
12 TBHM-502 Group Theory – II 5
13 TBHM-601 Metric Spaces and Complex
Analysis 5
14 TBHM-602 Ring Theory and Linear Algebra – II 5
Course Structure & Syllabus of B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
LIST OF ABILITY ENHANCEMENT COMPULSORY COURSES
S.No Course Code Course Name Credits Remarks
1. TBEC-104 English Communication 2
2. PBHA-105 Educational Visit/Activities 1
3. TBES-104 Environmental Science 2
4. TBHE-205 Human Ethics and Professional
Values 2
5. PBHS-306 Seminar 1
6. PBHW-406 Workshop/Activity 1
7. PBSM-505 Seminar 2
8. ADP-605 Aptitude & Reasoning Skills 1
Course Structure & Syllabus of B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
ELECTIVE COURSES
• List of Generic Elective (GE) Courses
S.
No. Course Code Course Name Credits Remarks
1
TBHG/PBHG- 103(1)-(2)
Fundamentals of Computers (P)
6 Choose any
One 2
Object Oriented Programming
in C++ (P)
1
TBHG/PBHG- 203(1)-(2)
Concepts of Programming (P)
6 Choose any
One 2
DBMS and Networking
Concepts (P)
1
TBHG/PBHG- 304(1)-(4)
Total Quality Management
5 Choose any
One 2 Intellectual Property Rights
3 Statics
1
TBHG/PBHG- 404(1)-(3)
Non-Conventional Energy
Resources
5 Choose any
One 2 Data Structure
3 Dynamics
Course Structure & Syllabus of B.Sc. (Hons.) Mathematics
Applicable for Batch: 2018-21
• List of Skill Enhancement Courses (SEC)
S. No Course Code Course Name Credits Remarks
1 TBHM-305
Logic and Sets 2
Choose any
One 2 Computer Graphics
1
TBHM-405
Graph Theory
2 Choose any
One 2 Combinatorial Mathematics
3 Applications of Algebra
• List of Discipline Specific Electives (DSE) Courses
S.No Course Code Course Name Credits Remarks
1.
TBHM-503
Portfolio Optimization
5 Choose any
One 2. Number Theory
3. Boolean Algebra and Automata Theory
4.
TBHM-504
Theory of Equations
5 Choose any
One 5. Analytical Geometry
6. Probability and Statistics
7.
TBHM-603
Industrial Mathematics
5 Choose any
One 8. Bio-Mathematics
9. Linear Programming
10.
TBHM-604
Mathematical Modelling
5 Choose any
One 11. Mechanics
12. Differential Geometry
13 Dissertation
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
PROGRAM EDUCATIONAL OBJECTIVES (PEOs), PROGRAM
OUTCOMES (POs) and PROGRAM SPECIFIC OUTCOMES (PSOs)
for
B.Sc. (Hons.) Mathematics- 3 Years
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
PROGRAM EDUCATIONAL OBJECTIVES (PEOs)
PEO 1. To equip students with knowledge, abilities and insight in mathematics and related fields
and enable them to work as a mathematical professional.
PEO 2. To develop the ability to utilize the mathematical problem-solving methods such as analysis,
modelling, and programming and mathematical software applications in addressing the practical
and heuristic issues.
PEO 3. Graduates will develop the skill to write entrance exam conducted by various Universities
and organizations to pursue higher studies/competent career.
PEO 4. Graduates will use their course as a training ground to develop their positive attitude, skills which
will enable them to become a multi facet personality shining in any chosen field.
PEO 5. The graduates will work and communicate effectively in inter-disciplinary environment, either
independently or in a team, and demonstrate leadership qualities.
PROGRAM OUTCOMES (POs)
PO 1. Disciplinary knowledge: Communicate various concepts of mathematics effectively in the
core subject of mathematics though various medium such as seminars, workshop,
presentations.
PO 2. Critical thinking and analytical reasoning: Analyze the results and apply them in various
problems appearing in different branches of mathematics.
PO 3. Problem solving: Provide new solutions using the domain knowledge of mathematics
acquired during this programme.
PO 4. Research-related skills: Inquiring about appropriate questions and advances relating to the
concepts in various fields of mathematics.
PO 5. Information/digital literacy: Create, select, and apply appropriate techniques, resources,
and modern scientific and IT tools with their limitations.
PO 6. Self-directed learning: Work independently and do in-depth study of various notions to
effectively enhance the communication skills.
PO 7. Moral and ethical awareness/reasoning: Educate the students about human values &
professional ethics related to society and environment.
PO 8. Lifelong learning: Prepare graduates according to broadest context of technological
change and ability to work independently and in group with lifelong learning skills in
society and Industry.
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
PROGRAM SPECIFIC OUTCOMES (PSOs)
PSO 1. Acquire knowledge pertaining to concepts of mathematics and widespread specific disciplines
including Calculus, Mathematical Analysis, Abstract Algebra, Number theory, Statics, LPP,
Statistics, Numerical analysis, logic & sets etc. along with allied fields including environment
science, computer fundamental and human ethics.
PSO 2. Strong foundation of Differential Equation, Linear algebra Mathematical modeling,
Dynamics, Graph theory and Operation Research which have strong link and application
in engineering, technology and physical sciences.
PSO 3. Identify the potential and applicability of concepts of applied mathematics to design/ drive
a solution to complex problems pertaining to industry, society and multidisciplinary
environment and simultaneously enhancing their critical thinking, practical, presentation,
communication and professional skills.
PSO 4. Enhance eligibility and increase competence to appear in various competitive examinations
for higher studies and pursue career in academia, industry, organizations etc.
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
COMPREHENSIVE TABLE
for B.Sc. (Hons.) Mathematics- 3 Years
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
S.N
o.
Course
Code
Course
Name
P
O1
P
O2
P
O3
P
O4
P
O5
P
O6
P
O7
P
O8
PS
O1
PS
O2
PS
O3
PS
O4
1 TBHM –
101 Calculus 2 2.5 2.5 1.5 2.5 - -
1.7
5 2.5 - 2 1.5
2 PBHM -
101 Calculus Lab 2 2.6 2 2 1.7 - - 1.5 2.6 - 2.3 2
3 TBHM-
102 Algebra 3 2.3 2 2 2.3 - - 1.5 2 1.7 1.5 1.8
4
TBHG-
103 (GE-
1)
Fundamental
of Computers - - - - 1.2 0.6 0.6 0.8 - - 0.2 0.4
5
PBHG-
103 (GE-
1)
Fundamental
of Computers
(Lab)
0.5 - - - 1.5 0.2 0.7 1.5 - - 0.5 0.75
6
TBHG-
103 (GE-
1)
Object
Oriented
Programming
in C++
2.4 2.2 1.8 2.2 2.4 - - - 2.2 - 2 -
7
PBHG-
103 (GE-
1)
Object
Oriented
Programming
in C++ (Lab)
- - - - 1.5 0.2 0.7 1.5 - - 0.5 0.75
8 TBEC -
104
English
Communicati
on
3 - 1 - - 3 - - 1 - 2 1
9 PBHA-
105
Educational
Visit 2 2 2.2 2 - 2 2 2 - - 1.5 -
10 TBHM-
201 Real Analysis
1.7
5 2 1 - 3 - - 2 2 - 2 2
11 TBHM-
202
Differential
Equations
2.2
5
2.2
5 2
1.7
5 1.5 - 2 2 2 2 - 2
12 PBHM –
202
Differential
Equations Lab 2
2.3
3 2
2.3
3 2 2 2 2 2 2.33 2 2
13
TBHG-
203 (GE-
2)
Concepts of
Programming 0.2 - - 0.2 1 - 1 1.2 - - 0.4 0.6
14
PBHG-
203 (GE-
2)
Concepts of
Programming
(Lab)
- - 0.3 0.3 1.3 0.3 0.6 1.3 - - 0.6 1
15
TBHG-
203 (GE-
2)
DBMS and
Networking
Concepts
1 1 2 1.5 2 - - - 2 1 1.5 1.2
16
PBHG-
203 (GE-
2)
DBMS and
Networking
Concepts
(Lab)
1 1 2 1 1.7
5 - - - 1 1 1.6 1.6
17 TBES-
204
Environmenta
l Science 2 - - - - 1 1 2 1 -- - 2
18 TBHE -
205
Human Ethics
&
Professional
Values
- - - - - - 3 - 1 - - -
19 TBHM-
301
Theory of
Real
Functions
3 2.5 2.3 1.8 1 2.3 2.5 2 2.3 1.8
20 TBHM-
302
Group
Theory-I 2.3 2.3 1.7 1 2 - - 1.8 3 - 1.5
1.8
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
21 TBHM-
303
PDE and
system of
ODE
2.5 2.5 2 2 2.3 - - 2 - 2.5 2.2 1
22 PBHM -
303
PDE and
Systems of
ODE Lab
2.6 2 2 1 2 - - 1.5 - 2.33 2.5 2
23
TBHG-
304 (GE-
3)
Total Quality
Management 1 2 2.3 1 2 3 2 2.75
24
TBHG-
304 (GE-
3)
Intellectual
Property
Rights
1 1 1 1
25
TBHG-
304 (GE-
3)
Statics 3 2 2 1.7 2.3 - 1 1.5 1.8 1.5 1.5 1.8
26
TBHM-
305
(SEC-1)
Logic and
Sets 3 2.5 2.5 2.5 2 - - 2 2.8 2.3 2.5 2.3
27
TBHM-
305
(SEC-1)
Computer
Graphics 1
1.2
5 1.5 1.5
2.2
5 - - - 1.5 1 1 1.5
28 PBHS-
306 Seminar 1.5 2 - 2 3 1 2 - 2 1.7 2
29 TBHM-
401
Numerical
Methods 3 1.8 1.8 2 1.3 - 1 1.8 2.5 1.5 1 1.5
30 PBHM-
401
Numerical
Methods Lab 3 1.3 2 1.7 2 - - 1.7 2.7 1.5 2.7 1.7
31 TBHM-
402
Riemann
Integration
and Series of
Functions
2 2 2 1.5 1.5 - - 1.5 2 - 2 2
32 TBHM-
403
Ring Theory
and Linear
Algebra – I
2.3 2.3 2.5 1.7 2 - - 1.8 1.3 1.7 1.8 1.5
33
TBHG-
404 (GE-
4)
Non-
Conventional
Energy
Resources
2 1.5 1.2
5 2 2 1 2 - 1 2.25 2.5 2
34
TBHG-
404 (GE-
4)
Data Structure 1 1.2
5 1.5 1.5
2.2
5 - - - 1.5 1 1 1.5
35
TBHG-
404 (GE-
4)
Dynamics 3 2.8 2.5 2.3 1 - - 2.5 2 3 2.3 2
36
TBHM-
405
(SEC-2)
Graph Theory 3 1.5 2 1.5 2 - - 2 - 2.3 1.67 1.67
37
TBHM-
405
(SEC-2)
Combinatorial
Mathematics 3 1.8 1.8 2 1.3 - 1 1.8 2.5 1.5 1 1.5
38
TBHM-
405
(SEC-2)
Applications
of Algebra 2.5 2.7 2.5 1.5 1.3 - - 2.2 2 2 2.25 2
39 PBHW-
406
Workshop/Act
ivities 1.5 2 - 2 3 1 2 - - 2 1.7 2
40 TBHM-
501
Multivariate
Calculus 2.5 2.8 1.8 1.3 1 - - 2 2.5 1 2 1.5
41 TBHM-
502
Group Theory
– II 1.8 2 2.3 2.3 2.5 - - 1.3 2.3 - 2
2.3
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
42
TBHM-
503
(DSE-1)
Portfolio
Optimization 2 2 2 1.5 1.5 - - 1.5 2 - 2 2
43
TBHM-
503
(DSE-1)
Number
Theory 3 1.5 2 1.3 2.3 - 1 1.8 2.3 - 1.7 1.5
44
TBHM-
503
(DSE-1)
Boolean
Algebra and
Automata
Theory
3 2 2 1.5 1.8 - 1 1.8 3 2.3 1.5 1.8
45
TBHM-
504
(DSE-2)
Theory of
Equations 2 1.7 1.3 1.5 1.8 - 1 1.5 3 1.7 1.5 1.5
46
TBHM-
504
(DSE-2)
Analytical
Geometry 3 1.3 1.5 1.5 1.3 - 1 2 3 1.7 1.5 1.3
47
TBHM-
504
(DSE-2)
Probability
and Statistics 1.7 2 1.5 2 2.3 - - 2 2.25 - 1.5 2.25
48 PBSM-
505 Seminar 1.5 2 - 2 3 1 2 - - 2 1.7 2
49 TBHM-
601
Metric Spaces
and Complex
Analysis
2.7 2.2 2 1.5 1.2 - - 1.7 3 - 2.7 2
50 TBHM-
602
Ring Theory
and Linear
Algebra – II
- 1.6
7
2.2
5 2 2.3 - - 1.7 2 2 1.5 2
51
TBHM-
603
(DSE-3)
Industrial
Mathematics 3 1.7 1.5 1 1 - 1 2.3 2.5 1.7 1.3 1.8
52
TBHM-
603
(DSE-3)
Bio-
Mathematics 3 1.7 1.3 1.5 1.8 - 1 2 - 1.7 1.5 1.8
53
TBHM-
603
(DSE-3)
Linear
Programming
problems
2.5 2.7 2.5 1.5 1.3 - - 2.2 2 2 2.25 2
54
TBHM-
604
(DSE-4)
Mathematical
Modeling 3 2 2 1.5 1.8 - 1 1.8 3 2.3 1.5 1.8
55
TBHM-
604
(DSE-4)
Mechanics 3 2 2 1.5 1.8 - 1 1.8 3 2.3 1.5 1.8
56
TBHM-
604
(DSE-4)
Differential
Geometry 3 2 2 1.5 1.8 - 1 1.8 3 2.3 1.5 1.8
57
TBHM-
604
(DSE-4)
Dissertation
1.5 2.5 3 - 3 1.5 2 - 2 2.5 3 2
58 ADP-
605
Aptitude &
Reasoning
Skills
3 2 2 1.5 1.8 - 1 1.8 3 2.3 1.5 1.8
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
SYLLABUS
of
B.Sc. (Hons.) Mathematics- 3 Years
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
SEMESTER -I
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code TBHM – 101 Credit 4
Year/Sem 1/1 L-T-P 4-0-0
Course Name Calculus
Objectives of the Course:
1. To learn the basic techniques of differentiation and integration.
2. To develop the concept of Leibnitz rule, curve tracing, asymptotes and its applications.
3. To derive parametric representations for plane curves, compute length for parametric
curves, use polar coordinates, and its conversion.
4. To identify the polar equations for lines, circles and conics. Learn to use the techniques
of Dirichlet’s integrals and Liouville’s extension.
UNIT-I (Total Topics- 8 and Hrs.- 9)
Hyperbolic functions, higher order derivatives, Leibniz rule and its applications to problems
of type𝑒𝑎𝑥+𝑏𝑠𝑖𝑛𝑥, 𝑒𝑎𝑥+𝑏𝑐𝑜𝑠𝑥, (𝑎𝑥 + 𝑏)𝑛𝑠𝑖𝑛𝑥, (𝑎𝑥 + 𝑏)𝑛𝑐𝑜𝑠𝑥.
UNIT -II (Total Topics -8 and Hrs-9)
Concavity and inflection points, asymptotes, curve tracing in Cartesian coordinates, tracing
in polar coordinates of standard curves, L’ Hospital’s rule, applications in business,
economics and life sciences.
UNIT- III (Total Topics -9 and Hrs-9)
Reduction formulae, derivations and illustrations of reduction formulae of the type
∫ sin 𝑛𝑥𝑑𝑥 , ∫ cos 𝑛𝑥𝑑𝑥 , ∫ tann 𝑛𝑥𝑑𝑥 , ∫ sec 𝑛𝑥𝑑𝑥 , ∫(log 𝑥)𝑛𝑑𝑥 , ∫ 𝑠𝑖𝑛𝑛𝑥𝑠𝑖𝑛𝑚𝑥𝑑𝑥
volumes by slicing, disks and washers methods, volumes by cylindrical shells, parametric
equations.
UNIT-IV (Total Topics -10and Hrs-9)
Parameterizing a curve, arc length, arc length of parametric curves, area of surface of
revolution. Techniques of sketching conics, reflection properties of conics, rotation of axes
and second-degree equations, classification into conics using the discriminant, polar
equations of conics.
UNIT-V (Total Topics -7 and Hrs-9)
Triple product, introduction to vector functions, operations with vector-valued functions,
limits and continuity of vector functions, differentiation and integration of vector functions,
tangent and normal components of acceleration.
Course Outcomes (COs):
TBHM- 101 CO 1.Acquire the sound knowledge of nth derivatives of the product of two
function, reduction formula. Scientifically and graphically comprehend the nature of
function.
TBHM- 101 CO 2.Develop key ideas of Leibnitz rule, learn applications of asymptotes,
concavity & point of inflexion in curve tracing to examine the real-world situations.
TBHM- 101 CO 3.Elaborate the standards of essential to take care of an assortment of
fundamental issues such as length of parametric curves, polar co-ordinates in sciences.
TBHM- 101 CO 4.Propose the solution of Dirichlet’s integrals and Liouville’s extension
and its formulation.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
References:
1. Thomas, G.B. and Finney, R.L., Calculus, Pearson Education, Delhi, 2005, 9th Ed.
2. Strauss, M.J., Bradley, G.L. and Smith, K. J., Calculus, Dorling Kindersley (India) P.
Ltd. (Pearson Education), Delhi, 2007, 3rdEd.
3. Anton, H., Bivens, I. and Davis, S., Calculus, John Wiley And Sons (Asia) P. Ltd.,
Singapore, 2002, 7th Ed.
4. Courant R., and John, F., Introduction to Calculus and Analysis (Volumes I & II),
Springer- Verlag, New York, Inc., 1989.
CO-PO Matrix Calculus TBHM-101
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
101CO1 2 3 3 2 3 _ _ 2 3 _ 2 2
TBHM-
101CO2 2 3 2 1 2 _ _ 2 2 _ 2 1
TBHM-
101CO3 2 2 2 1 2 _ _ 1 2 _ 3 1
TBHM-
101CO4 2 2 3 2 3 _ _ 2 3 _ 1 2
Average CO
(TBHM-101) 2 2.5 2.5 1.5 2.5 _ _
1.7
5 2.5 _ 2 1.5
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code PBHM - 101 Credit 1
Year/Sem 1/1 L-T-P 0-0-2
Course Name Calculus Lab
Objectives of the Course:
1. To visualize and to draw curve through curve tracing, concavity and convexity. Plotting
of graph of complex functions.
2. To sketch and evaluate arc length. Obtain area of surface of revolution through graphical
methods.
3. Classification and properties of conics and sketching of conics.
List of Practical’s
(i) Plotting of graphs of function eax + b, log (ax + b), 1/ (ax + b), sin (ax + b), cos (ax + b),
|ax + b| and to illustrate the effect of a and b on the graph.
(ii) Plotting the graphs of polynomial of degree 4 and 5, the derivative graph, the second
derivative graph and comparing them.
(iii) Sketching parametric curves (Eg. Trochoid, cycloid, epicycloids, hypocycloid).
(iv) Obtaining surface of revolution of curves.
(v) Tracing of conics in Cartesian coordinates/ polar coordinates.
(vi) Matrix operation (addition, multiplication, inverse, transpose).
Course Outcomes (COs):
PBHM- 101 CO 1. Construction of the graph of function to demonstrate the outcome of
different parameters to diagram.
PBHM- 101 CO 2. Sketch and trace the cartesian, parametric and polar curve with the
method of POSTAR by using the imagination capabilities.
PBHM- 101 CO 3. Improve the capacity of utilizing geometrical understanding of
mathematics in examining true issues of science and innovation.
References:
1. Thomas, G.B. and Finney, R.L., Calculus, Pearson Education, Delhi, 2005, 9th Ed.
2. Strauss, M.J., Bradley, G.L. and Smith, K. J., Calculus, Dorling Kindersley (India) P.
Ltd. (Pearson Education), Delhi, 2007, 3rd Ed.
3. Anton, H., Bivens, I. and Davis, S., Calculus, John Wiley and Sons (Asia) P. Ltd.,
Singapore, 2002, 7th Ed.
4. Courant R., and John, F., Introduction to Calculus and Analysis (Volumes I & II),
Springer- Verlag, New York, Inc., 1989.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix Calculus Lab PBHM-101
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
PBHM-
101CO1 2 2 2 1 1 _ _ _ 3 _ 3 2
PBHM-101
CO2 2 3 2 2 2 _ _ 2 2 _ 2 2
PBHM-101
CO3 2 3 2 3 2 _ _ 1 3 _ 2 _
Average CO
(PBHM-101) 2 2.6 2 2 1.7 _ _ 1.5 2.6 _ 2.3 2
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 25 25
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHM-102 Credit 5
Year/Sem 1/1 L-T-P 4-1-0
Course Name Algebra
Objectives of the Course:
1. To develop the basic concept of graphical representation of complex numbers.
2. To identify the relations and Functions, and its applications.
3. To derive the Division and Euclidean algorithms and evaluate the Congruence relation
between integers.
4. To learn the concept of Systems of linear equations and Provide the knowledge to find
Eigen values, and Eigen Vectors and its applications.
UNIT- I (Total Topics- 4 and Hrs- 8)
Polar representation of complex numbers, nth roots of unity, De Moivre’s theorem for rational
indices and its applications.
UNIT -II (Total Topics -7 and Hrs-9)
Equivalence relations, Functions, Composition of functions, Invertible functions, One to one
correspondence and cardinality of a set, Well-ordering property of positive integers.
UNIT- III (Total Topics -6 and Hrs-9)
Division algorithm, Divisibility and Euclidean algorithm, Congruence relation between
integers, Principles of Mathematical Induction, statement of Fundamental Theorem of
Arithmetic.
UNIT-IV (Total Topics -8 and Hrs-9)
Systems of linear equations, row reduction and echelon forms, vector equations, the matrix
equation Ax = b, solution sets of linear systems, applications of linear systems, linear
Independence.
UNIT-V (Total Topics -9 and Hrs-10)
Introduction to linear transformations, matrix of a linear transformation, inverse of a matrix,
characterizations of invertible matrices. Subspaces of 𝑅𝑛, dimension of subspaces of 𝑅𝑛and
rank of a matrix, Eigen values, Eigen Vectors and Characteristic Equation of a matrix.
Course Outcomes (COs):
TBHM-102 CO 1.Acquire the basic knowledge of arithmetic operations on complex number
and evaluated the argument of Complex numbers by using appropriate techniques.
TBHM-102 CO 2.Apply the matrix principle to examine the quantitative & qualitative
aspects of resolutions of mathematical models in scientific areas. & understand the concept
of different algebraic systems of equations.
TBHM-102 CO 3.Develop the critical thinking skills by using Principles of mathematical
induction and fundamental theorem of arithmetic.
TBHM-102 CO 4.Acquire knowledge of equivalence relations on sets and various types of
functions with application in real word.
References:
1. Andreescu, T. and Andrica D.,Complex Numbers from A to Z, Birkhauser.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
2. Goodaire, E.G. and Parmenter M. M., Discrete Mathematics with Graph Theory, Pearson
Education (Singapore) P. Ltd., Indian Reprint, 3rd Ed.
3. Lay ,D.C., Linear Algebra and its Applications, Pearson Education Asia, Indian Reprint,
2007, 3rdEd.
