(Resubmission of Previous Proposal for a BSc (Hons ...

University of Ontario Institute of Technology

BSc (Hons) - Applied and Industrial Mathematics 1

Faculty of Science

BSc (Hons) in Applied and

Industrial Mathematics

(Resubmission of Previous Proposal for a

BSc (Hons) Program in Mathematics)

May 4, 2005



1. Table of Contents

Section Title Page

1. Table of Contents 2

2. Background 3

3. Executive Summary 5

4. Program Map 7

5. Program Learning Outcomes 8

6. Similar or Complementary Programs Elsewhere in Ontario 10

7. Resource Requirements 12

8. Applicant Acknowledgement and Agreement Form 12

Appendix 1 - Course Descriptions for New/Modified Courses 13



2. Background

Whereas the UOIT undergraduate programs in Biology, Chemistry and Physics lead to a B.Sc. with the respective discipline name, students can only pursue a mathematics program of study via a B.Sc. in Physical Science with specialization in Mathematics. This proposal is essentially a renaming and reorganization of the currently existing mathematics specialization courses into a standalone program that is unique in Ontario, is in keeping with the market orientation of UOIT, and is expected to be attractive to students. We propose to name the degree obtained from this program a B.Sc. in Applied and Industrial Mathematics. This document details the changes required to accomplish the objective.

The background for this proposal lies in the historical development of the UOIT Science programs. When the proposal for the undergraduate Mathematics program was originally submitted to PEQAB in early 2002, it was, along with Chemistry and Physics, a specialization within an Honours B.Sc. in Physical Science. The specializations in mathematics, physics and chemistry consisted of collections of courses that amounted to standalone programs in each area. Upon implementation of the Physical Science program in 2003, it was discovered that prospective students either did not realize, or they felt prospective employers/institutions would not realize, that the specializations were equivalent to an Honours B.Sc. in each area. As a result, students were choosing to enroll elsewhere, in programs in which the discipline of the Honours degree is named explicitly. An attempt was made to remedy this situation in 2003 for Fall 2004 entry, when a request was submitted to PEQAB to “unbundle” the mathematics, chemistry, and physics specializations within Physical Science to become standalone programs renamed as distinct honours degrees. Permission was received to offer chemistry and physics as distinct standalone programs, but not the mathematics program.

This proposal should therefore be viewed as a second request to rename the mathematics specialization program. We have chosen a name that better suits the program’s purpose, proposing some changes that will focus the degree to this end and implementing some of the very useful ideas of the previous mathematics assessor. In addition, there will be a very natural transition from the revised undergraduate program into the proposed M.Sc. in Modelling and Computational Science, which is currently being prepared for review by OCGS. We feel that the resulting changes will distinguish the program, and will attract students that would otherwise not have chosen UOIT as a venue at which to study Mathematics.

The B.Sc. in Applied and Industrial Mathematics has resulted from modifying the existing B.Sc. Physical Science with specialization in Mathematics as follows.

1. Four courses have been removed and replaced by four new courses. Removed Added Set Theory Applied Functional Analysis Linear Algebra II Industrial Mathematics Biomathematics Topics in Applied Mathematics I Operations Research II Topics in Applied Mathematics II



The “topics courses” are a result of the assessor’s comments, and the contents are designed to be sufficiently flexible to suit the needs and interests of the students and the available instructors. These courses and the Industrial Mathematics course will allow the student to develop important research, problem-solving and communication skills to a higher degree than is the case in many other Mathematics programs.

2. We have changed the names of four courses, to accurately reflect their modified content and objectives Previous name New name Partial Differential Equations Mathematical Modelling Advanced Partial Differential Eqs. Partial Differential Equations Advanced Differential Equations Dynamical Systems and Chaos Operations Research I Optimization The topics in these courses have been rearranged and/or modified.

Note regarding students enrolled in the existing program: Because the changes are predominantly in the third and fourth years of the program, there will be no effect on the students enrolled in the existing program. The second-year course MATH2080U that has been introduced can be taken in third year by students in the existing program. The only issue is if a student currently enrolled prefers the existing degree name instead of the new degree name. For this reason, we will request that PEQAB recommend to the Minister that she grant consent for UOIT to offer the new program under both the old and new names until the currently enrolled students have graduated. These revisions were approved by UOIT Faculty of Science Faculty Council, March 18, 2005 and the University's Academic Council on April 19, 2005.



3. Executive Summary The UOIT Bachelor of Science program in Applied and Industrial Mathematics will be a four-year honours program and will serve students studying the sciences as well as providing support and elective courses to the Faculties of Engineering and Education. Curriculum Design Students in the Applied and Industrial Mathematics Program will learn concepts, principles, qualitative and quantitative methods and innovative problem solving skills. Mathematics is a basic component of every aspect of scientific endeavor and underlies much of our daily activities. Mathematics is a key component of problem solving, from the modelling of atmospheric physics to the complexities of managing financial markets. Mathematics and computational science interrelate in many aspects of our daily lives in ways that few people appreciate or understand. The courses in the program will provide a broad scope of useful tools for the graduate. Students will gain valuable experience by learning state-of-the-art algorithms and software in courses and by means of research projects related to the workplace. Mathematics graduates need to be able to apply relevant advanced numerical skills, including statistical analysis of data, modelling of physical or biological phenomena, and computer implementation of algorithms related to their eventual employment. These abilities will be developed in the mathematics courses offered in the upper years. They will also be regularly reinforced and practiced during learning activities in many other science courses. Exposure to the distinctive assumptions and modes of analysis of other disciplines will be provided in the non-science electives available in each year of the program. The curriculum also provides a basic foundation in chemistry, physics, and computing science, providing settings within which to