CO-PO Matrix Algebra TBHM-102
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-102
CO1 3 - 2 2 3 - - 1 3 - 1 2
TBHM-102
CO2 3 2 2 2 2 - - 2 1 2 1 2
TBHM-102
CO3 3 3 - - - - - 1 1 1 3 1
TBHM-102
CO4 3 2 2 2 2 - - 2 3 2 1 2
Average CO
(TBHM-102) 3.0 2.3 2.0 2.0 2.3 - - 1.5 2.0 1.7 1.5 1.8
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHG-103 Credit 4
Year/Sem 1/1 L-T-P 4-0-0
Course Name Fundamental of Computers
Objectives of the Course:
1. To describe the organization and operation of acomputer system, primary and secondary
memory, input, output devices.
2. To discuss the basic concepts of DOS and windows operating system.
3. Toidentify the various computer networks and the components used for networking.
4. To understand thefundamentals of number system like binary decimal, octal and
hexadecimal.
UNIT- I (Total Topics- 15 and Hrs.- 8)
Basics of Hardware and Software
Introduction to computers, primary memory, secondary memory, hardware, software, types
of software-system software, application software, history of computers, data and
information, input devices, output devices, generation of computer languages, compiler,
assembler, interpreter.
UNIT- II (Total Topics -18 and Hrs-10)
Operating System and its Functions
Introduction to DOS, operating system, types of operating system-batch processing system,
real time operating system, need of operating system, multitasking, introduction to DBMS,
concept of primary key, candidate key, super key, data redundancy, inconsistency, DBMS
v\s file system, applications of DBMS, types of attributes, integrity constraint, domain
constraint.
UNIT- III (Total Topics -12 and Hrs-10)
Number System
Introduction to number system, binary number system, octal number system, hexa-decimal
number system, interconversion of number system, 1’s complement, 2’s complement, logic
gates, binary addition, subtraction, BCD & gray codes.
UNIT-IV (Total Topics -12 and Hrs-12)
Fundamentals of Computer Network
Introduction to computer networks, client-server architecture, LAN, MAN, WAN,
advantages of computer network, modes of transmission, protocols, network topologies,
Introduction to transmission media, OSI reference model, functions of various layers of OSI.
UNIT-5: (Total Topics -12 and Hrs-8)
Basics of Software Engineering
Introduction to software engineering, software development life cycle, software development
models-water fall model, prototype model, types of software testing-black-box testing, white
box testing, alpha testing, beta testing, acceptance testing.
Course Outcomes (COs):
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
TBHG-103 CO 1.Acquire the knowledge about basic concepts of hardware and software
components and the role of these components in professional life as well as in daily life.
TBHG-103 CO 2.Know the difference between DOS and windows operating system.
TBHG-103 CO 3.Solve numerical problems by using binary subtraction, binary addition
and interconversion of binary number system.
TBHG-103 CO 4.Analyze the knowledge regarding computer networks, different
components of networking and also get to know various internet related concepts.
TBHG-103 CO 5.Attain knowledge and apply software development models and techniques
to implement, design, maintain and test a software system.
References:
1. Sinha , P. K. , Computer Fundamentals , BPB publications.
2. Rajaraman ,V. , Fundamentals of Computers, Prentice Hall.
3. Goel , A., Computer Fundamentals, Pearson.
4. Thareja , R., Computer fundamentals and programming in C, Oxford Publication.
5. Balagurusamy, E., Computer Fundamentals and C Programming, TMH.
6. Silveschatza, P. J., Operating System Concepts , Willey.
7. Das,S., Unix Concepts and applications, TMH, 2003.
CO-PO Matrix Fundamental of Computers TBHG-103
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHG-
103CO1
- - - - 1 1 1 - - - 1 1
TBHG-
103 CO2
- - - - 1 - - 1 - - - -
TBHG-
103 CO3
- - - - 1 1 - 1 - - - -
TBHG-
103 CO4
- - - - 2 - 1 1 - - - -
TBHG-
103 CO5
- - - 1 1 1 1 - - - 1
Average
CO
(TBHG-
103)
- - - - 1.2 0.6 0.6 0.8 - - 0.2 0.4
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B. Sc (H) Mathematics Programme Code 26
Course Code PBHG-103 Credit 2
Year/Sem 1/1 L-T-P 0-0-4
Course Name Fundamental of Computers (Lab)
Objectives of the Course:
1. To provide basic ideas related to operating system, DOS commands, use of operating
systems.
2. To familiarize students with installation of operating system and the use of system tools.
3. To provide knowledge about different computer application MS-Word, MS-Power point,
MS-Excel.
Experiments: At least 08 experiments from the following:
1. Getting familiar with Operating System
2. Creating File & folders, Renaming files, performing various operations on the file
3. DOS commands- CD, MKDIR, DATE, DIR, TIME, CALANDER, HELP CAT, TYPE,
MV CP, RENAME, BREAK etc.
4. Creating slides using Power points.
5. Creating resume using MS-word & practice on all other formatting system
6. Creating the Excel sheets &apply the basic formulas.
7. Creating E-mail account, Sending & receiving mail, File attachments.
8. Installation of Operating System
9. How to make Bootable Storage device
10. How to make a static web page using HTML.
Course Outcomes (COs):
PBHG-103 CO 1. Demonstrate and understanding the fundamental of software installation,
E-mail account and apply application software in an office environment.
PBHG-103 CO 2. Apply various HTML/CSS tags for creating webpages.
PBHG-103 CO 3. Identify the different types of operating system and their functions. Which
will be used in skill development.
PBHG-103 CO 4. Create documents that makes student efficient in the use of word
documents, spreadsheets and presentation applications.
References:
1. Rajaraman, V., Fundamentals of Computers, PHI,2004,4thEd.
2. Sinha, P.K and Priti, Computer fundamentals , BPB , 2003, 6thEd.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix Fundamental of Computers PBHG-103
Course Outcome P
O1
P
O2
P
O3
P
O4
P
O5
P
O6
P
O7
P
O8
PS
O1
PS
O2
PS
O3
PS
O4
PBHG-103CO1 - - - - 1 1 1 2 - - - -
PBHG-103 CO2 - - - - 1 - - 1 - - - -
PBHG-103 CO3 - - - - 2 - 1 2 - - 1 1
PBHG-103 CO4 2 - - - 2 - 1 1 - - 1 2
Average CO
(PBHG-103)
0.5 - - - 1.5 0.2 0.7 1.5 - - 0.5 0.75
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 25 25
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHG-103 Credit 4
Year/Sem 1/1 L-T-P 4-0-0
Course Name Object Oriented Programming in C++
Objectives of the Course:
1. To provide thorough knowledge of Object-Oriented Programming Using C++ and
2. To enhance the programming skills of the students by giving practical assignments to be
done in labs.
UNIT- I (Total Topics- 7 and Hrs.- 8)
OOP Paradigm: Comparison of Programming paradigms, Characteristics of Object-Oriented
Programming Languages, Object-based programming languages C++.
UNIT- II (Total Topics -8 and Hrs-8)
Brief History of C++, Structure of a C++ program, Difference between C and C++ - cin,
cout, new, delete operators, ANSI/ISO Standard C++, Comments, Working with Variables
and const Qualifiers.
UNIT- III (Total Topics -12 and Hrs-9)
Enumeration, Arrays and Pointer. Implementing oops concepts in C++ Objects, Classes,
Encapsulation, Data Abstraction, Inheritance, Polymorphism, Dynamic Binding, Message
Passing, Default Parameter Value,Using Reference variables with Functions.
UNIT-IV (Total Topics -12 and Hrs-10)
Abstract data types, Class Component, Object & Class, Constructors Default and Copy
Constructor, Assignment operator deep and shallow coping, Access modifiers – private,
publicand protected. Implementing Class Functions within Class declaration or outside the
Class declaration. instantiation of objects, Scope resolution operator, Working with Friend
Functions,
UNIT-5: (Total Topics -13 and Hrs-10)
Using Static Class members. Understanding Compile Time Polymorphism function
overloading Rules of Operator Overloading (Unary and Binary) as member function/friend
function, Implementation of operator overloading of Arithmetic Operators, Overloading
Output/Input,Prefix/ Postfix Increment and decrement Operators, Overloading comparison
operators, Assignment, subscript and function call Operator , concepts of namespaces.
Course Outcomes (COs):
TBHG-103 CO 1. Assess an object – oriented approach to the development of software
based on modelling objects from the real world.
TBHG-103 CO 2. Categorize a set of OOPs concepts and a language-independent graphic
notation, the Object Modeling method which can be used to analyze problem requirements,
propose a solution to the problem and then implement the solution in a programming
language.
TBHG-103 CO 3. Formulate an OO software development methodology from analysis,
through design, to implementation and comparison of high-level, conceptual analytics and
design processes.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
TBHG-103 CO 4. Construct an abstract way of thinking about a problem using concepts of
the real world, rather than computer concepts.
TBHG-103 CO 5. Illustrate the logic of overloading and overriding, functions, inheritance,
polymorphism and file handling. Contrast the major OOPs strategies for implementation of
programs using C++.
References:
1. Venugopal, A. R., Rajkumar, and Ravishanker, T. Mastering C++, TMH, 1997.
2. Lippman, S. B. and Lajoie, J.,C++ Primer, Addison Wesley, 2000,3rd Ed.
3. Eckel, B,Thinking in C++, President, Mindview Inc., Prentice Hall,2nd Ed.
4. Parasons, D.,Object Oriented Programming with C++, BPB Publication.
5. Stroustrup,,The C++ Programming Language, Addison Welsley, 3rd Ed.
CO-PO Matrix Object Oriented Programming in C++
TBHG-103
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHG-
103CO1 3 3 2 2 3 - - - 3 - 1 -
TBHG-103
CO2 2 3 2 3 3 - - - 2 - 3 -
TBHG-103
CO3 2 1 1 2 2 - - - 2 - 2 -
TBHG-103
CO4 2 2 2 1 2 - - - 2 - - -
TBHG-103
CO5 3 2 2 3 2 - - - 2 - 2 -
Average CO
(TBHG-103) 2.4 2.2 1.8 2.2 2.4 - - - 2.2 - 2 -
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B. Sc (H) Mathematics Programme Code 26
Course Code PBHG-103 Credit 2
Year/Sem 1/1 L-T-P 0-0-4
Course Name Object Oriented Programming in C++ (Lab)
Objectives of the Course:
1. To evaluate the problem-solving techniques by using the basic concepts of C ++
language.
2. To understand the fundamental of flowchart and algorithm to develop the programs and
to solve the problems.
3. To acquire knowledge about C++ language program structure.
1. Simple C++ Programs to Implement “If and loop” Control Structures.
2. Write a C++ program to show the use of object and classes.
3. Write a C++ program to show the concept of inheritance.
4. Write a C++ program to demonstrate the concept of constructor and destructor.
5. Write a C++ program to show function overloading
6. Write a C++ program to show the implementation of function overriding.
7. Write a C++ program to Understand Friend Function & Friend Class.
8. Write a C++ program to show the use of copy constructor
Course Outcomes (COs):
PBHG-103 CO 1. Create the C++ program for given algorithm and flowchart.
PBHG-103 CO 2. Solve real time problems by using objects and classes.
PBHG-103 CO 3. Create any application by applying logics and concepts of C++ language
like constructor, function overloading and Inheritance.
References:
1. Venugopal, A. R., Rajkumar, and Ravishanker, T. Mastering C++, TMH, 1997.
2. Lippman, S. B. and Lajoie, J.,C++ Primer, Addison Wesley, 2000,3rd Ed.
3. Eckel, B,Thinking in C++, President, Mindview Inc., Prentice Hall,2nd Ed.
4. Parasons, D.,Object Oriented Programming with C++, BPB Publication.
5. Stroustrup,,The C++ Programming Language, Addison Welsley, 3rd Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix Object Oriented Programming in C++Lab PBHG-103
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
PBHG-
103CO1
- - - - 1 1 1 2 - - - -
PBHG-103
CO2
- - - - 1 - - 1 - - - -
PBHG-103
CO3
- - - - 2 - 1 2 - - 1 1
Average CO
(PBHG-103)
- - - - 1.5 0.2 0.7 1.5 - - 0.5 0.75
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 25 25
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBEC -104 Credit 2
Year/Sem 1/1 L-T-P 2-0-0
Course Name English Communication
Objectives of the Course:
The specific objectives of this course are to develop in the student the ability to demonstrate
the following:
1. Understanding of the process of communication and its classification
2. Writing,Listening and Speaking skills
3. Assessment and critical analysis of literary texts
4. Reflect effective communication and overcome the barriers to communication enable
self-directed learning
5. Proper usage of language skills to communicate in professional situations to enhance the
competency.
UNIT- I (Total Topics- 7and Hrs- 5)
English Writing Skills
Grammar& Vocabulary:
1.1 Parts of Speech
1.2 Tenses
1.3 Agreement of Verb with Subject
1.4 Antonym and synonym
1.5 One word substitution
1.6 Homophones
1.7 Jargons, Prefix and Suffix
UNIT- II (Total Topics -7 and Hrs-5)
Reading Skills:
2.1 Process of Reading skills, Importance of Reading skills, Methods to improve reading
skills.
Some Literature based reading:
Poem:
2.2 “If” by Rudyard Kipling
2.3 “Stopping by the woods on a snowy evening” by Robert Frost
Stories:
2.4 “Under a Banyan tree” by R.K.Narayan
2.5 “The Eyes are not here” by Ruskin Bond
Value based Prose:
2.6 Abraham Lincoln’s Letter to his son’s teacher
2. 7 “I Have a Dream” by Martin Luther king
UNIT- III (Total Topics 4- and Hrs-10)
Business Correspondence:
3.1 Memorandum, Notice, Agenda, Minutes of the meeting
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
3.2 Business letters: Sales, Inquiry, Complaint
3.3 Job Application and Resume writing
3.4 Report writing : Feature, Structure, Types
UNIT-IV (Total Topics -3 and Hrs-10)
Communication:
4.1 Communication: Meaning, Types, Process, Barriers
4.2 Listening skills, Process,types, Methods to improve listening skills
4.3 Speaking skills, Conversation, Stress, Intonation.
Course Outcomes (COs):
TBEC -104 CO 1.Understand the meaning and the process of communication along with its
types and barriers.
TBEC -104 CO 2.Develop proficiency in English Language through vocabulary building
and correct use of grammar.
TBEC -104 CO 3.Acquire competency in reading and listening by understanding the skills
involved and assessing &analyzing literary texts critically.
TBEC -104 CO 4.Form a clear concept of writing style in technical communication and
develop technical writing skills.
TBEC -104 CO 5.Develop speaking skills by understanding the basic concepts and enhance
proficiency in verbal and non- verbal communication.
References:
1. Revathi, S., Communicating Effectively in English, Book-I ,Abhishek Publications,
Chandigarh.
2. Sasikumar ,V. and Dhamija, P.V., Spoken English, Tata McGraw Hill.
3. Aslam, M., Introduction of English Phonetics and Phonology, Cambridge.
4. Pal and Rorualling , Essentials of Business Communication , Sultan Chand and Sons.
5. Kohli ,A.L., New Design English Grammar, Reading and Writing Skills ( Course A
and Course B ), Kohli Publishers, 34 Industrial Area Phase- II, Chandigarh.
6. Raina, M.K., Developing English Communication, Orient Blackswan.
7. Krishna Mohan and Banerji, M., Developing Communication Skills, MacMillan
India
8. Sharma ,S.D., Communication Skills,Natraj Publishing House, Karnal
9. Thomson and Marlinet, A Practical English Grammar.
10. Wren and Martin , High School Grammar and Composition, S. Chand & Company
Ltd., Delhi
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix English Communication TBEC-104
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBEC-104
CO1 3 - - - - 3 - - 1 - 2 1
TBEC-104
CO2 3 - - - - 3 - - 1 - 2 1
TBEC-104
CO3 3 - - - - 3 - - 1 - 2 1
TBEC-104
CO4 3 - 1 - - 3 - -- 1 - 2 1
TBEC-104
CO5 3 - - - - 3 - - 1 - 2 1
Average CO
(TBEC-104) 3 - 1 - - 3 - - 1 - 2 1
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code PBHA-105 Credit 1
Year/Sem 1/1 L-T-P 0-0-2
Course Name Educational Visit
Objectives of the Course:
1. To widen the understudy's frame of reference and worldwide social mindfulness through
connection with the expert specialists.
2. To provide students a chance to relate the study to the present reality circumstances.
3. To supplement class room program with field visits and profession centered agenda.
4. To enable the students to recognize and explore the non-test research.
Students will visit the scientific and educational places and will study the impact of different
aspects socially and economically and will prepare summary report.
Course Outcomes (COs):
PBHA-105 CO 1.Analyze many ground real factors and a chance to associate and talk about
with the business heads/academicians.
PBHA-105 CO 2.Carries to all the students to a typical stage independent of their social,
monetary and cultural foundation.
PBHA-105 CO 3.Appraise to discover answers for genuine issues and makes them inventive.
PBHA-105 CO 4.Opportunity to advance and be on their own which improves relational
abilities and makes them all the more explorative.
CO-PO Matrix Educational Visit PBHA -105
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
PBHA-105
CO1 2 2 2 _ _ 2 2 2 _ _ 1 _
PBHA-105
CO2 2 2 2 2 _ 2 2 _ _ _ 2 _
PBHA-105
CO3 2 2 3 2 _ 2 _ 2 _ _ 2 _
PBHA-105
CO4 2 2 2 2 _ 2 2 2 _ _ 1 _
Average CO
(PBHA -105) 2 2 2.2 2 _ 2 2 2 _ _ 1.5 _
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 25 25
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
SEMESTER -II
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHM-201 Credit 5
Year/Sem 1/2 L-T-P 4-1-0
Course Name Real Analysis
Objectives of the Course:
1. To demonstrate the Algebraic properties & order properties of Real Numbers.
2. To develop a basic knowledge of important mathematical concepts in real analysis such
as neighborhood, isolated point, bounded or unbounded sets and limit point.
3. To acquire the knowledge of completeness property of Real numbers for rational and
irrational number.
4. To learn the concept of Sequence and series and their tests for convergence or
divergence.
UNIT-I (Total Topics- 14 and Hrs- 9)
Review of Algebraic and Order Properties of R, 𝛿-neighborhood of a point in R, Idea of
countable sets, uncountable sets and uncountability of R. Bounded above sets, Bounded
below sets, Bounded Sets, Unbounded sets, Suprema and Infima.
UNIT- II (Total Topics -8 and Hrs-10)
The Completeness Property of R, TheArchimedean Property, Density of Rational (and
Irrational) numbers in R, Intervals. Limit points of a set, Isolated points, Illustrations of
Bolzano-Weierstrass theorem for sets.
UNIT- III (Total Topics -7 and Hrs-9)
Sequences, Bounded sequence, Convergent sequence, Limit of a sequence. Limit Theorems,
Monotone Sequences, Monotone Convergence Theorem.
UNIT-IV (Total Topics -7 and Hrs-10)
Subsequences, Divergence Criteria, Monotone Subsequence Theorem (statement only),
Bolzano Weierstrass Theorem for Sequences. Cauchy sequence, Cauchy’s Convergence
Criterion.
UNIT-V (Total Topics -14 and Hrs-9)
Infinite series, convergence and divergence of infinite series, Cauchy Criterion, Tests for
convergence: Comparison test, Limit Comparison test, Ratio Test, Cauchy’s nth root test,
Integral test, Alternating series, Leibniz test, Absolute and Conditional convergence.
Course Outcomes (COs):
TBHM-201 CO 1.Enhance the knowledge regarding basic properties of the field of real
numbers and improved and outline the logical thinking.
TBHM-201 CO 2.Define and recognized the series of real numbers and convergence and
enhanced the critical thinking ability.
TBHM-201 CO 3.Acquire the knowledge of convergence and divergence of series using
interpretation of data and appropriate tools and techniques.
TBHM-201 CO4.Apply the application of real analysis in multidisciplinary environment.
References:
1. Bartle,R.G.andSherbert, D. R., Introduction to Real Analysis, John Wiley and Sons
(Asia) Pvt. Ltd., Singapore, 2002, 3rd Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
2. BilodeauG. G., Thie ,P. R., Keough, G. E., An Introduction to Analysis, Jones & Bartlett,
2010, 2nd Ed.
3. Thomson, B. S., Bruckner, A.M. and Bruckner, J. B., Elementary Real Analysis, Prentice
Hall, 2001.
4. Berberian, S.K., A First Course in Real Analysis, Springer Verlag, New York, 1994.
CO-PO Matrix (Real Analysis) TBHM-201
Course
Outcom
e
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
201CO1 2 _ _ _ _ _ _ 2 3 _ 1 3
TBHM-
201CO2 2 _ _ _ _ _ _ 2 2 _ 2 2
TBHM-
201CO3 1 2 1 _ 3 _ _ 2 2 _ _ 2
TBHM-
201CO4 2 2 1 _ _ _ _ _ 1 _ 3 1
Averag
e CO
(TBHM
-201)
1.7
5 2 1 _ 3 _ _ 2 2 _ 2 2
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code TBHM-202 Credit 4
Year/Sem 1/2 L-T-P 4-0-0
Course Name Differential Equations
Objectives of the Course:
1. To identify a differential equation and evaluate by apply appropriate analytical
techniques.
2. To understand DE’s of 1st order as well as separable, exact, homogeneous and linear &
compute existence and uniqueness of differential equations.
3. To solve higher order linear D. E’s. Determine central solutions and independence using
the Wronskian.
4. To create and analyze mathematical models.
UNIT-I (Total Topics- 15 and Hrs.- 10)
Differential equations and mathematical models. General, particular, explicit, implicit and
singular solutions of a differential equation. Exact differential equations and integrating
factors, separable equations and equations reducible to this form, linear equation and
Bernoulli equations, special integrating factors and transformations.
UNIT -II (Total Topics -5 and Hrs-9)
General solution of homogeneous equation of second order, principle of super position for
homogeneous equation, Wronskian: its properties and applications.
UNIT- III (Total Topics -5 and Hrs-9)
Linear homogeneous and non-homogeneous equations of higher order with constant
coefficients, Euler’s equation, method of undetermined coefficients, method of variation of
parameters.
UNIT-IV (Total Topics -4 and Hrs-10)
Introduction to compartmental model, exponential decay model, lake pollution model (case
study of Lake Burley Griffin), drug assimilation into the blood (case of a single cold pill,
case of a course of cold pills).
UNIT-V (Total Topics -3 and Hrs-9)
Exponential growth of population, limited growth of population, limited growth with
harvesting.
Course Outcomes (COs):
TBHM-202 CO 1.Develop critical thinking by identifying, analyzing and afterward
evaluate physical conditions whose comportment could defined by ODE’s.
TBHM-202 CO 2.Elaborate the use of appropriate techniques such as existence and
uniqueness theorems.
TBHM-202 CO 3.Propose the solution of higher order differential equations and explain
importance of technique’s as Wronskian.
TBHM-202 CO 4.Determine the solution and formulation of mathematical models using
differential equations.
References:
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
1. Barnes,B. and Fulford,G.R, Mathematical Modeling with Case Studies, A Differential
Equation Approach using MAPLE and MATLAB, Taylor and Francis group, London
and New York, 2009, 2nd Ed.
2. Edwards C.H., and Penny, D.E., Differential Equations and Boundary Value problems
Computing and Modeling, Pearson Education, India, 2005.
3. Ross, S.L., Differential Equations, John Wiley and Sons, India, 2004,3rd Ed.
4. Abell, M.L., Braselton, J.P., Differential Equations with MATHEMATICA, Elsevier
Academic Press, 2004, 3rdEd.
CO-PO Matrix Differential Equations TBHM-202
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
202CO1 3 3 2 2 1 _ 2 3 2 2 _ 2
TBHM-202
CO2 2 2 2 1 2 _ _ 1 2 2 _ _
TBHM-202
CO3 2 2 1 2 2 _ _ 1 2 2 _ _
TBHM-202
CO4 2 2 3 2 1 _ 2 3 2 2 _ 2
Average CO
(TBHM-202)
2.2
5
2.2
5 2
1.7
5 1.5 _ 2 2 2 2 _ 2
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code PBHM – 202 Credit 1
Year/Sem 1/2 L-T-P 0-0-2
Course Name Differential Equations Lab
Objectives of the Course:
1. To design and develop the various mathematical models and construct the differential
equation and propose solutions.
2. To sketch the graphical representations of integral surfaces of PDE.
3. To determine the convergence of sequences through graphical representations.
List of Practical’s
1. Plotting of second order solution family of differential equation.
2. Plotting of third order solution family of differential equation.
3. Growth model (exponential case only).
4. Decay model (exponential case only).
5. Lake pollution model (with constant/seasonal flow and pollution concentration).
6. Case of single cold pill and a course of cold pills.
7. Limited growth of population (with and without harvesting).
8. Battle model (basic battle model, jungle warfare, long range weapons).
9. Plotting of recursive sequences.
10. Study the convergence of sequences through plotting.
11. Cauchy’s root test by plotting nth roots.
12. Ratio test by plotting the ratio of nth and (n+1)th term.
Course Outcomes (COs):
PBHM-202 CO 1.Create, identify, analyze and solve the mathematical models to
understand the real-world problems.
PBHM-202 CO 2.Elaborate appropriate techniques such as characteristics method, method
of separation of variables to sketch the graph of integral surfaces of PDE.
PBHM-202 CO 3.Enhance advance knowledge and critical thinking ability by graphing
the ratios of sequence and series.
References:
1. Barnes, B. and Fulford, G.R., Mathematical Modeling with Case Studies, A Differential
Equation Approach using MAPLE and MATLAB, Taylor and Francis group, London
and New York, 2009, 2nd Ed.
2. Edwards C.H., and Penny, D.E., Differential Equations and Boundary Value problems
Computing and Modeling, Pearson Education, India, 2005.
3. Ross, S.L., Differential Equations, John Wiley and Sons, India, 2004, 3rd Ed.
4. Abell, M.L., Braselton, J.P., Differential Equations with MATHEMATICA, Elsevier
Academic Press, 2004, 3rd Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix Differential Equations Lab PBHM-202
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
PBHM-
202CO1 2 3 2 3 2 _ 2 3 2 3 2 2
PBHM-202
CO2 2 2 2 2 2 _ _ 1 _ 2 2 _
PBHM-202
CO3 2 2 2 2 2 _ _ 2 _ 2 2 _
Average CO
(PBHM-202) 2
2.3
3 2
2.3
3 2 2 2 2 2 2.33 2 2
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 25 25
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHG-203 Credit 4
Year/Sem 1/2 L-T-P 4-0-0
Course Name Concepts of Programming
Objectives of the Course:
1. To understand the basic concepts of C language.
2. To understand the fundamental of flowchart and algorithmto develop logics and design
new ideas.
3. To acquire knowledge about C language syntax, declaration of variables and different
data types.
UNIT-I (Total Topics- 10and Hrs.- 12)
OOPs and Basics of C Introduction to C, variables, constants, keywords, conditional
statements, procedural language, object oriented language, features of OOPs, data types,
format specifiers, flow-chart, algorithms, operator precedence and associativity, complexity
of algorithm, factors influencing complexity of algorithm.
UNIT -II (Total Topics -9 and Hrs-8)
Fundamentals of loops
Introduction to loops, use of for, while, do-while loop, relational and logical operators,
Introduction to printf () and scanf () functions, nesting of loops, switch statement, difference
between while and do-while loop.
UNIT- III (Total Topics -9 and Hrs-8)
Functions
Introduction to functions, advantages of function, types of function: function with no return
type and no argument, function with no return type with argument, function with return type
and no argument, function with return type and with argument, storage classes, recursion.
UNIT-IV (Total Topics -13 and Hrs-8)
Array and structures
Array, structures, advantages of structure over array, strings, string handling functions, use
of gets() and puts, difference between gets and scanf().
UNIT-V (Total Topics -13 and Hrs-12)
Pointers and dynamic memory allocation
Introduction to pointers, call by value and call by reference, static memory allocation,
dynamic memory allocation, memory allocation using calloc(), malloc() and realloc(),
printing a string using pointers, pointers and arrays, pointers and structures, 2-D array.
Course Outcomes (COs):
TBHG-203CO 1. Create the flowchart and an algorithm to develop C program for any
problem.
TBHG-203CO 2. Solve real time problems by using user defined functions.
TBHG-203CO 3. Construct any applicationby applying logics and concepts of C language
like conditional statements and iterative statements.
TBHG-203CO 4. Acquire knowledge about the use of pointers,strings, functions and arrays.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
TBHG-203CO 5. Compose C program and familiar with the concept of structures and
unions.
References:
1. BalaGuruswamy, E.,Programming In C,TMH Publications.
2. Kanetkar, Let us C.
CO-PO Matrix Concepts of Programming TBHG-203
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHG-
203CO1 1 - - 1 1 - 1 1 - - 1 1
TBHG-203
CO2 - - - - 1 - 1 1 - - - 1
TBHG-203
CO3 - - - - 1 - 1 2 - - 1 1
TBHG-203
CO4 - - - - 1 - 1 1 - - - -
TBHG-203
CO5 - - - - 1 - 1 1 - - - -
Average CO
(TBHG-203 ) 0.2 - - 0.2 1 - 1 1.2 - - 0.4 0.6
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc.(H) Math’s Programme Code 26
Course Code PBHG-203 Credit 2
Year/Sem 1/2 L-T-P 0-0-4
Course Name Concepts of Programming (Lab)
Objectives of the Course:
1. To evaluate the problem-solving techniques by using the basic concepts of C language.
2. To understand the fundamental of flowchart and algorithm to develop the programs and
to solve the problems.
3. To acquire knowledge about C language program structure.
At least 14 experiments from the following:
1. WAP to check that the given number is even or odd.
2. WAP of swapping two numbers without using third variable.
3. WAP to find the fibonacci series up to the given limit.
4. WAP to find that the given year is leap year or not.
5. WAP to find that the given number is prime or not.
6. WAP to insert and delete number from given array.
7. WAP to find the factorial of a given number using function.
8. WAP to check for armstrong number.
9. WAP to add two numbers using pointers.
10. WAP to read and print name and other details of 50 students using Structure.
11. WAP in c to print any string using pointers.
12. WAP in c to find factorial of any number using recursion.
13. WAP in c to show nesting of loops.
14. WAP in c to swap two numbers using call by reference.
15. WAP in c to show the use of string handling functions.
Course Outcomes (COs):
PBHG-203CO 1.Create the C program for given algorithm and flowchart.
PBHG-203CO 2.Solve real time problems by using arrays, pointers and structures.
PBHG-203CO 3.Create any application by applying logics and concepts of C language like
derived data types, operators
References:
1.BalaGuruswamy, E.,Programming In C, TMH, 2003,3rd Ed..
2.Thareja, R., Computer fundamentals and programming in C, Oxford, 2016, 2nd Ed.
3.Kanetkar, Yashwant ,Let us C, BPB , 2017 , 4th Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix Concepts of Programming (Lab)PBHG-203
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
PBHG-
203CO1 - - 1 - 1 - 1 2 - - 1 1
PBHG-
203CO2 - - - - 1 - 1 1 - - 1 1
PBHG-
203CO3 - - - 1 2 1 - 1 - - - 1
Average CO
(PBHG-203 ) - - 0.3 0.3 1.3 0.3 0.6 1.3 - - 0.6 1
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 25 25
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHG-203 Credit 4
Year/Sem 1/2 L-T-P 4-0-0
Course Name DBMS and Networking Concepts
Objectives of the Course:
1. To present an introduction to database management systems, with an emphasis on how
to organize, maintain and retrieve - efficiently, and effectively - information from a
DBMS.
2. Also, it includes learning about computer network organization and implementation,
obtaining a theoretical understanding of data communication and computer networks,
3. Gaining practical experience in installation, monitoring, and troubleshooting of current
LAN systems
UNIT-I (Total Topics- 10and Hrs.- 12)
Introduction: An overview of database management system, database system Vs file system,
Database system concepts and architecture, data models schema and instances, data
independence and data base language and interfaces, Data definitions language, DML, Data
Modeling using the Entity Relationship Model: ER model concepts, notation for ER diagram,
mapping constraints, keys, Concepts of Super Key, Candidate key, primary key, weak entity
sets, reduction of an ER diagrams to tables, Extended ER features.
UNIT -II (Total Topics -13 and Hrs-12)
Relational data Model and Language: Relational data model concepts, integrity constraints:
entity integrity, referential integrity, Keys constraints, Domain constraints, relational
algebra, Introduction to SQL: Characteristics of SQL. Advantage of SQL. SQL data types
and literals. Types of SQL commands. SQL operators and their procedure. Tables, views,
Queries and subqueries. Aggregate functions. Insert, update and delete operations. Joins,
Unions, Intersection, Minus.
UNIT- III (Total Topics -9 and Hrs-10)
History of Internet, Introduction to web(www), protocols governing the web- HTTP-SMTP
etc., web development strategies, Web applications, web project, web team. Interactive and
social web: Blogs, wikis, and social networking sites – The technology behind these
applications.
UNIT-IV (Total Topics -8 and Hrs-10)
Introduction Concepts: Goals and Applications of Networks, Network structure and
architecture, Network categories(LAN, MAN, WAN), The OSI reference model, services,
Network Topologies, Back Bone Design. Physical Layer Transmission Media, ISDN.
Course Outcomes (COs):
TBHG-203CO 1. Discover the challenges of Database and classify different DBMS services
and deployment models.
TBHG-203CO 2. Find importance of E-R model along with their notations in DBMS.
TBHG-203CO 3. Create, select, and apply appropriate queries to analyze different type of
information.
TBHG-203CO 4. Survey of modern challenges in networking technologies.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
References:
1. Date, C.J. An Introduction to Database Systems, Pearson Education; (2006) 8 edition.
2. Andrew S. T., Computer Networks, Pearson; (27 September 2010) 5 edition
3. Forouzan,B. A.,Data Communications And Networking (Sie) Paperback – 20 May 2006
4. SilberschatzDatabase System Concepts Paperback – 1 Dec 2013,Korth, McGraw Hill
Education India Private Limited; (1 December 2013), Sixth edition.
CO-PO Matrix DBMS and Networking ConceptsTBHG-203
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHG-
203CO1
1 1 - 1 1 - - - 2 - 1 1
TBHG-203
CO2
1 1 3 1 - - - - 1 1 2 1
TBHG-203
CO3
1 1 1 - 2 - - - 2 - 2 2
TBHG-203
CO4
1 1 - 1 3 - - - 3 1 1 1
Average CO
(TBHG-203 )
1 1 2 1.5 2 - - - 2 1 1.5 1.2
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc.(Hons.) Mathematics Programme Code 26
Course Code PBHG-203 Credit 2
Year/Sem 1/2 L-T-P 0-0-4
Course Name DBMS and Networking Concepts (Lab)
Objectives of the Course:
1. Learn basic concepts of computer networking and acquire practical notions of protocols
with the emphasis on TCP/IP.
2. A lab provides a practical approach to Ethernet/Internet networking: networks are
assembled, and experiments are made to understand the layered architecture and how do
some important protocols work.
3. Objective of this lab includes to provide a strong formal foundation in database
concepts, technology and practice to the participants to groom them into well-informed
database application developers.
1. Write the queries for Data Definition and Data Manipulation Language.
2. Write SQL queries using logical operations (=, <,>, etc)
3. Write SQL queries using SQL operators
4. Write SQL query using character, number, date and group functions
5. Execute the following Network Oriented Commands (with all their options) and observe
their Output:
a. PING
b. TRACERT
c. ROUTE
d. IPCONFIG
e. ARP
f. NETSTAT
g. NBTSTAT
h. HOSTNAME
i. NETSEND
j. DNS Configuration
6. Formation of data cable.
Course Outcomes (COs):
PBHG-203CO 1. Write the queries for Data Definition and Data Manipulation Language.
PBHG-203CO 2. Write SQL queries using SQL operators as well as Logical Operators
(=,>, <) etc.
PBHG-203CO 3. Write SQL queries for relational algebra and referential Integrity.
PBHG –204 CO4: Write SQL queries for extracting data from more than one table.
PBHG –204 CO5: Execute network-oriented commands-Netstat, Ping, Route, Ipconfig,
ARP.
References:
1. Date, C.J. An Introduction to Database Systems, Pearson Education; (2006) 8 edition.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
2. Andrew S. T., Computer Networks, Pearson; (27 September 2010) 5 edition
3. Forouzan, B. A., Data Communications And Networking (Sie) Paperback – 20 May 2006
4. Silberschatz Database System Concepts Paperback – 1 Dec 2013,Korth, McGraw Hill
Education India Private Limited; (1 December 2013), Sixth edition.
CO-PO Matrix DBMS and Networking Concepts (Lab)PBHG-203
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
PBHG-
203CO1
1 1 - 1 1 - - - 1 - 2 2
PBHG-
203CO2
1 1 2 - 2 - - - - 1 2 1
PBHG-
203CO3
1 1 2 - 2 - - - 1 - 1 2
PBHG-
203CO4
1 1 2 - 2 - - - - - 1 2
PBHG-
203CO5
1 1 - - - - - - - - 2 1
Average
CO
(PBHG-
203 )
1 1 2 1 1.7
5
- - - 1 1 1.6 1.6
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 25 25
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code TBES-204 Credit 2
Year/Sem 1/2 L-T-P 2-0-0
Course Name Environmental Science
Objectives of the Course:
1. Fundamental concepts related to Environmental Studies to be introduced in a simple
manner.
2. To make students aware of natural resources, their importance, and problems of
environmental pollution.
3. To create awareness about environmental acts related to wildlife, forest etc.
UNIT-I (Total Topics- 16 and Hrs- 8)
Introduction to environmental studies & Natural Resources, Multidisciplinary nature of
environmental studies, Scope and importance: Concept of sustainability and sustainable
development., Land resources: Land degradation, soil erosion and desertification.
Deforestation: Causes and impacts due to mining, dams- benefits and problems
Water: Use and over--‐exploitation of surface and ground water, floods, droughts, conflicts
over water (international & inter--‐state).
UNIT-II Ecosystem& Biodiversity (Total Topics – 14 and Hrs-7)
Ecosystem & Biodiversity
Ecosystem- Structure and function of ecosystem; Energy flow in an ecosystem: food chains,
food webs Ecological Pyramids. Biodiversity: Classification: genetic, species and ecosystem
diversity. Values of Biodiversity. Biogeographic zones of India; Hot spots of India, India as
a mega-biodiversity nation; Endangered and endemic species of India.
Threats to biodiversity: Habitat loss, poaching of wildlife, man--‐wildlife conflicts,
Conservation of biodiversity: In-situ and Ex-situ conservation of biodiversity.
UNIT- III Environmental Pollution (Total Topics -8 and Hrs-8)
Environmental Pollution
Environmental pollution: Air Pollution: causes, effects and control measures.
Water Pollution: Sources, effects and control measures.
Noise Pollution: causes effects and Limits of noise as prescribed by CPCB
Nuclear hazards and Human health risks
Solid waste management: Control measures of urban and industrial waste.
UNIT-IV (Total Topics -8 and Hrs-6)
Environmental Issues: Climate change, Global warming, Ozone layer depletion, Acid rain
Disaster management: floods, earthquake, cyclones and landslides.
UNIT-V (Total Topics -8 and Hrs-6)
Environmental Ethics, Policies & Practices
Environmental Ethics, Environmental movements: Chipko, Silent valley, Bishnois of
Rajasthan, Environment Laws: Environment Protection Act; Wildlife Protection Act; Forest
Conservation Act. International agreements: Montreal and Kyoto protocols.
Course Outcomes (COs)
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
TBES-204CO 1. Master foundational knowledge enabling them to have life –long learning
related to one’s surroundings.
TBES-204CO 2. Develop critical thinking skills in relation to environmental affairs and
articulate multidisciplinary context of the subject.
TBES-204CO 3. Acquire knowledge about natural resources and assess aesthetic and
ethical importance of all the living flora and fauna.
TBES-204CO 4. Interpret and propose solutions for effective management of different
types of environmental pollution
TBES-204CO 5. Keep updated and communicate knowledge regarding social issues and
laws related to environment.
References:
1. Kaushik, A., Environmental Studies.
2. Barucha ,E., Environmental Studies.
3. Deswal&Deswal, Environmental Studies.
CO-PO Matrix Environmental Science TBES-204
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBES-204
CO1
2 - - - - 1 1 2 1 - - 2
TBES-204
CO2
2 - - - - 1 1 2 1 - - 2
TBES-204
CO3
2 - - - - 1 1 2 1 - - 2
TBES-204
CO4
2 - - - - 1 1 2 1 - - 2
TBES-204
CO5
2 - - - - 1 1 2 1 - - 2
Average CO
(TBES-204)
2 - - -- - 1 1 2 1 -- - 2
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHE -205 Credit 2
Year/Sem 1/2 L-T-P 2-0-0
Course Name Human Ethics & Professional Values
Objectives of the Course:
1. To enable the students to understand the significance of Values and Ethical Behavior in
the personal and Professional lives.
2. To understand the correct appraisal of human needs by learning about self and body.
3. To appreciate family values and also to learn how to establish and develop harmony in
family and society.
4. To appreciate the significance of universal order by understanding harmony in nature.
5. To address the ethical issues that arises in the work environment and also to understand
the importance of a Holistic perspective in human life
6. To develop ability to develop scope and characteristics of eco friendly techniques.
UNITI (Total Topics- 3 and Hrs- 5)
Course Introduction &self-exploration: Need, Basic Guidelines, Content and Process for
Value Education, Relationship and Physical Facilities- the basic requirements for fulfillment
of aspirations of every human being with their correct priority, Understanding Happiness
and Prosperity correctly- A critical appraisal of the current scenario
UNIT II (Total Topics -3 and Hrs-5)
Understanding of human being as a co-existence of the sentient ‘I’ and the material ‘Body’:
Understanding the needs of Self (‘I’) and ‘Body’ - Sukh and Suvidha. Understanding the
harmony of I with the Body: Sanyam and Swasthya; correct appraisal of Physical needs,
meaning of Prosperity in detail
UNIT- III (Total Topics -3 and Hrs-5)
Understanding Harmony in the Family and Society: Harmony in Human-Human
Relationship, Trust (Vishwas) and Respect (Samman) as the foundational values of
relationship, Understanding the meaning of Samman, Difference between respect and
differentiation, Visualizing a universal harmonious order in society- concept of Undivided
Society (Akhand Samaj).
UNIT-IV (Total Topics -2 and Hrs-5)
Understanding Harmony in the Nature and Existence:Whole existence as Co-existence,
(Sah-astitva
UNIT: 5 (Total Topics -4 and Hrs-5)
Implications of Holistic Understanding of Harmony on Professional Ethics:
Ability to identify the scope and characteristics of people-friendly and eco-friendly
production systems, technologies and management models, Natural acceptance of human
values, Definitiveness of Ethical HumanConduct, Basis for Humanistic Education,
Humanistic Constitution and Humanistic Universal Order. Competence in Professional
Ethics. Ability to identify the scope and characteristics of people-friendly and eco-friendly
production systems, technologies and management models
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Course Outcomes (COs):
TBHE -205CO 1. Recognize the role of ethics in human life and to apply creative thinking
to fulfill the aspirations of every human being.
TBHE -205CO2.Understand the dimension of ethical human conduct and to determine how
values can be converted to rules of behavior that can be derived as ethics. Understand the
correct appraisal of physical needs.
TBHE -205CO3. Delineate the difference between respect and differentiation and analyze
the concept of undivided society in real life.
TBHE -205CO4. Describe how different orders in nature have mutually fulfilling
coexistence, develop the ability of identifying people-friendly and eco-friendly production
systems, and understand the implication of holistic understanding of harmony on
professional ethics.
References:
1. Gaur, R.R,Sangal,R,Bagaria,G.P., A Foundation Course in Human Values and
Professional Ethics, Excel Books, New Delhi, 2009.
2. Nagraj, A.,JeevanVidyaEkParichay,Divya Path Sansthan, Amarkantak, 1998.
3. Tripathy, A.N. , Human Values, New Age International Publishers, 2003.
4. Seebauer,E.G.& Berry, R.L., Fundamentals of Ethics for Scientists & Engineers,
Oxford University Press ,2000.
CO-PO Matrix Human Ethics and Professional Values (TBHE-205)
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHE-
205C01 - - - - - - - - 1 - - -
TBHE-
205C02 - - - - - - - - 1 - - -
TBHE-
205C03 - - - - - - 3 - 1 - - -
TBHE-
205C04 - - - - - - 3 - 1 - - -
Average
CO(TBH
E-205)
- - - - - - 3 - 1 - - -
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
SEMESTER -III
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHM-301 Credit 5
Year/Sem 2/3 L-T-P 4-1-0
Course Name Theory of Real Functions
Objectives of the Course:
1. To expose the student to fundamental properties of real number.
2. To develop the deep understanding of limit, continuity and differentiability of functions.
3. To improve the ability to solve critical problems in mathematical analysis.
4. To assess of fundamental properties of real function in basic research and scientific
problems.
UNIT- I (Total Topics- 10 and Hrs-09)
Limits of functions ( 𝜖 − 𝛿 approach), sequential criterion for limits, divergence criteria.
Limit theorems, one sided limits. Infinite limits and limits at infinity. Continuous functions,
sequential criterion for continuity and discontinuity.
UNIT- II (Total Topics -10 and Hrs-10)
Algebra of continuous functions. Continuous functions on an interval, intermediate value
theorem, location of roots theorem, preservation of intervals theorem. Uniform continuity,
non-uniform continuity criteria, uniform continuity theorem.
UNIT- III (Total Topics -06 and Hrs-09)
Differentiability of a function at a point and in an interval, Caratheodory’s theorem, algebra
of differentiable functions. Relative extrema, interior extremum theorem.
UNIT-IV (Total Topics -07 and Hrs-10)
Rolle’s theorem, Mean value theorem, intermediate value property of derivatives, Darboux’s
theorem. Applications of mean value theorem to inequalities and approximation of
polynomials, Taylor’s theorem to inequalities.
UNIT-V (Total Topics -10 and Hrs-09)
Cauchy’s mean value theorem. Taylor’s theorem with Lagrange’s form of remainder,
Taylor’s theorem with Cauchy’s form of remainder, application of Taylor’s theorem to
convex functions, relative extrema. Taylor’s series and Maclaurin’s series expansions of
exponential and trigonometric functions, ln (1 + x), 1/ ax+b and (1 + 𝑥)𝑛.
Course Outcomes (COs):
TBHM-301CO 1. Acquire the knowledge about fundamental properties of the real numbers
and that lead to the formal development of pure mathematics.
TBHM-301 CO 2. Demonstrate deep understanding of limits, continuity and
differentiability of real function in abstract ways and how they are applicable in engineering
and scientific problems.
TBHM-301 CO 3. Develop the logical thinking to proof the basic and standard results of
mathematical analysis.
TBHM-301 CO 4. Create and analyze theories, methods and interpretations that develop
critical thinking skills and advance mathematical knowledge.
References:
1. Bartle, R. and Sherbert ,D.R., Introduction to Real Analysis, John Wiley and Sons.
2. Ross, K.A., Elementary Analysis: The Theory of Calculus, Springer, 2004.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
3. Mattuck, Introduction to Analysis, Prentice Hall, 1999.
4. Ghorpade, S.R. and Limaye, B.V.,A Course in Calculus and Real Analysis, Springer.
CO-PO Matrix-Theory of Real Functions TBHM-301
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PS
O4
TBHM-
301CO1
3 2 2 2
2 3
2 2
TBHM-
301CO2
3 3 3 1 1
3 3 2 3 2
TBHM-
301CO3
3 2 2 2
2 2
1 1
TBHM-
301CO4
3 3 2 2
2 2
3 2
Average
CO
(TBHM-
301)
3.0 2.5 2.3 1.8 1.0
2.3 2.5 2.0 2.3 1.8
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B. Sc (Hons.) Mathematics Programme Code 26
Course Code TBHM-302 Credit 5
Year/Sem 2/3 L-T-P 4-1-0
Course Name Group Theory-I
Objectives of the Course:
1. To develop the relationships between basic abstract algebraic structures and number
systems.
2. To develop a basic knowledge of important mathematical concepts in abstract algebra
such as group, subgroup, cyclic group and order of group.
3. To be familiar with normal subgroups, quotient group, permutation group and Abelian
group and understand the structure and characteristics of these groups.
4. To understand the important concepts of homeomorphisms and isomorphism in group
theory
UNIT-I (Total Topics- 06 and Hrs-09)
Symmetries of a square, Dihedral groups, definition and examples of groups including
permutation groups and quaternion groups (illustration through matrices), elementary
properties of groups.
UNIT- II (Total Topics -05 and Hrs-09)
Subgroups and examples of subgroups, centralizer, normalizer, center of a group, product of
two subgroups.
UNIT- III (Total Topics -07 and Hrs-09)
Properties of cyclic groups, classification of subgroups of cyclic groups. Cycle notation for
permutations, properties of permutations, even and odd permutations, alternating group.
UNIT-IV (Total Topics -10 and Hrs-10)
properties of cosets, Lagrange’s theorem and consequences including Fermat’s Little
theorem. External direct product of a finite number of groups, normal subgroups, factor
groups, Cauchy’s theorem for finite abelian groups.
UNIT-V (Total Topics -06 and Hrs-09)
Group homomorphisms, properties of homomorphisms, Cayley’s theorem, properties of
isomorphism, First, Second and Third isomorphism theorems.
Course Outcomes (COs):
TBHM-302 CO 1. Identify and analyze the properties of algebraic structure called group.
TBHM-302 CO 2. Acquire the basic knowledge of Cyclic Groups, Normal Subgroup and
Quotient group.
TBHM-302 CO 3. Analyze the notion of permutations graphically and analytically.
TBHM-302 CO 4. Develope the capability of critical thinking about isomorphism and
homomorphism and analyzed its applications
References:
1. Fraleigh, J.B., A First Course in Abstract Algebra, Pearson, 2002, , 7th Ed.
2. Artin, M., Abstract Algebra, Pearson, 2011, 2nd Ed.
3. Gallian, J. A., Contemporary Abstract Algebra , Narosa Publishing House, New Delhi,
1999, 4th Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
4. Rotman, J. J., An Introduction to the Theory of Groups, Springer Verlag, 1995, 4th Ed.
5. Herstein, I.N., Topics in Algebra, Wiley Eastern Limited, India, 1975.
CO-PO Matrix (Group Theory-I) TBHM-302
Course
Outcome
PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PSO1 PSO2 PSO3 PSO4
TBHM-
302 CO1
2 2 1 1 _ _ _ 2 3 _ 2 2
TBHM-
302 CO2
3 _ _ 1 _ _ _ 1 3 _ 1 2
TBHM-
302 CO3
1 2 2 _ 2 _ _ 1 3 _ 1 1
TBHM-
302 CO4
3 3 2 1 2 _ _ 3 3 _ 2 2
Average
CO
(TBHM-
302)
2.3 2.3 1.7 1.0 2.0 _ _ 1.8 3.0 _ 1.5 1.8
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code TBHM-303 Credit 4
Year/Sem 2/3 L-T-P 4-0-0
Course Name PDE and system of ODE
Objectives of the Course:
1. To be competent in solving applied problems associated to various form of PDE.
2. To develop the use of appropriate techniques such as analytical and numerical methods.
3. To obtain the solution of heat’s equation, wave’s equation & Laplace’s equation.
4. To describe canonical forms and systems of linear differential equations.
UNIT- I (Total Topics- 13 and Hrs-10)
Partial Differential Equations – Basic concepts and Definitions, Mathematical Problems.
First-Order Equations: Classification, Construction and Geometrical Interpretation. Method
of Characteristics for obtaining General Solution of Quasi Linear Equations. Canonical
Forms of First-order Linear Equations. Method of Separation of Variables for solving first
order partial differential equations.
UNIT- II (Total Topics -07 and Hrs-09)
Derivation of Heat equation, Wave equation and Laplace equation. Classification of second
order linear equations as hyperbolic, parabolic or elliptic. Reduction of second order Linear
Equations to canonical forms.
UNIT- III (Total Topics -09 and Hrs-09)
The Cauchy problem, the Cauchy-Kowaleewskaya theorem, Cauchy problem of an infinite
string. Initial Boundary Value Problems, Semi-Infinite String with a fixed end, Semi-Infinite
String with a Free end, Equations with non-homogeneous boundary conditions, Non-
Homogeneous Wave Equation.
UNIT-IV (Total Topics -03 and Hrs-09)
Method of separation of variables, Solving the Vibrating String Problem, Solving the Heat
Conduction problem.
UNIT-V (Total Topics -11 and Hrs-10)
Systems of linear differential equations, types of linear systems, differential operators,
anoperator method for linear systems with constant coefficients, Basic Theory of linear
systems in normal form, homogeneous linear systems with constant coefficients: Two
Equations in two unknown functions, The method of successive approximations, the Euler
method, the modified Euler method, The Runge-Kutta method.
Course Outcomes (COs):
TBHM-303 CO 1.Develop critical thinking by identifying, analyzing& subsequently
explaining physical circumstances by using PDE & ODE.
TBHM-303 CO 2.Elaborate the use of appropriate techniques such as analytical and
numerical.
TBHM-303 CO 3.Evaluate practical problems of ODE & PDE and Learn to create
mathematical models.
TBHM-303 CO 4.Propose the solutions and classifications of PDE through initial and
boundary situations and its reduction to canonical forms.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
References:
1. Tyn,M.U. and Debnath,L,Linear Partial Differential Equations for Scientists and
Engineers, Springer, Indian reprint, 2006, 4th Ed..
2. Ross, S.L., Differential equations, John Wiley and Sons, India, 2004, 3rd Ed.
3. Abell M. L. and Braselton J.P., Differential equations with MATHEMATICA, Elsevier
Academic Press, 2004, 3rd Ed.
CO-PO Matrix PDE and System of ODE TBHM-303
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PS
O1
PS
O2
PS
O3
PS
O4
TBHM-
303CO1 3 3 2 2 _ _ _ 2 _ 3 2 1
TBHM-
303CO2 2 2 2 2 2 _ _ 2 _ 2 2 1
TBHM-
303CO3 3 2 2 2 3 _ _ 2 _ 3 2 1
TBHM-
303CO4 2 3 2 2 2 _ _ 2 _ 2 3 1
Average CO
(TBHM-303) 2.5 2.5 2 2 2.3 _ _ 2 _ 2.5 2.2 1
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code PBHM - 303 Credit 1
Year/Sem 2/3 L-T-P 0-0-2
Course Name PDE and Systems of ODE Lab
Objectives of the Course:
1. To obtain the solution of Cauchy problem for first order PDE and to find its characteristic
equations.
2. To identify the various form of PDE and to plot the integral surfaces of PDE.
3. To propose the solution of Heat equation and Wave equation with various associated
conditions.
List of Practical’s
Course Outcomes (COs):
PBHM-303 CO 1.Create, identify, analyze and solve the heat equation, wave equation &
Laplace equation to understand the real-world problems.
PBHM-303 CO 2.Discuss appropriate techniques such as characteristics method, method
of separation of variables to sketch the graph of integral surfaces of PDE.
PBHM-303 CO 3.Enhance critical thinking ability by solving Cauchy initial value and
boundary value problems.
References:
1. Tyn, M.U. and Debnath, L, Linear Partial Differential Equations for Scientists and
Engineers, Springer, Indian reprint, 2006, 4th Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
2. Ross, S.L., Differential equations, John Wiley and Sons, India, 2004, 3rd Ed.
3. Abell M. L. and Braselton J.P., Differential equations with MATHEMATICA, Elsevier
Academic Press, 2004, 3rd Ed.
CO-PO Matrix PDE and System of ODE Lab PBHM-303
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
PBHM-303
CO1
3 2 2 1 1 _ _ 2 1 3 3 2
PBHM-303
CO2
2 2 2 1 3 _ _ 1 _ 2 2 _
PBHM-303
CO3
3 2 2 1 2 _ _ _ _ 2 _ _
Average CO
(PBHM-303)
2.6 2 2 1 2 _ _ 1.5 _ 2.33 2.5 2
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 25 25
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code TBHG-304 Credit 5
Year/Sem 2/3 L-T-P 4-1-0
Course Name Total Quality Management
Objectives of the Course:
1. To appraise the students about concept of ISO & various standards.
2. To appraise management systems with documentation required for development of
organization with its sustainability.
3. To appraise about regulatory bodies with specifications requirements for environment
protection.
4. To do assessment and analysis of data by using modern tools like statistical methods
for problem analysis
UNIT- I (Total Topics-12 and Hrs-08)
TQM & QMS
Definition of quality, quality product, General introduction about ISO & History, various
standards, TQM definition, Introduction about QMS-ISO 9001 General, Scope &
Applications of QMS, Terms & definitions used in QMS, Process approach(PDCA
cycle),General Requirements of ISO 9001, Documentation , Quality Policy, Quality
objectives, customer satisfaction, Nonconformance of product ,corrective and preventive
action.
UNIT-II (Total Topics -15 and Hrs-08)
EMS & OHSAS
Scope & Applications of EMS & OHSAS, Terms & definitions used in EMS & OHSAS ,
General & Legal Requirements of ISO 14001 & ISO 18001, Documentation, EIA,
significant aspect-impact analsyis, introduction about EPA, . Introduction about regulatory
bodies, CPCB & SPCB. EPA /CPCB Standards for discharge of effluents from common
chemical industries. , Training & Emergency Preparedness, non-conformance & corrective
action
UNIT- III (Total Topics -09 and Hrs-8)
Other ISO standards
Introduction about ISO 22000(FSMS) , 27000(ISMS) & 50000( Energy Management
System) . Hazard Analysis and Critical Control Points (HACCP),ISO for Food Industry,
introduction about GMP(good manufacturing process), cGMP& Concept of house keeping
(5S), Concept of six sigma in Industry.
UNIT-IV (Total Topics -12 and Hrs-7)
Measurement & Analysis of data -1 Statistical Analysis of data Statistical methods of
analysis of data, mean, mode, median, standard deviation, standard error, t-test, chi-square
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
test, correlation& regression. Statistical quality control, introduction about SPSS. Concept
of control charts. Use of computers for analysis of data.
UNIT-V (Total Topics -04 and Hrs-06)
Measurement & Analysis of data -2
General definition, concept of Permutation (nPr) concept of combination (nCr) and
Probability. Applications of permutation, combination and probability.
Course Outcomes (COs):
TBHG-304CO 1. Understanding of concept of quality, ISO & various standards.
TBHG-304 CO 2. Learning of various management systems with SOPs, six sigma & 5S
TBHG-304 CO 3. Well verse with regulatory bodies and environmental standards for
environment protection.
TBHG-304 CO 4. Knowledge about assessment and analysis of data by using modern
computational & statistical methods for problem solution.
References:
1. Singh, A, Total Quality Management and Outlook on TQM,Vani Publication.
2. Evans, J.R. and Lindsay, W.M., Total Quality Management, ,Cengage Learning.
CO-PO Matrix Total Quality Management TBHG-304
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHG-
304CO1
1 2
1
2
TBHG-
304CO2
3 2
3
TBHG-
304CO3
3
3
TBHG-
304CO4
1 1 2
2
3
3
Average CO
(TBHG-304)
1 2 2.3 1
2
3 2
2.75
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code TBHG-304 Credit 5
Year/Sem 2/3 L-T-P 4-1-0
Course Name Intellectual Property Rights
Objectives of the Course:
1. To explain about Intellectual Property and Copyrights
2. To explain about software patents and their importance.
3. To gain knowledge about trade marks
4. To layout design of integrated circuits and Industrial Designs
5. To Illustrate layout design and Different International Agreements
UNIT- I (Total Topics-6 and Hrs-08)
Introduction to Intellectual Property: Historical Perspective, Different Types of IP,
Importance of protecting IP.
Copyrights: Introduction, How to obtain, Differences from Patents.
UNIT-II (Total Topics -15 and Hrs-08)
Trade Marks: Introduction, How to obtain, Different types of marks – Collective marks,
certification marks, service marks, Trade names, etc, Differences from Designs.
Patents: Historical Perspective, Basic and associated right, WIPO, PCT system, Traditional
Knowledge, Patents and Healthcare-balancing promoting innovation with public health,
Software patents and their importance for India.
UNIT- III (Total Topics -09 and Hrs-8)
Geographical Indications: Definition, rules for registration, prevention of illegal
exploitation, importance to India.
Industrial Designs: Definition, How to obtain, features, International design registration.
Layout design of integrated circuits: Circuit Boards, Integrated Chips, Importance for
electronic industry.
UNIT-IV (Total Topics -6 and Hrs-7)
Trade Secrets: Introduction and Historical Perspectives, Scope of Protection, Risks
involved and legal aspects of Trade Secret Protection.
UNIT-V (Total Topics -17 and Hrs-06)
(a) Word Trade Organization (WTO):
(i) General Agreement on Tariffs & Trade (GATT), Trade Related Intellectual Property
Rights (TRIPS) agreement
(ii) General Agreement on Trade related Services (GATS),
(iii) Madrid Protocol
(iv) Berne Convention, (v) Budapest Treaty
(b) Paris ConventionWIPOand TRIPS, IPR and Plant Breeders Rights, IPR and Biodiversity
IP Infringement issue and enforcement – Role of Judiciary, Role of law enforcement
agencies – Police, Customs etc. Economic Value of Intellectual Property – Intangible assets
and their valuation, Intellectual Property in the Indian Context – Various laws in India
Licensing and technology transfer.
Course Outcomes (COs):
TBHG-304CO 1. Acquire knowledge about Intellectual property rights, copyrights,
trademarks and patents.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
TBHG-304 CO 2. Appraise about geographical indications, industrial designs, trade secrets
and different international agreements including paris convention, Budapest treaty etc.
TBHG-304 CO 3. Analyze layout designs of integrated circuits, risks involved in trade
secret protection, international design registration, rules for registration of geographical
indications etc.
TBHG-304 CO 4. Assess introduction and historical perspectives of trade secrets, working
of WTO, Madrid protocol, different type of IPs, trademarks, copyrights etc.
References:
1. Acharya, N.K.: Textbook on intellectual property rights, Asia Law House (2001).
2. Guru, M,&Rao, M.B., Understanding Trips: Managing Knowledge in Developing
Countries, Sage Publications (2003).
3. Ganguli, P. ,Intellectual Property Rights: Unleashing the Knowledge Economy, Tata
McGraw-Hill (2001),71
4. Miller,A,R,MichealH.Davis; Intellectual Property: Patents, Trademarks and Copyright
in a Nutshell, West Group Publishers (2000).
5. Watal, J., Intellectual property rights in the WTO and developing countries, Oxford
University Press, Oxford.
CO-PO Matrix Intellectual Property RightsTBHG-304
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHG-304
CO1
1
1
2 1
TBHG-304
CO2
2
1
1 2
TBHG-304
CO3
1
1
1 1
TBHG-304
CO4
1
1
1 1
Average
CO
(TBHG-
304)
1
1
1 1
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code TBHG-304 Credit 5
Year/Sem 2/3 L-T-P 4-1-0
Course Name Statics
Objectives of the Course:
1. To derive principle of virtual work, Work done by the tension and thrust of an extensible
string and its applications.
2. To provide knowledge of stable and unstable equilibrium position.
3. To develop important concepts of centre of gravity and catenary and its applications
4. To identify an equilibrium of forces in three dimensions.
UNIT- I (Total Topics-10 and Hrs-09)
Virtual Works: Definitions of virtual displacement and virtual work done, Difference
between work done and virtual work done with examples, The principle of virtual work,
Work done by the tension and thrust of an extensible string during a small displacement,
Some solved problems.
UNIT-II (Total Topics -06 and Hrs-08)
Equilibrium: Stable and unstable equilibrium, Moments and couples and Varignon’s
theorem of moments and some solved problems
UNIT- III (Total Topics -09 and Hrs-10)
Centre of Gravity: Definition centre of gravity (C.G.) and examples, A system of particles
lying in a line, A number of particles lying in a plane, Compound body, Remainder body,
Uniform plane curve, Plane area, An area enclosed between two curves and solved problems
UNIT-IV (Total Topics -12 and Hrs-10)
Strings in Two Dimensions: Definition and examples of catenary, Definitions axis of the
catenary, Vertex of the catenary, Parameter of the catenary, Directrix of the catenary, Span
and Sag of the catenary. Intrinsic and cartesian equations of common catenary, Some
important relations for the common catenary, Approximation to the common catenary and
sag of tightly stretched wires (definitions and examples).
UNIT-V (Total Topics -04 and Hrs-09)
Equilibrium in Three Dimensions: Equilibrium of forces in three dimensions, Wrench and
screw, Pitch of the wrench and solved problems.
Course Outcomes (COs):
TBHG-304CO 1. Acquire the basic knowledge of resultant, component of a force, coplanar
forces, moment of a force and couple with examples, virtual work, virtual displacement for
extensible and inextensible string and thrust and its applications in real life and engineering
problems.
TBHG-304 CO 2. Develop critical thinking skills and apply the statics to precise advance
problems in math’s, engineering, physics or in additional areas..
TBHG-304 CO 3. Acquire the basic knowledge of centre of gravity for a system of particles
lying in line, plane, and compound body, uniform plane curve, enclosed by two curves and
applied in mechanical and civil engineering for real life problems.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
TBHG-304 CO 4. Propose the ideas of equilibrium for two and three dimensions, stable and
unstable, and its applications in society.
References:
1. Verma, R. S., A Text Book on Statics, PothishalaPvt. Ltd., Allahabad.
2. Loney, S. L., An Elementary Treatise on Statics, Kalyani Publishers, New Delhi.
CO-PO Matrix Statics TBHG-304
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PS
O1
PS
O2
PS
O3
PS
O4
TBHG-304CO1 3 - 2 2 3 - - 1 3 1 1 2
TBHG-304CO2 3 3 2 - - - - 1 1 - 3 1
TBHG-304CO3 3 2 2 2 2 - - 2 2 2 1 2
TBHG-304CO4 3 1 - 1 2 - 1 2 1 - 1 2
Average CO
(TBHG-304) 3.0 2.0 2.0 1.7 2.3 -
1.0 1.5 1.8 1.5 1.5 1.8
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHM-305 Credit 2
Year/Sem 2/3 L-T-P 2-0-0
Course Name Logic and Sets
Objectives of the Course:
1. To provide sound knowledge about axiomatic set theory and elementary logics.
2. To expose the student to properties of integers, real or complex numbers, sets, relations,
cardinalities and functions.
3. To understand the construction of un-quantified or quantified arguments by reproducing
valid examples.
4. To develop ability to translate real world problem into mathematical statements and
solution, interpretations of those problems.
UNIT- I (Total Topics- 12 and Hrs-05)
Introduction, propositions, truth table, negation, conjunction and disjunction. Implications,
bi-conditional propositions, converse, contra positive and inverse propositions and
precedence of logical operators.
UNIT-II (Total Topics -07 and Hrs-04)
Propositional equivalence: Logical equivalences. Predicates and quantifiers: Introduction,
Quantifiers, Binding variables and Negations.
UNIT-III (Total Topics -13 and Hrs-05)
Sets, subsets, Set operations and the laws of set theory and Venn diagrams. Examples of
finite and infinite sets. Finite sets and counting principle. Empty set, properties of empty set.
Standard set operations. Classes of sets. Power set of a set.
UNIT-IV (Total Topics -05 and Hrs-04)
Difference and Symmetric difference of two sets. Set identities, Generalized union and
intersections.
UNIT-V (Total Topics -09 and Hrs-06)
Relation: Product set, Composition of relations, Types of relations, Partitions, Equivalence
Relations with example of congruence modulo relation, Partial ordering relations, binary
relations.
Course Outcomes (COs):
TBHG-305 CO 1.Analyze and determine the truth value of quantified sentences, given its
universal set by constructing truth value table or by applying the concept of solution sets.
TBHG-305 CO 2.Construct un-quantified or quantified arguments by reproducing valid
examples in deducing a tautology or laws of deduction/inference.
TBHG-305 CO 3.Justify propositions related to the properties of integers, real or complex
numbers, sets, relations, cardinalities and functions.
TBHG-305 CO 4.Synthesis symbolic laws of logic to natural science languages and develop
tools and techniques for the application in engineering and technology.
References:
1. Grimaldi, R.P., Discrete Mathematics and Combinatorial Mathematics, Pearson
Education.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
2. Kamke, E., Theory of Sets, Dover Publishers, 1950.
CO-PO Matrix- Logic and Sets TBHM-305
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
305CO1
3 3 3 2
- - 2 3
2 2
TBHM-
305CO2
3 2 3 2 2 - - 2 3 2 3 2
TBHM-
305CO3
3 2 2 3
- - 2 3 2 2 2
TBHM-
305CO4
3 3 2 3 2 - - 2 2 3 3 3
Average CO
(TBHM-
305)
3.0 2.5 2.5 2.5 2.0 - - 2.0 2.8 2.3 2.5 2.3
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHM – 305 Credit 2
Year/Sem 2/3 L-T-P 2-0-0
Course Name Computer Graphics
Objectives of the Course:
1. To introduce the use of the components of a graphics system and become familiar with
building approach of graphics system components and algorithms related with them.
2. To learn the basic principles of 3- dimensional computer graphics.
3. Provide an understanding of how to scan convert the basic geometrical primitives, how
to transform the shapes to fit them as per the picture definition.
4. Provide an understanding of mapping from a world coordinates to device coordinates,
clipping, and projections.
UNIT- I (Total Topics- 12 and Hrs-12)
Introduction to computer Graphics: Raster Scan and Random Scan display, aspect ratio,
CRT, displays processors and character generators, color display techniques, interactive
input/output devices.
UNIT-II (Total Topics -14 and Hrs-13)
Points, lines and curves: Scan conversion, line-drawing algorithms, circle and ellipse
generation, polygon filling antialiasing. Two-dimensional viewing: Coordinate systems,
linear transformations, line and polygon clipping algorithms.
Course Outcomes (COs):
TBHM – 305 CO 1. Implement of various scan, convert the basic geometrical primitives,
transformations, Area filling, clipping algorithms.
TBHM – 305 CO 2. Discuss the application of computer graphics concepts for the
development of computer games, information visualization, and business applications.
TBHM – 305 CO 3. Define the fundamentals of animation, virtual reality and its related
technologies.
TBHM – 305CO 4. Describe the significance of viewing and projections in real world
objects.
References:
1. Hearn, D., and Baker, M.P., Computer Graphics, Prentice–Hall of India, 2nd Ed.
2. Rogers, D.F., Procedural Elements in Computer Graphics, McGraw Hill Book
Company, 2001, 2nd Ed.,
3. Rogers, D.F., and Admas, A.J., Mathematical Elements in Computer Graphics, McGraw
Hill Book Company, 1990, 2nd Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix-Computer Graphics TBHM-305
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
305CO1
1 2 - 2 3 - - - 1 2 - 1
TBHM-
305CO2
2 1 2 1 2 - - - 2 - 2 2
TBHM-
305CO3
1 1 2 2 2 - - - 1 1 2 1
TBHM-
305CO4
- 1 2 1 2 - - - 2 1 - 2
Average
CO
(TBHM-
305)
1 1.2
5
1.5 1.5 2.2
5
- - - 1.5 1 1 1.5
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code PBHS-306 Credit 1
Year/Sem 2/3 L-T-P 0-0-2
Course Name Seminar
Objectives of the Course:
1. To provide the detail knowledge for preparing presentation and seminar.
2. To develop the concept of team work, presentation skills of data in conferences,
symposia , seminar etc.
3. To demonstrate knowledge and understand mathematical tools and techniques in
seminar.
Seminar: Participation/ paper presentation in the national /international conferences.
Course Outcomes (COs):
1. PBHS-306CO 1. Developed the idea for preparing presentation for their possible future
profession.
PBHS -306 CO 2. Enhanced the critical thinking skills, communication skills and build
team work for conferences, symposia, seminar etc.
PBHS -306 CO 3. Demonstrate the knowledge of mathematical tools and techniques for
presentations of research data in seminar and conferences.
CO-PO Matrix (Seminar) PBHS-306
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PSO
1
PSO
2
PSO
3
PSO
4
PBHS-
306 CO1 2 _ _ 2 3 _ 2 _ 2 1 2
PBHS -
306 CO2 _ 2 _ 2 3 _ 2 _ 2 2 2
PBHS -
306 CO3 1 _ _ 2 3 1 2 _ 2 2 2
Average
CO
(PBHS -
306)
1.5 2.0 _ 2.0 3.0 1.0 2.0 _ 2.0 1.7 2.0
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 25 25
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
SEMESTER -IV
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHM-401 Credit 4
Year/Sem 2/4 L-T-P 4-0-0
Course Name Numerical Methods
Objectives of the Course:
1. To learn the numerical techniques to solve algebraic and transcendental equations and it
applications.
2. To provide knowledge of system of linear equations and its applications
3. To develop the concept of interpolation and numerical integration.
4. To derive the numerical solution of initial value problems.
UNIT- I (Total Topics- 10 and Hrs-09)
Algorithms, Convergence, Errors: Relative, Absolute, Round off, Truncation.
Transcendental and Polynomial equations: Bisection method, Newton’s method, Secant
method. Rate of convergence of these methods.
UNIT-II (Total Topics -06 and Hrs-09)
System of linear algebraic equations: Gaussian Elimination and Gauss Jordan methods.
Gauss Jacobi method, Gauss Seidel method and their convergence analysis.
UNIT-III (Total Topics -05 and Hrs-09)
Interpolation: Lagrange and Newton’s methods. Error bounds. Finite difference operators.
Gregory forward and backward difference interpolation.
UNIT-IV (Total Topics -04 and Hrs-09)
Numerical Integration Trapezoidal rule, Simpson rule, Simpson 3/8 rule, Boole’s rule,
Midpoint rule, Composite Trapezoidal rule, Composite Simpson rule.
UNIT-V (Total Topics -05 and Hrs-09)
Ordinary Differential Equations: Euler’s method. Runge-Kutta methods of orders two and
four.
Course Outcomes (COs):
TBHM-401CO 1. Analyze the concept of error inherent in different numerical methods for
solution in real world problems.
TBHM-401CO 2. Propose ideas for finding numerical solution of algebraic and
transcendental equation by numerical methods to solve and analyses complex engineering
problems.
TBHM-401CO 3. Acquire the basic knowledge of method of interpolation for scientific
problems with consideration for industry, environment and society.
TBHM-401CO 4. Ability to assess and prepare the numerical solution of differential
equation, integral equation, linear and nonlinear polynomials.
References:
1. Bradie, B., A Friendly Introduction to Numerical Analysis, Pearson Education, India,
2007.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
2. Jain, M.K., Iyengar, S.R.K. and Jain, R.K., Numerical Methods for Scientific and
Engineering Computation, New age International Publisher, India6th Ed.
3. Gerald, C.F. and Wheatley, P.O., Applied Numerical Analysis, Pearson Education, India,
2008.
4. Ascher, U. M. and Greif, C., A First Course in Numerical Methods, PHI Learning Private
Limited, 2013, 7th Ed.
5. Mathews, J.H. and Fink, K. D., Numerical Methods using Matlab, PHI Learning Private
Limited, 2012, 4th Ed.
CO-PO Matrix Numerical Methods TBHM-401
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PS
O1
PS
O2
PS
O3
PS
O4
TBHM-
401CO1 3 2 2 2 - - -
2 3 1 1 1
TBHM-
401CO2 3 2 2 2 1 - -
1 2 2 -
1
TBHM-
401CO3 3 1 2 2 2 -
1 2 2 - -
2
TBHM-
401CO4 3 2 1 -
1 - -
2 3 - -
2
Average CO
(TBHM-401) 3.0 1.8 1.8 2.0 1.3 -
1.0 1.8 2.5 1.5 1.0 1.5
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code PBHM-401 Credit 1
Year/Sem 2/4 L-T-P 0-0-2
Course Name Numerical Methods Lab
Objectives of the Course:
1. To learn concept of different numerical methods with the help of C/C++ languages.
2. To provide basic knowledge of system of linear equations with the help of software.
3. To develop the concept of initial value problem, numerical integration and interpolation
with lab knowledge.
List of Practical’s
(i) Calculate the sum 1/1 + 1/2 + 1/3 + 1/4 + ----------+ 1/ N.
(ii) To find the absolute value of an integer.
(iii) Enter 100 integers into an array and sort them in an ascending order.
(iv) Bisection Method.
(v) Newton Raphson Method.
(vi) Secant Method.
(vii) RegulaiFalsi Method.
(viii) LU decomposition Method.
(ix) Gauss-Jacobi Method.
(x) SOR Method or Gauss-Siedel Method.
(xi) Lagrange Interpolation or Newton Interpolation.
(xii) Simpson’s rule.
Course Outcomes (COs):
PBHM-401CO 1. Application of techniques of different numerical methods for solution in
real world problems.
PBHM-401CO 2. Finding numerical solution of algebraic and transcendental equation by
numerical methods to solve engineering problems.
PBHM-401CO 3. Acquire the basic knowledge of method of interpolation and numerical
solution of differential equations with the help of C/C++ languages.
References:
1. Sharma, J. N., Numerical Methods for Engineers and Scientists, Narosa
2. Grewal, B. S., Numerical Methods for Engineering and Science with Program C & C++,
DhanpatRai
3. Jain, M. K., Iyengar, S. R. K. and Jain, R. K., Numerical Methods for Scientific and
Engineering Computation, 6th Ed., New age International Publisher, India.
4. Gerald, C. F. and Wheatley, P. O., Applied Numerical Analysis, Pearson Education,
India, 2008.
5. Ascher, Uri M. and Greif, Chen, A First Course in Numerical Methods, 7th Ed., PHI
Learning Private Limited, 2013.
6. Mathews, John H. and Fink, Kurtis D., Numerical Methods using Matlab, 4th Ed., PHI
Learning Private Limited, 2012.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix Numerical Methods Lab PBHM-401
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
PBHM-
401CO1 3 2 2 1 2 - -
2 3 2 3 2
PBHM-
401CO2 3 1 2 2 2 - -
1 3 1 3 2
PBHM-
401CO3 3 1 2 2 2 - -
2 2 -
2 1
Average CO
(PBHM-401) 3.0 1.3 2.0 1.7 2.0 - -
1.7 2.7 1.5 2.7 1.7
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 25 25
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHM-402 Credit 5
Year/Sem 2/4 L-T-P 4-1-0
Course Name Riemann Integration and Series of Functions
Objectives of the Course:
1. To understand and illustrate the theory & applications of the Riemann integral and
improper integrals, piece-wise continuous, uniform & point-wise convergence and
monotonic functions.
2. To illustrate a partition of an interval and Riemann sum for a function on a given interval.
3. To state the definitions of fundamental concepts in each integration theory and etc.
4. To learn the concept of Beta and Gamma function and their tests for convergence or
divergence.
UNIT- I (Total Topics- 10 and Hrs-10)
Riemann integration; inequalities of upper and lower sums; Riemann conditions of
integrability. Riemann sum and definition of Riemann integral through Riemann sums;
equivalence of two definitions; Riemann integrability of monotone and continuous
functions.
UNIT-II (Total Topics -09 and Hrs-10)
Properties of the Riemann integral; definition and integrability of piecewise continuous and
monotone functions. Intermediate Value theorem for Integrals; Fundamental theorems of
Calculus. Improper integrals; Convergence of Beta and Gamma functions.
UNIT-III (Total Topics -06 and Hrs-09)
Pointwise and uniform convergence of sequence of functions. Theorems on continuity,
derivability and integrability of the limit function of a sequence of functions. Series of
functions.
UNIT-IV (Total Topics -06 and Hrs-09)
Theorems on the continuity and derivability of the sum function of a series of functions;
Cauchy criterion for uniform convergence and Weierstrass M-Test.
UNIT-V (Total Topics -09 and Hrs-10)
Limit superior and Limit inferior. Power series, radius of convergence, Cauchy Hadamard
Theorem, Differentiation and integration of power series; Abel’s Theorem; Weierstrass
Approximation Theorem.
Course Outcomes (COs):
TBHM-402CO 1. Develop critical thinking by identifying, analyzing and subsequently
solved Riemann Integration and their applications.
TBHM-402CO 2. Application of appropriate techniques to study uniform &point-wise
convergence of sequence of function and its applications to real world situations.
TBHM-402CO 3. Obtain the idea of integral and its implementation’s, various theorems
and their explanations through their applications in multidisciplinary situation.
TBHM-402CO 4. Enhance critical thinking ability by learning application of Beta-gamma
functions, convergence theorem, piece-wise continuous and monotonic functions and its
advanced knowledge.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
References:
1. Ross, K.A., Elementary Analysis, The Theory of Calculus, Undergraduate Texts in
Mathematics, Springer (SIE), Indian reprint, 2004.
2. Bartle, R.G. and Sherbert, D.R., Introduction to Real Analysis, John Wiley and Sons
(Asia) Pvt. Ltd., Singapore, 2002, 3rd Ed.
3. Denlinger, C. G., Elements of Real Analysis, Jones & Bartlett (Student Edition), 2011.
CO-PO Matrix (Riemann Integration and Series of Functions) TBHM-402
Course
Outcom
e
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
402CO
1 2 2 2 1 1 _ _ 1 3 _ 2 2
TBHM-
402CO
2 3 2 2 2 3 _ _ 1 2 _ _ 2
TBHM-
402CO
3 2 2 2 2 1 _ _ 2 2 _ 2 2
TBHM-
402CO
4 1 2 2 1 1 _ _ 2 1 _ 2 2
Averag
e CO
(TBHM
-402)
2 2 2 1.5 1.5 _ _ 1.5 2 _ 2 2
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHM-403 Credit 5
Year/Sem 2/4 L-T-P 4-1-0
Course Name Ring Theory and Linear Algebra – I
Objectives of the Course:
1. To analyze the fundamental idea in ring theory and vector space.
2. To create depth knowledge about range, rank and nullity of linear transform.
3. To understand the important concepts of basis and dimension of vector space.
4. To explore the knowledge about ring homomorphism and ring isomorphism.
UNIT- I (Total Topics- 12 and Hrs-10)
Definition and examples of rings, properties of rings, subrings, integral domains and fields,
characteristic of a ring. Ideal, ideal generated by a subset of a ring, factor rings, operations
on ideals, prime and maximal ideals.
UNIT-II (Total Topics -07 and Hrs-09)
Ring homomorphisms, properties of ring homomorphisms, Isomorphism theorems I, II and
III, field of quotients.
UNIT-III (Total Topics -12 and Hrs-09)
Vector spaces, subspaces, algebra of subspaces, quotient spaces, linear combination of
vectors, linear span, linear independence, basis and dimension, dimension of subspaces.
UNIT-IV (Total Topics -07 and Hrs-09)
Linear transformations, null space, range, rank and nullity of a linear transformation,
matrixrepresentation of a linear transformation, algebra of linear transformations.
UNIT-V (Total Topics -05 and Hrs-09)
Isomorphisms, Isomorphism theorems, invertibility and isomorphisms, change of coordinate
matrix.
Course Outcomes (COs):
TBHM-403CO 1. Analyze the fundamental concepts in ring theory and vector space
TBHM-403CO 2. Application of ring homomorphism to enhance the capability of critical
thinking
TBHM-403CO 3. Application of appropriate techniques to formulate the proof of
theorems in ring theory and vector space
TBHM-403CO 4. Obtain in-depth understanding about range, rank and nullity of linear
transform and its applications
References:
1. Fraleigh, J.B., A First Course in Abstract Algebra, Pearson, 2002, 7th Ed.
2. Artin, M., Abstract Algebra, Pearson, 2011, 2nd Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
3. Friedberg S.H. and Insel A.J., Spence,L.E.,Linear Algebra, Prentice Hall of India
Pvt. Ltd., New Delhi, 2004, 4th Ed.
4. Gallian, J.A., Contemporary Abstract Algebra, Narosa Publishing House, New
Delhi, 1999, 4th Ed.
5. Lang, S., Introduction to Linear Algebra, Springer, 2005,2nd Ed.
6. Strang, G., Linear Algebra and its Applications, Thomson, 2007.
7. Kumaresan, S., Linear Algebra- A Geometric Approach, Prentice Hall of India,1999.
8. Hoffman, K. and Kunze, R.A., Linear Algebra, Prentice-Hall of India Pvt. Ltd., 1971,
2nd Ed.
9. Wallace, D.A.R., Groups, Rings and Fields, Springer Verlag London Ltd., 1998.
CO-PO Matrix (Ring Theory-I) TBHM-403
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
403 CO1
2 3 2 _ _ _ _ 2 2 2 1 2
TBHM-
403 CO2
3 2 2 2 2 _ _ 1 1 _ 1 1
TBHM-
403 CO3
2 3 3 2 3 _ _ 1 1 1 3 2
TBHM-
403 CO4
2 1 3 1 1 _ _ 3 _ 2 2 1
Average
CO
(TBHM-
403)
2.3 2.3 2.5 1.7 2.0 _ _ 1.8 1.3 1.7 1.8 1.5
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHG-404 Credit 5
Year/Sem 2/4 L-T-P 4-1-0
Course Name Non-Conventional Energy Resources
Objectives of the Course:
1. To know about non-conventional energy sources.
2. To understand NCER harvesting process.
3. To look out feature scope of renewable energy sources.
4. To analyze various non-conventional energy resources & their applications.
UNIT- I (Total Topics- 08 and Hrs-08)
Introduction: Various non-conventional energy resources- Introduction, availability of Solar
Energy, Wind energy, Geothermal energy, Ocean thermal, Tidal and wave energy, Fuel cells,
& Their relative merits and demerits. Waste Recycling Plants.
UNIT-II (Total Topics -11 and Hrs-08)
Solar Cells & Solar Thermal Energy: Theory of solar cells Photovoltaic effect, Efficiency
of solar cells. Solar cell materials, solar cell power plant, limitations. Flat plate collectors
and their materials, applications and performance, focusing of collectors and their materials,
applications and performance; solar thermal power plants, thermal energy storage for solar
heating and cooling & limitations.
UNIT-III (Total Topics -12 and Hrs-8)
Geothermal Energy& Magneto-Hydrodynamics (MHD)
Resources of geothermal energy, Structure of earth’s interior, Site selection for geothermal
power plants, thermodynamics of geo-thermal energy Conversion-electrical conversion,
non-electrical conversion, Problems associated with geothermal conversion. Principle of
working of MHD Power plant, performance, Power output, efficiency and its limitations.
UNIT-IV (Total Topics -15 and Hrs-08)
Fuel Cells, Thermo-Electrical and Thermionic Conversions
Principle of operation of an acidic fuel cell, Reusable cells, Ideal fuel cells, other types of
fuel cells and their Comparison, Efficiency and EMF of fuel cells, Operating characteristics
of fuel cells, Advantages of fuel cell power plants. Thermo-Electrical and Thermionic
Conversions- Principle of working, performance and limitations.
UNIT-V (Total Topics -17 and Hrs-8)
Wind Energy: Wind power and its sources, Properties of wind, site selection criterion,
momentum theory, classification of rotors, concentrations and augments, wind
characteristics, performance and limitations of energy conversion systems.
Bio-Mass: Availability of bio-mass and its conversion theory. Problems involved in bio gas
production .Types of Bigas Plant
Wave And Tidal Wave: Principle of working, performance and limitations. Theory of Ocean
Thermal Energy Conversion (OTEC)
Course Outcomes (COs):
TBHG -404CO 1. Understand non conventional Energy Sources.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
TBHG -404CO 2. Analyze ample inputs on a various issues in harnessing renewable
Energy.
TBHG -404CO 3. Recognize present and forthcoming role of renewable energy sources.
TBHG -404CO 4. Interpret various renewable energy resources, technologies and their
Applications.
References:
1. Saeed, S.H.,Sharma,D.K., Non Conventional Energy Resources, katsons.
2. Garg, H.P., Reidel D. Advanced in Solar Energy Technology, Publishing Co., Drdricht.
3. Sukhatme, S.P., Solar Energy, Tata McGrew Hill Company Ltd., New Delhi.
4. Twidell&Wier,AW., Renewable energy resources, English Language book, Society I
E&FNSpon (1986).
5. Bansal. N.K., Kleeman M. &MieleeM.,Renewable conversion technology, TataMcGraw
Hill, New Delhi.
6. Duffle and Beckman Solar Thermal Engineering Process, John Wiley & Sons, NewYork
CO-PO Matrix- Non-Conventional Energy Resources TBHG-404
Course Outcome PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PS
O 1
PS
O 2
PS
O 3
PS
O 4
TBHG-404CO1 2 2 1 2 - 1 2 - 1 2 2 2
TBHG-404CO2 2 1 1 1 2 1 2 - 1 2 3 2
TBHG-404CO3 2 2 1 3 - 1 2 - 1 3 2 2
TBHG-404CO4 2 1 2 2 - 1 2 - 1 2 3 2
Average CO
(TBHM-404) 2 1.5
1.2
5 2 2 1 2 - 1 2.25 2.5 2
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHG-404 Credit 5
Year/Sem 2/4 L-T-P 4-1-0
Course Name Data Structure
Objectives of the Course:
1. To understand the fundamentals of concept and the importance of data structure in
implementing efficient algorithms.
2. Students demonstrate an ability to apply mathematical foundations, algorithmic
principles, and computer science theory in the modelling and design of computer-based
systems.
UNIT- I (Total Topics- 12 and Hrs-09)
Introduction to Data Structures
Data structures and Algorithms Introduction: Concept of data structure, types of data
structures, different operations in data structure, Algorithm and its complexity, Time-Space
trade-off.Arrays: Introduction, One Dimensional Arrays, address calculation of a location in
array, Different operations on array: traversal, selection, searching, insertion, deletion,
Spares matrices
UNIT-II (Total Topics -11 and Hrs-10)
Stacks and Queues
Stacks, array representation of stack, operations on stack, applications of stacks, Conversion
of Infix to Prefix and Postfix Expressions, Evaluation of postfix expression using stack,
Recursion in C, example of recursion, Tower of Hanoi, , Array representation of Linear
Queues, Circular Queues,De-queues, priority queues, Applications of Queues.
UNIT-III (Total Topics -12 and Hrs-9)
Pointers and Linked Lists
Pointers: Introduction to pointers, Pointer variables, pointers and Dynamic memory
allocation, Linked Lists: Introduction to linear linked list, Circular linked list, doubly linked
list, operations on linked lists, Concepts of header linked lists, Linked representation of Stack
and its operation, Linked representation of Queues and its operation.
UNIT-IV (Total Topics -15 and Hrs-10)
Trees and Graphs
Trees: Introduction to trees, binary tree, representation and traversal of Binary tree,
operations on binary trees, types of binary trees, BST, operations in BST, threaded binary
trees, Balanced search trees, AVL trees, Application of trees.
Graphs: Introduction, terminology, representation, traversal and searching in graph, types of
graphs, Introduction to Minimum Cost Spanning tree, Prims and kruskal method for finding
MCST.
UNIT-V (Total Topics -9and Hrs-9)
Advanced Data Structure/Miscellaneous Top
Searching techniques: Linear search and Binary search, Sorting: Selection sort, bubble
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
sort,quick sort, Heapsort, insertion sort, Hashing: Hash Table, hash functions, collision
Resolution Strategies, hash table Implementation, Huffman algorithm & Huffman tree.
Course Outcomes (COs):
TBHG -404CO 1. Demonstrate how linked list, stacks, arrays, queues and trees
represented in memory by using algorithms.
TBHG -404CO 2. Demonstrate the efficiency of algorithms for searching and sorting.
TBHG -404CO 3. Evaluate the different methods of traversing trees.
TBHG -404CO 4. Solve the real word problems involving graphs, trees and heaps
References:
1. Lipschuz, S., Data Structure, Schaum’s Outlines Series.
2. Kanetker, Y.. Data Structures Through C, BPB Publication.
CO-PO Matrix-Data Structure TBHG-404
Course Outcome PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PS
O1
PS
O2
PS
O3
PS
O4
TBHG-404CO1 1 2 - 2 3 - - - 1 2 - 1
TBHG-404CO2 2 1 2 1 2 - - - 2 - 2 2
TBHG-404CO3 1 1 2 2 2 - - - 1 1 2 1
TBHG-404CO4 - 1 2 1 2 - - - 2 1 - 2
Average CO
(TBHM-404)
1 1.2
5
1.5 1.5 2.2
5
- - - 1.5 1 1 1.5
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHG-404 Credit 5
Year/Sem 2/4 L-T-P 4-1-0
Course Name Dynamics
Objectives of the Course:
1. To expose the student to basic principles of kinematics, rectilinear motion in plane.
2. To develop conceptual understanding of simple harmonic motion, cycloid motion and
projectile motion.
3. To provide sound knowledge that how to solve modern dynamical problems related to
Simple harmonic motion and projectile motion.
4. To develop ability to translate real world problem into mathematical problems and
solution, interpretations of those problems.
UNIT- I (Total Topics- 08 and Hrs-08)
Kinematics: Motion in a straight line and plane and some examples, Radial velocity and
acceleration, Transverse velocity and acceleration with solved problems.
UNIT-II (Total Topics -11 and Hrs-09)
Velocity and Acceleration: Angular velocity and acceleration, Tangential velocity and
acceleration, Normal velocity and acceleration, Rectilinear motion with constant
acceleration and some problems.
UNIT-III (Total Topics -06 and Hrs-10)
Simple Harmonic Motion: Definition of simple harmonic motion (SHM) and examples,
Equation of simple harmonic motion, Hook’s law for horizontal and vertical strings with
solved problems.
UNIT-IV (Total Topics -06 and Hrs-09)
Cycloid: Definition of cycloid and examples, Parametric equation of the cycloid, Intrinsic
equation of the cycloid, Cycloid motion with solved problems.
UNIT-V (Total Topics -13 and Hrs-10)
Projectiles: Definitions of projectile (Trajectory, Velocity of projection, Angle of projection,
Point of projection, Range, Time of flight and greatest height), Position of projectile at any
time, Equation of trajectory, Maximum height, Maximum horizontal range of the projectile,
Range and time of flight up an inclined plane and solved problems.
Course Outcomes (COs):
TBHG -404CO 1. Understanding the principles and methods used in analyzing rectilinear
motion of a particle and apply these to solve typical problems by integration to find position,
velocity, acceleration or time.
TBHG -404CO 2. Demonstrate the concept of simple harmonic motion, projectile motion
and cycloid motion and apply these to find solution of problems related to real world.
TBHG -404CO 3. Acquire the knowledge that how to solve modern dynamical problems
with appropriate information, techniques and solution strategy.
TBHG -404CO 4. Translating real world problem into mathematical statements and
solution, interpretations of those problems.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
References:
1. Loney, S. L., AnElementary Treatise on the Dynamics of a Particle and of Rigid Bodies,
Kalyani Publishers, New Delhi.
2. Ray, M., A Textbook on Dynamics, S. Chand and Company Limited, New Delhi ,13th
Ed..
CO-PO Matrix-Dynamics TBHG-404
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHG-
404CO1
3 3 2 2 1 - - 2 2 3 2 2
TBHG-
404CO2
3 3 3 2 1 - - 3 2 3 2 2
TBHG-
404CO3
3 2 2 2 1 - - 2 2 3 2 2
TBHG-
404CO4
3 3 3 3 1 - - 3 2 3 3 2
Average CO
(TBHM-404)
3.0 2.8 2.5 2.3 1.0 - - 2.5 2.0 3.0 2.3 2.0
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHM-405 Credit 2
Year/Sem 2/4 L-T-P 2-0-0
Course Name Graph Theory
Objectives of the Course:
1. To provide the basic of graph theory and its properties.
2. To gain the knowledge of graphs, theorems and algorithms for set up the solution.
3. To assess different type of problems like Chinese postman problems, travelling
salesman’s problem etc.
UNIT- I (Total Topics- 08 and Hrs-12)
Definition, examples and basic properties of graphs, pseudo graphs, complete graphs, bi-
partite graphs, isomorphism of graphs, paths and circuits.
UNIT-II (Total Topics -08 and Hrs-13)
Eulerian circuits, Hamiltonian cycles, the adjacency matrix, weighted graph, travelling
salesman’s problem, shortest path, Dijkstra’s algorithm, Floyd-Warshall algorithm.
Course Outcomes (COs):
TBHM-405CO 1. Knowledge of graphs and its properties and its application on different
problems of graph theory.
TBHM-405CO 2. Ability to assess the isomorphism of graph, path, circuits, Dijkstra’s and
Floyd-Warshall algorithm for solution of real life problems.
TBHM-405CO 3. Enhance understanding of graphs such as Euler graph, Hamiltonian
cycles, and travelling salesman problem for solution of engineering problems.
References:
1. Davey, B.A. and Priestley, H.A., Introduction to Lattices and Order, Cambridge
University Press, Cambridge, 1990.
2. Goodaire, E. G. and Parmenter, M.M., Discrete Mathematics with Graph Theory,
Pearson Education (Singapore) P. Ltd., Indian Reprint 2003, 2nd Ed.
3. Lidl, R. and Pilz, G., Applied Abstract Algebra, Undergraduate Texts in Mathematics,
Springer (SIE), Indian reprint, 2004, 2ndEd.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix (Graph Theory) TBHM-405
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
405CO1 3 _ 2 1 2 _ _ 2 _ 3 2 2
TBHM-
405CO2 3 1 2 _ 2 _ _ 2 _ 2 1 2
TBHM-
405CO3 3 2 2 2 2 _ _ 2 _ 2 2 1
Average CO
(TBHM-405) 3 1.5 2 1.5 2 _ _ 2 _ 2.3 1.67 1.67
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHM-405 Credit 2
Year/Sem 2/4 L-T-P 2-0-0
Course Name Combinatorial Mathematics
Objectives of the Course:
1. To learn the Basic counting principles, Permutations and Combinations
2. To develop the concept of Generating functions and models
3. To discuss the basic conceptsof Recurrence relations and Solution of recurrence relations
4. To acquire knowledge about Polya theory of counting and Latin squares
UNIT- I (Total Topics- 12 and Hrs-05)
Basic counting principles, Permutations and Combinations (with and without repetitions),
Binomial theorem, Multinomial theorem, Counting subsets, Set-partitions, Stirling numbers,
Principle of Inclusion and Exclusion, Derangements, Inversion formulae
UNIT-II (Total Topics -6 and Hrs-5)
Generating functions: Algebra of formal power series, Generating function models,
Calculating generating functions, Exponential generating functions.
UNIT-III (Total Topics -9 and Hrs-5)
Recurrence relations: Recurrence relation models, Divide and conquer relations, Solution of
recurrence relations, Solutions by generating functions, Integer partitions, Systems of
distinct representatives.
UNIT-IV (Total Topics -7 and Hrs-4)
Polya theory of counting: Necklace problem and Burnside’s lemma, Cyclic index of a
permutation group, Polya’s theorems and their immediate applications.
UNIT-V (Total Topics -5and Hrs-5)
Latin squares, Hadamard matrices, Combinatorial designs: t designs, BIBDs, Symmetric
designs.
Course Outcomes (COs):
TBHM -405CO 1. Appraise the concept of Basic counting principles, Permutations and
Combinations
TBHM-405CO 2. Develop the logical thinking about concept of Generating functions and
models
TBHM -405CO 3. Enhance critical thinking ability about Polya theory of counting and Latin
squares
TBHGM-405CO 4. Acquire the knowledge of Recurrence relations and Solution of
recurrence relations.
References:
1. van Lint, J.H., and Wilson, R.M. A Course in Combinatorics, Cambridge University
Press, 2001,2nd Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
2. Krishnamurthy, V.,Combinatorics, Theory and Application, Affiliated East-West Press
1985.
3. Cameron, P.J,.Combinatorics, Topics, Techniques, Algorithms, Cambridge University
Press, 1995.
4. Hall, M. Jr.,Combinatorial Theory, John Wiley & Sons, 1986,2nd Ed.
5. Sane, S.S.,Combinatorial Techniques, Hindustan Book Agency, 2013.
6. Brualdi, R.A.,IntroductoryCombinatorics, Pearson Education Inc.,5th Ed.
CO-PO Matrix-Combinatorial Mathematics TBHM-405
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
405CO1 3 2 2 2 - - - 2 3 1 1 1
TBHM-
405CO2 3 2 2 2 1 - - 1 2 2 - 1
TBHM-
405CO3 3 1 2 2 2 - 1 2 2 - - 2
TBHM-
405CO4 3 2 1 - 1 - - 2 3 - - 2
Average
CO
(TBHM-
405)
3.0 1.8 1.8 2.0 1.3 - 1.0 1.8 2.5 1.5 1.0 1.5
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code TBHM-405 Credit 2
Year/Sem 2/4 L-T-P 2-0-0
Course Name Applications of Algebra
Objectives of the Course:
1. To learn the concept of Balanced incomplete block designs (BIBD), Balanced
incomplete block designs and finite field
2. To develop the concept of Symmetry groups and permutation groups, groups of
symmetry
3. To discuss the basic concepts. color patterns and, generating functions for non-
isomorphic graphs
4. To acquire knowledge about Coding Theory, Hamming Codes, decoding and cyclic
codes.
UNIT- I (Total Topics- 8 and Hrs-08)
Balanced incomplete block designs (BIBD): definitions and results, incidence matrix of a
BIBD, construction of BIBD from difference sets, construction of BIBD using quadratic
residues, difference set families, construction of BIBD from finite fields.
UNIT-II (Total Topics -7and Hrs-5)
Coding Theory: introduction to error correcting codes, linear cods, generator and parity
check matrices, minimum distance, Hamming Codes, decoding and cyclic codes.
UNIT-III (Total Topics -5and Hrs-5)
Symmetry groups and color patterns: review of permutation groups, groups of symmetry and
action of a group on a set;
UNIT-IV (Total Topics -3 and Hrs-3)
Colouring and colouring patterns, Polya theorem and pattern
UNIT-V (Total Topics -3and Hrs-3)
Inventory, generating functions for non-isomorphic graphs.
Course Outcomes (COs):
TBHM -405CO 1. Appraise the concept Balanced incomplete block designs(BIBD),
Balanced incomplete block designs and finite field
TBHM-405CO 2. Develop the logical thinking about concept of Symmetry groups and
permutation groups, groups of symmetry
TBHM -405CO 3. Acquire the basic knowledge about color patterns and , generating
functions for non-isomorphic graphs
TBHGM-405CO 4. Enhance critical thinking ability of Coding Theory, Hamming Codes,
decoding and cyclic codes
References:
1. Herstein, I. N. and Winter, D. J., Primer on Linear Algebra, Macmillan Publishing
Company, New York, 1990.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
2. Nagpaul, S. R. and Jain, S. K., Topics in Applied Abstract Algebra, Thomson Brooks
and Cole, Belmont, 2005.
3. Klima, R. E. Sigmon, N., Stitzinger, E., Applications of Abstract Algebra with Maple,
CRC Press LLC, Boca Raton, 2000.
4. Lay, D.C., Linear Algebra and its Applications. Pearson Education Asia, Indian Reprint,
2007,3rd Ed.
5. Zhang, F., Matrix theory, Springer-Verlag New York, Inc., New York, 1999.
CO-PO Matrix-Applications of Algebra TBHM-405
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
405CO1
2 3 2 1 _ _ _ 2 2 2 2 2
TBHM-
405CO2
2 2 2 1 1 _ _ 2 2 2 1 2
TBHM-
405CO3
3 3 3 2 2 _ _ 2 2 2 3 2
TBHM-
405CO4
3 3 3 2 1 _ _ 3 2 2 3 2
Average CO
(TBHM-405)
2.5 2.7 2.5 1.5 1.3 _ _ 2.2 2 2 2.25 2
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code PBHW-406 Credit 1
Year/Sem 2/4 L-T-P 0-0-2
Course Name Workshop/Activities
Objectives of the Course:
1. To encourage students to participate in academic (seminar, conference, workshop) and
extracurricular activities (poster presentation, debates, etc)
2. To enhance their presentation and communication skill through participation in various
activities.
3. To inculcate critical thinking ability through discussions, exploring recent developments
in science, etc
Activities will be based on department allotted by the class Coordinator/HOD.
1. Presentation by students on the topic provided by HOD/ class coordinator.
2. Any social activities
3. Presentation on mathematical Model
Course Outcomes (COs):
PBHW -406CO 1.Demonstrate technical skills for effective preparation of presentations,
write-ups through participant in academic and extracurricular activities.
PBHW -406 CO 2. Exhibit good communication and presentation skills.
PBHW -406 CO 3. Acquire critical thinking ability to analyze and interpret observations,
recent scientific developments, etc.
CO-PO Matrix (Activity) PBHW-406
Course
Outcom
e
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PSO
1
PSO
2
PSO
3
PSO
4
PBHW-
406CO1
2 _ _ 2 3 _ 2 _ 2 1 2
PBHW-
406CO2
_ 2 _ 2 3 _ 2 _ 2 2 2
PBHW-
406 CO3
1 _ _ 2 3 1 2 _ 2 2 2
Average
CO
(PBHW-
406)
1.5 2.0 _ 2.0 3.0 1.0 2.0 _ 2.0 1.7 2.0
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 25 25
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
SEMESTER -V
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons) Mathematics Programme Code 26
Course Code TBHM-501 Credit 5
Year/Sem 3/5 L-T-P 4-1-0
Course Name Multivariate Calculus
Objectives of the Course:
1. Application of multivariable functions viz. double and triple integrals to solve the
complex variety of practical problems in multidisciplinary environment.
2. Implementation of multi variable calculus in defining the maxima-minima and two
times integrals for binary variable functions in the field of industry and society.
3. Appraise about multi variable functions, fractional derivatives and various properties
connected with by using mathematical techniques and tools.
4. Enhance the critical thinking ability by prove the usage of Multivariate calculus in
defining shape, equilibrium, outline in real world situation.
UNIT- I (Total Topics- 7 and Hrs. - 9)
Functions of several variables, limit and continuity of functions of two variables, Partial
differentiation, total differentiability and differentiability, sufficient condition for
differentiability.
UNIT- II (Total Topics -12and Hrs-6)
Chain rule for one and two independent parameters, directional derivatives, the gradient,
maximal and normal property of the gradient, tangent planes, Extrema of functions of two
variables, method of Lagrange multipliers, constrained optimization problems, Definition of
vector field, divergence and curl.
UNIT- III (Total Topics -12 and Hrs-12)
Double integration over rectangular region, double integration over non-rectangular region,
Double integrals in polar co-ordinates, Triple integrals, Triple integral over a parallelepiped
and solid regions. Volume by triple integrals, cylindrical and spherical co-ordinates.
UNIT-IV (Total Topics -7and Hrs-10)
Change of variables in double integrals and triple integrals. Line integrals, Applications of
line integrals: Mass and Work. Fundamental theorem for line integrals, conservative vector
fields, independence of path.
UNIT-V (Total Topics -5and Hrs-12)
Green’s theorem, surface integrals, integrals over parametrically defined surfaces. Stoke’s
theorem, The Divergence theorem.
Course Outcomes (COs):
TBHM-501 CO 1.Elaborate multi variable function by using double and triple integrals to
solve the complex problems.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
TBHM-501 CO 2.Implement multi variable calculus in defining the minimum – maximum
& double integrals.
TBHM-501 CO 3.Outline functions of multi-variable’s, fractional derivatives and various
properties.
TBHM-501 CO 4.Enhance the critical thinking ability by demonstrating the usage of
Multivariate calculus in real world situation
References:
1. Thomas, G.B. and Finney R.L., Calculus and Analytic Geometry, Pearson Education,
Delhi,2005,9th Ed.
2. Strauss, M.J., Bradley, G.L. and Smith, K.J., Calculus , Dorling Kindersley (India) Pvt.
Ltd. (Pearson Education), Delhi, 2007, 3rdEd.
3. Marsden, E., Tromba, A.J. and Weinstein, A., Basic Multivariable Calculus, Springer
(SIE), Indian reprint, 2005.
4. Stewart, James, Multivariable Calculus, Concepts and Contexts, Cole, Thomson
Learning, USA, 2001, 2nd Ed.
CO-PO Matrix-Multivariate Calculus TBHM-501
Course Outcome PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PS
O 1
PS
O2
PS
O3
PS
O4
TBHM-501CO1 2 2 1 1 _ _ _ 2 3 _ 2 1
TBHM-501CO2 2 3 1 1 1 _ _ 2 2 1 2 1
TBHM-501CO3 3 3 2 1 _ _ 2 2 1 2 2
TBHM-501CO4 3 3 3 2 1 _ _ 2 3 1 2 2
Average CO
(TBHM-501)
2.5 2.8 1.8 1.3 1.0 _ _ 2.0 2.5 1.0 2.0 1.5
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc.(Hons.) Mathematics Programme Code 26
Course Code TBHM-502 Credit 5
Year/Sem 3/5 L-T-P 4-1-0
Course Name Group Theory – II
Objectives of the Course:
1. Advance knowledge of important mathematical concepts in abstract algebra such as
automorphism, direct product of groups, group action, finite and infinite groups.
2. To understand the important advanced subgroups such as characteristic subgroups,
commutator subgroup and its properties
3. To understand the concepts of class equation and its applications
4. Prove theorems like Cayley’s theorem, Index theorem, Sylow’s theorems and Cauchy’s
theorem
UNIT- I (Total Topics- 9 and Hrs- 10)
Automorphism, inner automorphism, automorphism groups, automorphism groups of finite
and infinite cyclic groups, applications of factor groups to automorphism groups,
Characteristic subgroups, Commutator subgroup and its properties.
UNIT- II (Total Topics -4 and Hrs-9)
Properties of external direct products, the group of units modulo n as an external direct
product, internal direct products, Fundamental Theorem of finite abelian groups.
UNIT- III (Total Topics -7 and Hrs-9)
Group actions, stabilizers and kernels, permutation representation associated with a given
group action, Applications of group actions: Generalized Cayley’s theorem, Index theorem.
UNIT-IV (Total Topics - 4 and Hrs-9)
Groups acting on themselves by conjugation, class equation and consequences, conjugacy in
Sn.
UNIT-V (Total Topics - 6 and Hrs-9)
p-groups, Sylow’s theorems and consequences, Cauchy’s theorem, Simplicity of An for n ≥
5, non-simplicity tests.
Course Outcomes (COs):
TBHM-502CO 1.Enhance the advance knowledge of automorphism and learned its
applications in field of research and higher studies.
TBHM-502CO 2.Build an idea about group action and direct product.
TBHM-502CO 3.Elaborate the idea of subgroup and order of group using Cauchy theorem
and Sylow’s theorems and analyzed its applications.
TBHM-502CO 4.Application of appropriate technique to formulate the proof of
fundamental theorem of finite group, index theorem and Cayley’s theorem.
References:
1. Fraleigh,J.B., First Course in Abstract Algebra, Pearson, 2002, 7th Ed.
2. Artin, M., Abstract Algebra, Pearson, 2011, 2nd Ed.
3. Gallian,J.A., Contemporary Abstract Algebra, Narosa Publishing House, 1999, 4th Ed
4. Dummit, D. S. and Foote, R.M., Abstract Algebra, John Wiley and Sons (Asia) Pvt. Ltd.,
Singapore, 2004, 3rd Ed.
5. Durbin, J.R. ,Modern Algebra, John Wiley & Sons, New York Inc., 2000.
6. Wallace, D. A. R. ,Groups, Rings and Fields, Springer Verlag London Ltd., 1998.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix (Group Theory-II) TBHM-502
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
502CO1 2 2 1 3 _ _ _ 2 3 _ 2 3
TBHM-
502CO2 1 _ _ _ _ _ _ _ 2 _ _ 2
TBHM-
502CO3 2 2 3 2 2 _ _ 1 2 _ 2 2
TBHM-
502CO4 2 2 3 2 3 _ _ 1 2 _ 2 2
Average
CO
(TBHM-
502)
1.8 2.0 2.3 2.3 2.5 _ _ 1.3 2.3 _ 2.0 2.3
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc.(Hons) Mathematics Programme Code 26
Course Code TBHM-503 Credit 5
Year/Sem 3/5 L-T-P 4-1-0
Course Name Portfolio Optimization
Objectives of the Course:
1. To learn the concept of Financial markets. Investment objectives and Measures of return
and risk
2. To develop the concept Mutual funds and Mean-variance portfolio optimization
3. To discuss the basic concepts Capital market theory and Capital assets pricing model
4. To acquire knowledge about Index tracking optimization and Portfolio performance
evaluation measures.
UNIT- I (Total Topics- 5 and Hrs- 9)
Financial markets. Investment objectives. Measures of return and risk. Types of risks. Risk
free assets.
UNIT- II (Total Topics -4 and Hrs-8)
Mutual funds. Portfolio of assets. Expected risk and return of portfolio. Diversification.
UNIT- III (Total Topics -6and Hrs-9)
Mean-variance portfolio optimization- the Markowitz model and the two-fund theorem, risk-
free assets and one fund theorem, efficient frontier.
UNIT-IV (Total Topics 7and Hrs-9)
Portfolios with short sales. Capital market theory. Capital assets pricing model- the capital
market line, beta of an asset, beta of a portfolio, security market line.
UNIT-V (Total Topics -3 and Hrs-7)
Index tracking optimization models. Portfolio performance evaluation measures.
Course Outcomes (COs):
TBHM-503CO 1. Appraise the concept of Financial markets. Investment objectives and
Measures of return and risk
TBHM-503CO 2. Acquire the knowledge about Index tracking optimization and Portfolio
performance evaluation measures.
TBHM-503CO 3. Enhance critical thinking ability of Capital market theory and Capital
assets pricing model
TBHM-503CO 4. Develop the logical thinking about concept of Mutual funds and Mean-
variance portfolio optimization
References:
1. Reilly, F. K., Brown, K.C., Investment Analysis and Portfolio Management, ,South-
Western Publishers, 2011, 10th Ed.
2. Markowitz, H.M., Mean-Variance Analysis in Portfolio Choice and Capital Markets,
Blackwell, New York, 1987.
3. Best, M.J., Portfolio Optimization, Chapman and Hall, CRC Press, 2010.
4. Luenberger, D.G., Investment Science, Oxford University Press, 2013,2nd Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix Portfolio Optimization TBHM-503
Course Outcome PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PS
O 1
PS
O2
PS
O3
PS
O4
TBHM-503CO1 2 2 2 1 1 _ _ 1 3 _ 2 2
TBHM-503CO2 3 2 2 2 3 _ _ 1 2 _ _ 2
TBHM-503CO3 2 2 2 2 1 _ _ 2 2 _ 2 2
TBHM-503CO4 1 2 2 1 1 _ _ 2 1 _ 2 2
Average CO
(TBHM-503) 2 2 2 1.5 1.5 _ _ 1.5 2 _ 2 2
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons) Mathematics Programme Code 26
Course Code TBHM-503 Credit 5
Year/Sem 3/5 L-T-P 4-1-0
Course Name Number Theory
Objectives of the Course:
1. To assess different types of Linear Diophantine equation and evaluate prime counting
function, and Chinese Remainder theorem. To design the concept of Fermat’s Little
theorem, Number theoretic functions and Wilson’s theorem, and its applications.
2. To develop the concept of Inverse Mobius formula, Dirichlet product and Euler’s phi‐
function, and its applications
3. To identify the primitive roots and primitive roots for primes, and its applications of
number theory in cryptography
UNIT- I (Total Topics- 7 and Hrs- 9)
Linear Diophantine equation, prime counting function, statement of prime number theorem,
Goldbach conjecture, linear congruences, complete set of residues, Chinese Remainder
theorem.
UNIT- II (Total Topics -4 and Hrs-6)
Fermat’s Little theorem, Wilson’s theorem, sum and number of divisors, totally
multiplicative functions.
UNIT- III (Total Topics -8and Hrs-12)
Definition and properties of the Dirichlet product, the Mobius Inversion formula, the greatest
integer function, Euler’s phi‐function, Euler’s theorem, reduced set of residues, some
properties of Euler’s phi-function.
UNIT-IV (Total Topics 7and Hrs-9)
Order of an integer modulo n, primitive roots for primes, composite numbers having
primitive roots, Euler’s criterion, the Legendre symbol and its properties,
UNIT-V (Total Topics -6 and Hrs-9)
Quadratic Reciprocity, quadratic congruences with composite moduli. Public key
encryption, RSA encryption and decryption, the equation x2 + y2= z2, Fermat’s Last theorem.
Course Outcomes (COs):
TBHM-503CO 1.Acquire the basic knowledge of Number Theory and Theoretic Problems
in practical situations in real life environment and society.
TBHM-503CO 2.Create the ideas of Fermat’s, Euler’s & Chinese remainder theorems and
evaluated congruence equations ascend in numerous higher-level problems.
TBHM-503CO 3.Acquire the knowledge of number theoretic functions, Dirichlet product,
Mobius inverse formula, linear congruence and residue with some properties and learn its
application to higher studies.
TBHM-503CO 4.Develop the appropriate techniques to find primitive roots, quadratic
reciprocity, public key encryption, RSA encryption and their application in cryptography.
References:
1. Burton,D.M., Elementary Number Theory, Tata McGraw, Hill, Indian reprint, 2007,
6th Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
2. Robinns, Neville, Beginning Number Theory, Narosa Publishing House Pvt. Ltd.,
Delhi, 2007, 2nd Ed.
CO-PO Matrix Number Theory TBHM-503
Course Outcome P
O1
P
O2
P
O3
P
O4
P
O5
P
O6
P
O7
P
O8
PS
O1
PS
O2
PS
O3
PS
O4
TBHM-503CO1 3 2 2 1 2 - 1 2 3 - 2 1
TBHM-503CO2 3 1 2 1 3 - - 2 2 - 2 2
TBHM-503CO3 3 1 2 - - - - 1 2 - - 2
TBHM-503CO4 3 2 2 2 2 - - 2 2 - 1 1
Average CO
(TBHM-503) 3.0 1.5 2.0 1.3 2.3 - 1.0 1.8 2.3 - 1.7 1.5
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc.(Hons) Mathematics Programme Code 26
Course Code TBHM-503 Credit 5
Year/Sem 3/5 L-T-P 4-1-0
Course Name Boolean Algebra and Automata Theory
Objectives of the Course:
1. To provide sound knowledge about axiomatic set theory and elementary logics.
2. To expose the student to properties lattice, Boolean polynomial and circuit theory.
3. To understand the concept of finite automata, language with valid examples.
4. To develop ability to translate real world problem into mathematical statements and
solution, interpretations of those problems.
UNIT- I (Total Topics- 9 and Hrs- 7)
Definition, examples and basic properties of ordered sets, maps between ordered sets, duality
principle, lattices as ordered sets, lattices as algebraic structures, sublattices, products and
homomorphisms.
UNIT- II (Total Topics -10 and Hrs-9)
Definition, examples and properties of modular and distributive lattices, Boolean algebras,
Boolean polynomials, minimal forms of Boolean polynomials, Quinn‐McCluskey method,
Karnaugh diagrams, switching circuits and applications of switching circuits.
UNIT- III (Total Topics -10and Hrs-9)
Introduction: Alphabets, strings, and languages. Finite Automata and Regular Languages:
deterministic and non-deterministic finite automata, regular expressions, regular languages
and their relationship with finite automata, pumping lemma and closure properties of regular
languages.
UNIT-IV (Total Topics 15and Hrs-9)
Context Free Grammars and Pushdown Automata: Context free grammars (CFG), parse
trees, ambiguities in grammars and languages, pushdown automaton (PDA) and the language
accepted by PDA, deterministic PDA, Non- deterministic PDA, properties of context free
languages; normal forms, pumping lemma, closure properties, decision properties.
UNIT-V (Total Topics -12 and Hrs-10)
Turing Machines: Turing machine as a model of computation, programming with a Turing
machine, variants of Turing machine and their equivalence. Undecidability: Recursively
enumerable and recursive languages, undecidable problems about Turing machines: halting
problem, Post Correspondence Problem, and undecidability problems About CFGs.
Course Outcomes (COs):
TBHM-503CO 1. Understand Boolean algebra and basic properties of Boolean algebra;
able to simplify simple Boolean functions by using the basic Boolean properties.
TBHM-503CO 2. Able to design simple combinational logics using baisc gates. Able to
optimize simple logic using Karnaugh maps.
TBHM-503CO 3. Acquire a fundamental understanding of the core concepts in automata
theory and formal languages
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
TBHM-503CO 4. An ability to prove and disprove theorems establishing key properties of
formal languages and automata.
References:
1. Davey, B A. and Priestley, H. A., Introduction to Lattices and Order, Cambridge
University Press, Cambridge, 1990.
2. Goodaire, E. G. and Michael M. Parmenter, Discrete Mathematics with Graph Theory,
Pearson Education (Singapore) P.Ltd., Indian Reprint. (2nd Ed.)
3. Lidl, R. and Pilz, G., Applied Abstract Algebra, Undergraduate Texts in Mathematics,
Springer (SIE), Indian reprint, 2004,2nd Ed.
4. Hopcroft, J. E., Motwani, R. and Ullman, J. D., Introduction to Automata Theory,
Languages, and Computation, Addison-Wesley, 2001, 2nd Ed.
5. Lewis, H.R., Papadimitriou, C.H., Papadimitriou, C., Elements of the Theory of
Computation, Prentice-Hall, NJ, 1997,2nd Ed.
CO-PO Matrix Boolean Algebra and Automata TheoryTBHM-503
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
503CO1 3 - 2 - 2 - 1 2 - 3 1 1
TBHM-
503CO2 3 2 2 2 2 - - 2 - 2 2 2
TBHM-
503CO3 3 2 2 - 2 - - 1 - 2 1 2
TBHM-
503CO4 3 2 2 1 1 - - 2 3 - 2 2
Average
CO
(TBHM-
503)
3.0 2.0 2.0 1.5 1.8 - 1.0 1.8 3.0 2.3 1.5 1.8
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons) Mathematics Programme Code 26
Course Code TBHM-504 Credit 5
Year/Sem 3/5 L-T-P 4-1-0
Course Name Theory of Equations
Objectives of the Course:
1. To learn the Descarte’s rule of signs and Transformation of equations
2. To develop the concept of Polynomials and Equation and its properties.
3. To discuss the advanced concepts of Algebraic solutions of the cubic and bi-quadratic.
4. To acquire knowledge about Derived function and Newton’s theorem on the sums of
powers of roots.
UNIT- I (Total Topics- 7 and Hrs- 7)
General properties of polynomials, Graphical representation of a polynomial, maximum and
minimum values of a polynomials, General properties of equations.
UNIT- II (Total Topics -6 and Hrs-9)
Descarte’s rule of signs positive and negative rule, Relation between the roots and the
coefficients of equations.
UNIT- III (Total Topics -8 and Hrs-10)
Symmetric functions, Applications of symmetric function of the roots, Transformation of
equations. Solutions of reciprocal and binomial equations. Algebraic solutions of the cubic
and biquadratic. Properties of the derived functions.
UNIT-IV (Total Topics -5 and Hrs-9)
Symmetric functions of the roots, Newton’s theorem on the sums of powers of roots,
homogeneous products, limits of the roots of equations.
UNIT-V (Total Topics -6 and Hrs-9)
Separation of the roots of equations, Strums theorem, Applications of Strum’s theorem,
Conditions for reality of the roots of an equation and biquadratic. Solution of numerical
equations.
Course Outcomes (COs):
TBHM-504CO 1. Appraise the concept of Derived function and Newton’s theorem on the
sums of powers of roots.
TBHM-504CO 2.Demonstrate deep understanding about Polynomials, Equation and its
properties
TBHM-504CO 3.Demonstrate deep understanding about Polynomials, Equation and its
properties
TBHM-504CO 4. Develop the appropriate techniques to Descarte’s rule of signs and
Transformation of equations
References:
1. Burnside, W.S. and Panton, A.W., The Theory of Equations, Dublin University Press,
1954.
2. MacDuffee, C. C., Theory of Equations, John Wiley & Sons Inc., 1954.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix (Theory of Equations) TBHM-504
Course
Outcom
e
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
504CO
1
3 - 2 - 2 - 1 1 - 1 1 1
TBHM-
504CO
2
3 2 1 2 2 - - 2 - 2 2 2
TBHM-
504CO
3
1 1 1 - 2 - - 1 - 2 1 1
TBHM-
504CO
4
1 2 1 1 1 - - 2 3 - 2 2
Averag
e CO
(TBHM
-504)
2.0 1.7 1.3 1.5 1.8 - 1.0 1.5 3.0 1.7 1.5 1.5
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons) Mathematics Programme Code 26
Course Code TBHM-504 Credit 5
Year/Sem 3/5 L-T-P 4-1-0
Course Name Analytical Geometry
Objectives of the Course:
1. To develop the concept of Asymptotes and tracing the curves.
2. To discuss the concepts of cylinder and cone and their properties
3. To acquire knowledge about General equation of second degree
4. To assess of fundamental properties of Plane, line and spheres.
UNIT- I (Total Topics- 12 and Hrs- 9)
General equation of second degree, Pair of lines, Parabola, Tangent, Normal, Pole and Polar
and their properties, Ellipse, Hyperbola, Tangent, Normal, Pole and Polar, Conjugate
diameters.
UNIT- II (Total Topics -9and Hrs-9)
Asymptotes, Conjugate hyperbola and Rectangular hyperbola, Polar equation of a conics,
Polar equation of tangent, normal, polar and asymptotes, Tracing of parabola, Ellipse and
hyperbola.
UNIT- III (Total Topics -8 and Hrs-9)
Review of straight lines and planes, Equation of sphere, Tangent plane, Plane of contact and
polar plane, Intersection of two spheres, radical plane, Coaxial spheres,
UNIT-IV (Total Topics -7 and Hrs-9)
Equation of cylinder, Enveloping and right circular cylinders, Equations of central conicoids,
Tangent plane, Normal, Plane of contact and polar plane,
UNIT-V (Total Topics -8 and Hrs-10)
Equation of a cone, Intersection of cone with a plane and a line, Enveloping cone, Right
circular cone, Enveloping cone and enveloping cylinder, Equations of paraboloids and its
simple properties.
Course Outcomes (COs):
TBHM-504 CO1. Appraise the fundamental properties of cylinder, cone and their properties
TBHM-504 CO2. Demonstrate the deep understanding of General equation of second
degree
TBHM-504 CO3.Develop the logical thinking about concept of Asymptotes and tracing the
curves
TBHM-504 CO4.Acquire the knowledge of fundamental properties Plane, line and
spheres
References:
1. Thomas, G.B., and Finney, R.L., Calculus, Pearson Education, Delhi, 2005,9th Ed.
2. Anton, H., Bivens, I., and Davis, S., Calculus, John Wiley and Sons (Asia) Pvt. Ltd.
3. Loney, S.L., The Elements of Coordinate Geometry, McMillan and Company.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
4. Bell, R.J.T., Elementary Treatise on Coordinate Geometry of Three Dimensions,
McMillan India Ltd., 1994.
5. BallabhR.: Textbook of Coordinate Geometry, Prakashan Kendra.
6. Jain, P.K. and Ahmad K.: Textbook of Analytical Geometry, New Age International (P)
Ltd. Publishers, 1986.
7. Askwith, E. H.: A Course of Pure Geometry, Merchant Books, 2007.
CO-PO Matrix (Analytical Geometry) TBHM-504
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-504
CO1 3 - 2 - 1 - 1 2 - 1 1 1
TBHM-504
CO2 3 1 1 2 1 - - 2 - 2 2 2
TBHM-504
CO3 3 1 1 - 2 - - 2 - 2 1 1
TBHM-504
CO4 3 2 2 1 1 - - 2 3 - 2 1
Average
CO
(TBHM-
504)
3.0 1.3 1.5 1.5 1.3 - 1.0 2.0 3.0 1.7 1.5 1.3
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code TBHM-504 Credit 5
Year/Sem 3/5 L-T-P 4-1-0
Course Name Probability and Statistics
Objectives of the Course:
1. To learn Markov Chains, Chapman-Kolmogorov equations, classification of states.
2. To evaluate the correlation, rank correlation and regression lines.
3. To develop the concepts of moments, continuous distribution, discrete distribution, Joint
moment generating function, marginal and conditional Distributions.
4. To understand and illustrate the theory and applications of the probability and sample
space.
UNIT- I (Total Topics- 10 and Hrs- 10)
Sample space, probability axioms, real random variables (discrete and continuous),
cumulative distribution function, probability mass/density functions, mathematical
expectation, moments, moment generating function, characteristic function.
UNIT- II (Total Topics -6 and Hrs-7)
Discrete distributions: uniform, binomial, Poisson, geometric, negative binomial,
continuous distributions: uniform, normal, exponential.
UNIT- III (Total Topics -8 and Hrs-10)
Joint cumulative distribution function and its properties, joint probability density functions,
marginal and conditional distributions, expectation of function of two random variables,
conditional expectations, independent random variables.
UNIT-IV (Total Topics -5 and Hrs-8)
Bivariate normal distribution, correlation coefficient, joint moment generating function
(JMGF) and calculation of covariance from JMGF, linear regression for two variables
UNIT-V (Total Topics -10and Hrs-10)
Chebyshev’s inequality, statement and interpretation of (weak) law of large numbers and
strong law of large numbers, Central Limit theorem for independent and identically
distributed random variables with finite variance, Markov Chains, Chapman-Kolmogorov
equations, classification of states.
Course Outcomes (COs):
TBHM-504CO 1.Acquire the deep knowledge of various forms of discrete & continuous
probability distribution functions and its application in real world problems.
TBHM-504CO 2.Application of different statistical technique such as correlation &
regression to the actual life arithmetical data.
TBHM-504CO 3.Analysis of statistical data analytically and graphically for real world
problems.
TBHM-504CO 4.Appraise the concept of Markov Chains, Chapman-Kolmogorov
equations, classification of states.
References:
1. Hogg, R. V., McKean, J.W. and Craig, Allen T., Introduction to Mathematical Statistics,
Pearson Education, Asia, 2007, 8th Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
2. Miller, I., Miller, M., Freund, J.E., Mathematical Statistics with Applications, Pearson
Education, Asia, 2006, 7th Ed.
3. Ross, S., Introduction to Probability Models, Academic Press, Indian Reprint, 2007,
9thEd.
4. Mood, A.M., Graybill, F. A. and Boes, D. C., Introduction to the Theory of Statistics,
Tata McGraw- Hill, Reprint , 2007, 3rd Ed.
CO-PO Matrix (Probability and Statistics) TBHM-504
Course
Outcom
e
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
504CO
1
2 2 _ 1 _ _ _ 2 2 _ _ 3
TBHM-
504CO
2
2 2 _ _ 3 _ _ 2 3 _ 1 2
TBHM-
504CO
3
2 2 1 2 2 _ _ 2 2 _ _ 2
TBHM-
504CO
4
1 2 2 3 2 _ _ 2 2 _ 2 2
Averag
e CO
(TBHM
-504)
1.7 2 1.5 2 2.3 _ _ 2 2.25 _ 1.5 2.25
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc (Hons.) Mathematics Programme Code 26
Course Code PBSM-505 Credit 2
Year/Sem 3/5 L-T-P 0-0-3
Course Name Seminar
Objectives of the Course:
1. To provide the detail knowledge for preparing presentation and seminar.
2. To develop the concept of team work, presentation skills of data in conferences,
symposia, seminar etc.
3. To demonstrate knowledge and understand mathematical tools and techniques in
seminar.
Seminar: Participation/ paper presentation in the seminar
Course Outcomes (COs):
2. PBSM-505 CO 1. Developed the idea for preparing presentation for their possible future
profession.
3. PBSM -505 CO 2. Enhanced the critical thinking skills, communication skills and build
team work for conferences, symposia, seminar etc.
PBSM -505 CO 3. Demonstrate the knowledge of mathematical tools and techniques for
presentations of research data in seminar and conferences.
CO-PO Matrix (Seminar) PBSM-505
Course
Outcom
e
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PSO
1
PSO
2
PSO
3
PSO
4
PBSM-
505 CO1 2 _ _ 2 3 _ 2 _ 2 1 2
PBSM-
505 CO2 _ 2 _ 2 3 _ 2 _ 2 2 2
PBSM-
505 CO3 1 _ _ 2 3 1 2 _ 2 2 2
Average
CO
(PBSM -
505)
1.5 2.0 _ 2.0 3.0 1.0 2.0 _ 2.0 1.7 2.0
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 50 -
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
SEMESTER -VI
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons) Mathematics Programme Code 26
Course Code TBHM-601 Credit 5
Year/Sem 3/6 L-T-P 4-1-0
Course Name Metric Spaces and Complex Analysis
Objectives of the Course:
1. To define a metric space, absolute and uniform convergence of power series.
2. To elaborate convergent sequence and demonstrate equivalence of metrics.
3. To illustrate the concepts of Limits, continuity, regions in the complex plane, mappings,
C-R equation’s, sufficient & necessary conditions to differentiability.
4. To examine Liouville’s& Cauchy- Goursat theorem, analyticity & algebraic fundamental
theorem.
UNIT-I (Total Topics- 14and Hrs.- 9)
Metric spaces: definition and examples. Sequences in metric spaces, Cauchy sequences.
Complete Metric Spaces. Open and closed balls, neighbourhood, open set, interior of a set.
Limit point of a set, closed set, diameter of a set, Cantor’s theorem. Subspaces, dense sets,
separable spaces.
UNIT- II (Total Topics -9 and Hrs-9)
Continuous mappings, sequential criterion and other characterizations of continuity.
Uniform continuity. Homeomorphism, Contraction mappings, Banach Fixed point Theorem.
Connectedness, connected subsets of R.
UNIT- III (Total Topics -13 and Hrs-9)
Limits, Limits involving the point at infinity, continuity. Properties of complex numbers,
regionsin the complex plane, functions of complex variable, mappings. Derivatives,
differentiation formulas, Cauchy-Riemann equations, sufficient conditions for
differentiability.
UNIT-IV (Total Topics -13and Hrs-9)
Analytic functions, examples of analytic functions, exponential function, Logarithmic
function, trigonometric function, derivatives of functions, definite integrals of functions.
Contours, Contour integrals and its examples, upper bounds for moduli of contour integrals.
Cauchy-Goursat theorem, Cauchy integral formula.
UNIT-V (Total Topics - 9 and Hrs-9)
Liouville’s theorem and the fundamental theorem of algebra. Convergence of sequences and
series, Taylor series and its examples. Laurent series and its examples, absolute and uniform
convergence of power series.
Course Outcomes (COs):
TBHM-601CO 1.Develop the concept of compound variable function related to analytic
functions.
TBHM-601CO 2.Learn appropriate techniques such as Cauchy’s Theorem, Liouville’s
Theorem, Laurent’s and Taylor’s Theorem.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
TBHM-601CO 3.Setup and verify the solution of a metric space and its application in real
word situations.
TBHM-601CO 4.Enhance critical thinking ability by solving differentiation and
integration of complex functions.
References:
1. Shirali, S.andVasudeva,H.L., Metric Spaces, Springer Verlag, London, 2005.
2. Kumaresan, S. ,Topology of Metric Spaces, Narosa Publishing House, 2nd Ed.
3. Simmons G.F.,Introduction to Topology and Modern Analysis, McGraw Hill Education,
2017, 1st Ed
4. Brown,J.W. and Churchill,R.V., Complex Variables and Applications, McGraw – Hill
International Edition,2009, 8thEd.
5. Bak,J. and Newman,D.J., Complex Analysis, Undergraduate Texts in Mathematics,
Springer-Verlag New York, Inc., NewYork, 1997, 2nd Ed.
CO-PO Matrix Metric Space and Complex Analysis TBHM-601
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
601CO1
3 2 2 1 1 _ _ 2 3 _ 3 2
TBHM-
601CO2
3 2 2 2 2 _ _ 1 _ _ 2 2
TBHM-
601CO3
2 2 2 1 1 _ _ 3 _ _ 3 2
TBHM-
601CO4
3 3 2 2 1 _ _ 1 3 _ 3 2
Average CO
(TBHM-601)
2.7 2.2 2 1.5 1.2 _ _ 1.7 3 _ 2.7 2
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons) Mathematics Programme Code 26
Course Code TBHM-602 Credit 5
Year/Sem 3/6 L-T-P 4-1-0
Course Name Ring Theory and Linear Algebra – II
Objectives of the Course:
1. To develop advance knowledge of important mathematical concepts in such as
polynomial ring, irreducibility, Euclidean domain and division algorithm
2. To understand and prove the important theorems such as Cayley-Hamilton theorem,
Bessel’s inequality, projections and Spectral theorem
3. To develop the knowledge about dual space and inner product space
4. To evaluate orthogonal basis through Gram-Schmidt orthogonalization process
UNIT I (Total Topics- 9 and Hrs- 9)
Polynomial rings over commutative rings, division algorithm and consequences, principal
ideal domains, factorization of polynomials, reducibility tests, irreducibility tests, Eisenstein
criterion, unique factorization in Z[x].
UNIT II (Total Topics -5 and Hrs-9)
Divisibility in integral domains, irreducibles, primes, unique factorization domains,
Euclidean domains.
UNIT- III (Total Topics -11 and Hrs-10)
Dual spaces, dual basis, double dual, transpose of a linear transformation and its matrix in
the dual basis, annihilators, Eigen spaces of a linear operator, diagonalizability, invariant
subspaces and Cayley-Hamilton theorem, the minimal polynomial for a linear operator.
UNIT-IV (Total Topics -5 and Hrs-9)
Inner product spaces and norms, Gram-Schmidt orthogonalisation process, orthogonal
complements, Bessel’s inequality, the adjoint of a linear operator, Least Squares
Approximation.
UNIT-V (Total Topics -6 and Hrs-9)
Minimal solutions to systems of linear equations, Normal and self-adjoint operators,
Orthogonal projections and Spectral theorem.
Course Outcomes (COs):
TBHM-602CO 1. Develop advanced knowledge of rings & vector space and its application
in higher studies.
TBHM-602CO 2. Appraise about ring polynomial prime and irreducible elements and its
application.
TBHM-602CO 3. Establish the relationship between matrix and linear transform and
evaluated Eigen value and Eigen vector.
TBHM-602CO 4. Develop the concept of inner product spaces and interpreted the
orthogonality in inner product spaces.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
References:
1. Fraleigh, J.B.,A First Course in Abstract Algebra, Pearson, 2002, 7thEd.
2. Artin, M., Abstract Algebra, Pearson, 2011, 2ndEd.
3. Gallian, G.A., Contemporary Abstract Algebra, Narosa Publishing House, 1999, 4th Ed.
4. Friedberg, S.H., Insel, A. J. and Spence, L.E., Linear Algebra, Prentice Hall of India Pvt.
Ltd., New Delhi, 2004, 4th Ed.
5. Lang, S., Introduction to Linear Algebra, Springer, 2005, 2ndEd.
6. Strang, G., Linear Algebra and its Applications, Thomson, 2007.
7. Kumaresan, S, Linear Algebra- A Geometric Approach, Prentice Hall of India.
8. Hoffman, K and Kenneth, R.A., Linear Algebra, Prentice-Hall of India Pvt. Ltd., 1978,
2nd Ed.
CO-PO Matrix (Ring Theory-II) TBHM-602
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
602CO1 1 2 1 2 _ _ _ 2 2 2 2 3
TBHM-
602CO2 1 2 3 _ 2 _ _ 1 2 _ 2 2
TBHM-
602CO3 2 _ 3 2 2 _ _ 2 _ 2 1 1
TBHM-
602CO4 1 1 2 2 3 _ _ _ _ 2 1 2
Average
CO
(TBHM-
602)
1.6
7
2.2
5 2 2.3 1.7 2 2 1.5 2
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code TBHM-603 Credit 5
Year/Sem 3/6 L-T-P 4-1-0
Course Name Industrial Mathematics
Objectives of the Course:
1. To learn about the Medical Imaging, X-ray and CT scan based on the knowledge of
Mathematics
2. To develop the concept of Inverse problems through problems taught in Mathematics.
3. To discuss the basic concepts of Radon Transform and Back Projection.
4. To acquire knowledge about CT Scan using the properties of Fourier and inverse Fourier
transforms and applications of their properties in image reconstruction
UNIT I (Total Topics- 7 and Hrs- 8)
Medical Imaging and Inverse Problems. The content is based on Mathematics of X-ray and
CT scan based on the knowledge of calculus, elementary differential equations, complex
numbers and matrices.
UNIT II (Total Topics -12 and Hrs-10)
Introduction to Inverse problems: Why should we teach Inverse Problems? Illustration of
Inverse problems through problems taught in Pre-Calculus, Calculus, Matrices and
differential equations. Geological anomalies in Earth’s interior from measurements at its
surface (Inverse problems for Natural disaster) and Tomography.
UNIT- III (Total Topics -5 and Hrs-9)
X-ray: Introduction, X-ray behavior and Beers Law (The fundament question of image
construction) Lines in the place.
UNIT-IV (Total Topics -9and Hrs-9)
Radon Transform: Definition and Examples, Linearity, Phantom (Shepp-Logan Phantom -
Mathematical phantoms). Back Projection: Definition, properties and examples.
UNIT-V (Total Topics -8 and Hrs-10)
CT Scan: Revision of properties of Fourier and inverse Fourier transforms and applications
of their properties in image reconstruction. Algorithms of CT scan machine. Algebraic
reconstruction techniques abbreviated as ART with application to CT scan.
Course Outcomes (COs):
TBHM-603 CO 1. Acquire the knowledge about fundamental properties Medical Imaging,
X-ray and CT scan based on the knowledge of Mathematics
TBHM-603CO 2.Enhance critical thinking ability about concept of Inverse problems
through problems taught in Mathematics.
TBHM-603 CO 3. Develop the basic knowledge about Radon Transform and Back
Projection.
TBHM-603 CO 4. Appraise the concept of CT Scan using the properties of Fourier and
inverse Fourier transforms and applications of their properties in image reconstruction
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
References:
1. Feeman, T. G., The Mathematics of Medical Imaging, A Beginners Guide, Springer
Under graduate Text in Mathematics and Technology, Springer,
2. Groetsch, C.W.,Inverse Problems, Activities for Undergraduates, The Mathematical
Association of America, 1999.
3. Kirsch, A.An Introduction to the Mathematical Theory of Inverse Problems, Springer,
2011, 2nd Ed.
CO-PO Matrix- Industrial Mathematics TBHM-603
Course Outcome P
O1
P
O2
P
O3
P
O4
P
O5
P
O6
P
O7
P
O8
PS
O1
PS
O2
PS
O3
PS
O4
TBHM-603CO1 3 - 1 - 2 - 1 2 2 1 1 1
TBHM-603CO2 3 2 2 1 1 - - 2 - 2 1 2
TBHM-603CO3 3 1 1 - 0 - - 3 - 2 1 2
TBHM-603CO4 3 2 2 1 1 - - 2 3 - 2 2
Average CO
(TBHM-603) 3.0 1.7 1.5 1.0 1.0 - 1.0 2.3 2.5 1.7 1.3 1.8
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons) Mathematics Programme Code 26
Course Code TBHM-603 Credit 5
Year/Sem 3/6 L-T-P 4-1-0
Course Name Bio-Mathematics
Objectives of the Course:
1. To learn the Mathematical Biology and modeling process.
2. To develop the concept of Prey predator systems and LotkaVolterra equations
3. To discuss the advanced concepts of Spatial Models (one and Two species)and Discrete
Models
4. To acquire knowledge about Numerical solution of the models and its graphical
representation (Steady state solutions, Phase plane methods and qualitative solutions
UNIT I (Total Topics- 10 and Hrs- 9)
Mathematical Biology and the modeling process: an overview. Continuous models: Malthus
model, logistic growth, Allee effect, Gompertz growth, Michaelis-Menten Kinetics, Holling
type growth, Bacterial growth in a Chemostat, Harvesting a single natural population.
UNIT II (Total Topics -7 and Hrs-9)
Prey predator systems and Lotka Volterra equations, Populations in competitions, Epidemic
Models (SI, SIR, SIRS, SIC), Activator-Inhibitor system, Insect Outbreak Model: Spruce
Budworm.
UNIT- III (Total Topics -9 and Hrs-10)
Numerical solution of the models and its graphical representation. Qualitative analysis of
continuous models: Steady state solutions, stability and linearization, multiple species
communities and Routh-Hurwitz Criteria, Phase plane methods and qualitative solutions,
bifurcations and limit cycles with examples in the context of biological scenario.
UNIT-IV (Total Topics -11and Hrs-10)
Spatial Models: One species model with diffusion, Two species model with diffusion,
Conditions for diffusive instability, Spreading colonies of microorganisms, Blood flow in
circulatory system, Travelling wave solutions, Spread of genes in a population. Discrete
Models: Overview of difference equations, steady state solution and linear stability analysis,
UNIT-V (Total Topics -13 and Hrs-10)
Introduction to Discrete Models, Linear Models, Growth models, Decay models, Drug
Delivery Problem, Discrete Prey-Predator models, Density dependent growth models with
harvesting, Host-Parasitoid systems (Nicholson-Bailey model), Numerical solution of the
models and its graphical representation. Case Studies: Optimal Exploitation models, Models
in Genetics, Stage Structure Models, Age Structure Models.
Course Outcomes (COs):
TBHM-603 CO 1.Acquire the knowledge of Mathematical Biology and modeling
process
TBHM-603CO 2.Demonstrate understanding of Prey predator systems and
LotkaVolterraequations
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
TBHM-603 CO 3. Appraise the concept of Spatial Models (one and Two species)and
Discrete Models
TBHM-603 CO 4. Develop the appropriate techniques to Numerical solution of models ,
Qualitative analysis of continuous models and Routh-Hurwitz Criteria
References:
1. Keshet, L.E.,Mathematical Models in Biology, SIAM, 1988.
2. Murray, J. D.,Mathematical Biology, Springer, 1993.
3. Fung, Y.C.,Biomechanics, Springer-Verlag, 1990.
4. Brauer, F.,PDriessche.,V.D. and Wu, J.,Mathematical Epidemiology, Springer,
5. Kot, M.,Elements of Mathematical Ecology, Cambridge University Press, 2001.
CO-PO Matrix-Bio – Mathematics TBHM-603
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
603CO1 3 - 2 - 2 - 1 2 - 1 1 1
TBHM-
603CO2 3 2 1 2 2 - - 2 - 2 2 2
TBHM-
603CO3 3 1 1 - 2 - - 2 - 2 1 2
TBHM-
603CO4 3 2 1 1 1 - - 2 - - 2 2
Average
CO
(TBHM-
603)
3.0 1.7 1.3 1.5 1.8 - 1.0 2.0 - 1.7 1.5 1.8
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons.) Mathematics Programme Code 26
Course Code TBHM-603 Credit 5
Year/Sem 3/6 L-T-P 4-1-0
Course Name Linear Programming problems
Objectives of the Course:
1. To develop the fundamental concepts Linear Programming problems
2. To identify and obtain the solution of simplex method and duality
3. To construct the concepts of various type of solution viz. bounded solution, degeneracy
and optimal solution.
4. To solve transportation and assignment problem and create a depth understanding
about Game theory and its applications
UNIT I (Total Topics- 4 and Hrs- 8)
Introduction to linear programming problem, Theory of simplex method, optimality and
unboundedness,
UNIT II (Total Topics -6 and Hrs-8)
The simplex algorithm, simplex method in tableau format, introduction to artificial variables,
two‐phase method, Big‐M method and their comparison.
UNIT- III (Total Topics -4 and Hrs-9)
Duality, formulation of the dual problem, primal‐dual relationships, economic interpretation
of the dual.
UNIT-IV (Total Topics -4and Hrs-10)
Transportation problem and its mathematical formulation, northwest‐corner method least
cost method and Vogel approximation method for determination of starting basic solution,
algorithm for solving transportation problem, assignment problem and its mathematical
formulation, Hungarian method for solving assignment problem.
UNIT-V (Total Topics -5 and Hrs-9)
Game theory: formulation of two person zero sum games, solving two person zero sum
games, games with mixed strategies, graphical solution procedure, linear programming
solution of games.
Course Outcomes (COs):
TBHM-603 CO 1.Develop the fundamental concepts of Linear Programming problems
and its real-life applications.
TBHM-603CO 2.Elaborate the understanding of simplex method and duality
TBHM-603 CO 3.Explain various type of solution in LPP such that unbalanced,
boundedness, degeneracy and optimal solution.
TBHM-603 CO 4.Enhance and propose the idea about transportation, assignment
problem and game theory and its application
References:
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
1. Bazaraa, M. S., Jarvis,J.J. and Sherali, H. D., Linear Programming and Network Flows,
John Wiley and Sons, India, 2004, 2nd Ed.
2. Hillier, F.S. and Lieberman, G.J., Introduction to Operations Research, Tata McGraw
Hill, Singapore, 2009, 9th Ed.
3. Taha, H.A., Operations Research, An Introduction, PrenticeHall, India, 2006, 8th Ed.
4. Hadley,G.,Linear Programming, Narosa Publishing House, New Delhi ,2002.
CO-PO Matrix-Linear Progamming Problem TBHM-603
Course Outcome P
O1
P
O2
P
O3
P
O4
P
O5
P
O6
P
O7
P
O8
PS
O1
PS
O2
PS
O3
PS
O4
TBHM-603CO1 2 3 2 1 _ _ _ 2 2 2 2 2
TBHM-603CO2 2 2 2 1 1 _ _ 2 2 2 1 2
TBHM-603CO3 3 3 3 2 2 _ _ 2 2 2 3 2
TBHM-603CO4 3 3 3 2 1 _ _ 3 2 2 3 2
Average CO
(TBHM-603)
2.5 2.7 2.5 1.5 1.3 _ _ 2.2 2 2 2.25 2
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc.(Hons) Mathematics Programme Code 26
Course Code TBHM-604 Credit 5
Year/Sem 3/6 L-T-P 4-1-0
Course Name Mathematical Modeling
Objectives of the Course:
1. To learn the basic techniques of Power series solution of a differential equation and its
application.
2. To derive the concept Legendre equation, Bessel equation, Laplace transform and
initial value problems.
3. To provide the knowledge of Monte Carlo Simulation Modeling and its applications
4. To develop the concepts ofoptimizationmodeling, Linear Programming, and simplex
method.
UNIT I (Total Topics- 2 and Hrs- 9)
Power series solution of a differential equation about an ordinary point, solution about a
regular singular point.
UNIT II (Total Topics -5 and Hrs-10)
Bessel’s equation and Legendre’s equation, Laplace transform and inverse transform,
application to initial value problem up to second order.
UNIT- III (Total Topics -2 and Hrs-9)
Monte Carlo Simulation Modeling: simulating deterministic behavior (area under a curve,
volume under a surface)
UNIT-IV (Total Topics -4 and Hrs-9)
Generating Random Numbers: middle square method, linear congruence, Queuing Models:
harbor system, morning rush hour.
UNIT-V (Total Topics -4 and Hrs-9)
Overview of optimization modeling, Linear Programming Model: geometric solution
algebraic solution, simplex method, sensitivity analysis
Course Outcomes (COs):
TBHM-604CO 1.Acquire the basic knowledge of Power series solution of a ‘DE’ by usual
point and singular point and applications in real life environment and society.
TBHM-604 CO 2.Develop and apply the Simulation Modeling in real life situations
TBHM-604 CO 3.Create the ideas to produce arbitrary numbers: Queuing Models:
morning rush hour, harbor system, middle square method and their applications
TBHM-604 CO 1.Ability to assess and prepare the critical thinking skills of LPP Model:
graphical solution arithmetical solution, simplex method, sensitivity analysis &
optimization modeling.
References:
1. Tyn, M.U. and Debnath,L., Linear Partial Differential Equation for Scientists and
Engineers, Springer, Indian reprint, 2006.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
2. Giordano, F. R., Weir,M.D. and Fox,W.P.,A First Course in Mathematical Modeling,
Thomson Learning, London and New York, 2003.
CO-PO Matrix Mathematical Modeling TBHM-604
Course Outcome P
O1
P
O2
P
O3
P
O4
P
O5
P
O6
P
O7
P
O8
PS
O1
PS
O2
PS
O3
PS
O4
TBHM-604CO1 3 - 2 - 2 - 1 2 - 3 1 1
TBHM-604CO2 3 2 2 2 2 - - 2 - 2 2 2
TBHM-604CO3 3 2 2 - 2 - - 1 - 2 1 2
TBHM-604CO4 3 2 2 1 1 - - 2 3 - 2 2
Average CO
(TBHM-604) 3.0 2.0 2.0 1.5 1.8 - 1.0 1.8 3.0 2.3 1.5 1.8
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc.(Hons) Mathematics Programme Code 26
Course Code TBHM-604 Credit 5
Year/Sem 3/6 L-T-P 4-1-0
Course Name Mechanics
Objectives of the Course:
1. To learn the basic techniques of Moment of a force about a point and an axis, couple
and couple moment, Moment of a couple about a line, resultant of a force system, and
its application.
2. To derive the concept laws of Coulomb friction, application to simple and complex
surface contact friction problems, transmission of power through belts, screw jack.
3. To provide the knowledge of second moments and the product of area of a plane area,
transfer theorems, Conservative force field, conservation for mechanical energy, work
energy equation, kinetic energy and their applications.
4. To develop the concept of Chasles’ theorem, general relationship between time
derivatives of a vector for different references.
UNIT I (Total Topics-9 and Hrs- 10)
Moment of a force about a point and an axis, couple and couple moment, Moment of a couple
about a line, resultant of a force system, distributed force system, free body diagram, free
body involving interior sections, general equations of equilibrium, two point equivalent
loading, problems arising from structures, static indeterminacy.
UNIT II (Total Topics -5 and Hrs-10)
Laws of Coulomb friction, application to simple and complex surface contact friction
problems, transmission of power through belts, screw jack, wedge, first moment of an area
and the centroid, other centers.
UNIT- III (Total Topics -6 and Hrs-10)
Theorem of Pappus-Guldinus, second moments and the product of area of a plane area,
transfer theorems, relation between second moments and products of area, polar moment of
area, principal axes.
UNIT-IV (Total Topics -8 and Hrs-9)
Conservative force field, conservation for mechanical energy, work energy equation, kinetic
energy and work kinetic energy expression based on center of mass, moment of momentum
equation for a single particle and a system of particles, translation and rotation of rigid
bodies.
UNIT-V (Total Topics -6 and Hrs-8)
Chasles’ theorem, general relationship between time derivatives of a vector for different
references, relationship between velocities of a particle for different references, acceleration
of particle for different references.
Course Outcomes (COs):
TBHM-604CO 1.Acquire the basic knowledge of Moment of a force about a point and an
axis, couple and couple moment, Moment of a couple about a line, resultant of a force
system, and its application in society.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
TBHM-604 CO 2. Develop the knowledge of laws of Coulomb friction, application to
simple and complex surface contact friction problems, transmission of power through belts,
screw jack.
TBHM-604 CO 3.Create the ideas of second moments and the product of area of a plane
area, transfer theorems, Conservative force field, conservation for mechanical energy and
their applications
TBHM-604 CO 4.Ability to assess and prepare the critical thinking skills of Chasles’
theorem, general relationship between time derivatives of a vector for different references,
relationship between velocities of a particle for different references
References:
1. Shames, I.H., and Krishna, G.,Rao, M.,Engineering Mechanics: Statics and Dynamics,
Dorling Kindersley (India) Pvt. Ltd. (Pearson Education), Delhi, 2009. (4th Ed.).
2. Hibbeler, R.C. and Ashok Gupta, Engineering Mechanics: Statics and Dynamics,
Dorling Kindersley (India) Pvt.Ltd. (Pearson Education), Delhi,11th Ed.
CO-PO Matrix MechanicsTBHM-604
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
TBHM-
604CO1 3 - 2 - 2 - 1 2 - 3 1 1
TBHM-
604CO2 3 2 2 2 2 - - 2 - 2 2 2
TBHM-
604CO3 3 2 2 - 2 - - 1 - 2 1 2
TBHM-
604CO4 3 2 2 1 1 - - 2 3 - 2 2
Average
CO
(TBHM-
604)
3.0 2.0 2.0 1.5 1.8 - 1.0 1.8 3.0 2.3 1.5 1.8
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (Hons) Mathematics Programme Code 26
Course Code TBHM-604 Credit 5
Year/Sem 3/6 L-T-P 4-1-0
Course Name Differential Geometry
Objectives of the Course:
1. To analyse the equivalence of the two curves by applying some theorems.
2. To understand and illustrate the Fundamental forms and curvature of surfaces and
applications of the curvature
3. To learn the basic techniques of envelope & developable surface.
4. To understand the important concept of Local non-intrinsic properties of a surface.
UNIT I (Total Topics-10 and Hrs- 9)
Theory of Space Curves: Space curves, Planer curves, Curvature, torsion and Serret-Frenet
formulae. Osculating circles, Osculating circles and spheres. Existence of space curves.
Evolutes and involutes of curves.
UNIT II (Total Topics -6 and Hrs-8)
Theory of Surfaces: Parametric curves on surfaces. Direction coefficients. First and second
Fundamental forms. Principal and Gaussian curvatures. Lines of curvature.
UNIT- III (Total Topics -7 and Hrs-8)
Euler’s theorem. Rodrigue’s formula, Conjugate and Asymptotic lines. Developables:
Developable associated with space curves and curveson surfaces, Minimal surfaces.
UNIT-IV (Total Topics -12 and Hrs-10)
Geodesics: Canonical geodesic equations. Nature of geodesics on a surface of revolution.
Clairaut’s theorem. Normal property of geodesics. Torsion of a geodesic. Geodesic
curvature. Gauss-Bonnet theorem. Surfaces of constant curvature. Conformal mapping.
Geodesic mapping. Tissot’s theorem.
UNIT-V (Total Topics -12 and Hrs-10)
Tensors: Summation convention and indicial notation, Coordinate transformation and
Jacobian, Contra-variant and Covariant vectors, Tensors of different type, Algebra of tensors
and contraction, Metric tensor and 3-index Christoffel symbols, Parallel propagation of
vectors, Covariant and intrinsic derivatives, Curvature tensor and its properties, Curl,
Divergence and Laplacian operators in tensor form, Physical components.
Course Outcomes (COs):
TBHM-604CO 1. Develop the knowledge of differential geometry to other fields such as
tensor and Cosmology
TBHM-604 CO 2. Enhance critical thinking skills by solving problems related to differentia
geometry applicable to various circumstances in mathematical situations
TBHM-604 CO 3. . Analyze the complexity of considerate in mathematical topics in relative
to curves and surfaces.
TBHM-604 CO 1. Acquire the knowledge about possessions connected to curves in space,
osculating plane, developable surface, circle curvature and torsion
References:
1. Willmore, T.J.,An Introduction to Differential Geometry, Dover Publications.
2. O'Neill, B.,Elementary Differential Geometry, Academic Press, 2006,2nd Ed.
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
3. Weatherburn, C.E.,Differential Geometry of Three Dimensions, Cambridge University
Press 2003.
4. Struik, D.J.,Lectures on Classical Differential Geometry, Dover Publications.
5. Lang, S.,Fundamentals of Differential Geometry, Springer, 1999.
6. Spain, B.,Tensor Calculus: A Concise Course, Dover Publications, 2003.
CO-PO Matrix Differential GeometryTBHM-604
Course Outcome P
O1
P
O2
P
O3
P
O4
P
O5
P
O6
P
O7
P
O8
PS
O1
PS
O2
PS
O3
PS
O4
TBHM-604CO1 3 - 2 - 2 - 1 2 - 3 1 1
TBHM-604CO2 3 2 2 2 2 - - 2 - 2 2 2
TBHM-604CO3 3 2 2 - 2 - - 1 - 2 1 2
TBHM-604CO4 3 2 2 1 1 - - 2 3 - 2 2
Average CO
(TBHM-604) 3.0 2.0 2.0 1.5 1.8 - 1.0 1.8 3.0 2.3 1.5 1.8
Mode of Evaluation
Internal (MM-40) External (MM-60)
Component Sessional -1 Sessional -2 Assignments End Semester Examination
Weightage 10 10 20 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc. (H) Mathematics Programme Code 26
Course Code TBHM-604 Credit 5
Year/Sem 3/6 L-T-P 4-1-0
Course Name Dissertation
Objectives of the Course:
1. To acquire skills to operate various analytical techniques and their applicability in
research and utilize modern tools, e-resources for literature survey and data compilation
2. To demonstrate technical skills to conduct Software based experiments and ability to
record observation and interpret data to derive a solution/conclusion to complex
problem.
3. To exhibit competent writing (with critical analysis), communication and
presentation skills
Guidelines:
• Students will have to do a project related to any one subject of curriculum in the
college or in industry/Research Organization.
• Each student will submit 3 copies of hard bound in the department.
• Final evaluation will be done on the basis of quality of work, performance and
presentation
Course Outcomes (COs)
TBHM-604 CO1. Acquire skills to operate various analytical techniques and instruments,
identify their applicability in research and utilize modern tools, e-resources for literature
survey and data compilation
TBHM-604 CO2. Demonstrate technical skills to conduct software-based experiments and
ability to record observation and interpret data to derive a solution/conclusion to complex
problem.
TBHM-604 CO3. Exhibit competent writing (with critical analysis), communication and
presentation skills.
CO-PO Matrix Dissertation TBHM-604
Course Outcome PO1
PO2
PO3
PO4
PO5
PO6
PO7
PSO1
PSO2
PSO3
PSO4
TBHM-604 CO1. 2 2 3 - - 1 2 2 2 3 2
TBHM-604 CO2. 1 3 3 - - 2 2 2 3 3 2
TBHM-604 CO3. - - - - 3 - - - - - - Average CO (TBHM-604)
1.5 2.5 3 - 3 1.5 2 2 2.5 3 2
Mode of Evaluation
Internal (MM-50) External (MM-150)
Component Internal Assessment End Semester Examination
Weightage 40 60
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
Programme Name B.Sc.(Hons)
Mathematics
Programme Code 26
Course Code ADP-605 Credit 1
Year/Sem 3/5 L-T-P 0-0-2
Course Name Aptitude & Reasoning Skills
Objectives of the Course:
1. Enhance problem solving and analytical skills needed in an organization. Listening,
identifying and proposing solution to the problem.
2. To gamut the skills which facilitate them to enhance their employability quotient and
overall personality development.
3. To enable students to manage the placement challenges more effectively.
UNIT I (Total Topics- 2 and Hrs- 5 )
Direct Letter Coding, Number/Symbol Coding, Matrix Coding, Substitution, Deciphering
Message Word Code\s, Deciphering Number and Symbol Codes for Messages
UNIT II (Total Topics -3 and Hrs-5)
Blood Relations Relation Puzzles, Coding Relations. Direction Sense Test Problems based
on Distance and Direction, Problems based on Angles, Alphabet Test Letter Word
Problems, Rule Detection.
UNIT- III (Total Topics -5 and Hrs-9)
Alpha Numeric Sequence Puzzles Ranking and Time Sequence Test , Problems Based on
Seating/Standing Positions, Inequalities ,Coded Inequalities.
UNIT-IV (Total Topics -4 and Hrs-10)
Seating Linear Arrangement, Rectangular Arrangement, Classification Type Questions,
Comparison Type Question, Family Based Puzzles, Problems based on Numbers, Problems
based on Alphabets ,Data Sufficiency Coding Decoding etc.
Course Outcomes (COs)
ADP-605CO 1.Solve campus placements aptitude papers covering Logical Reasoning
ADP-605CO 2.Formulate the problem quantitatively and use appropriate arithmetical,
and/or statistical methods to solve the problem
ADP-605CO 3.Interpret quantitative information (i.e., formulas, graphs, tables, models,
and schematics) and draw implications from them.
ADP-605CO 4.Thinking critically and applying basic mathematics skills to interpret data,
draw conclusions, and solve problems; Developing proficiency in numerical reasoning
Reference:
1. Aggarwal R.S ,A Modern Approach to Logical Reasoning ,S. Chand Publisher,2017
2. Sharma Arun,Quantitative Aptitude , MHE Publisher,2018,8th Edition
Uttaranchal University-Syllabus of B.Sc. (Hons.) Mathematics (Applicable for Batch: 2018-21)
UTTARANCHAL UNIVERSITY (Established vide Uttaranchal University Act, 2012)
(Uttarakhand Act No. 11 of 2013)
Arcadia Grant, P.O. Chandanwari, Premnagar, Dehradun, Uttarakhand
CO-PO Matrix Aptitude Reasoning Skills ADP-605
Course
Outcome
PO
1
PO
2
PO
3
PO
4
PO
5
PO
6
PO
7
PO
8
PSO
1
PSO
2
PSO
3
PSO
4
ADP-605
CO1 3 - 2 - 2 - 1 2 - 3 1 1
ADP-605
CO2 3 2 2 2 2 - - 2 - 2 2 2
ADP-605
CO3 3 2 2 - 2 - - 1 - 2 1 2
ADP-605
CO4 3 2 2 1 1 - - 2 3 - 2 2
Average
CO
(ADP-
605)
3.0 2.0 2.0 1.5 1.8 - 1.0 1.8 3.0 2.3 1.5 1.8
Mode of Evaluation
Internal Practical (MM-25) External Practical (MM-25)
Internal Assessment External Assessment
Weightage 25 25
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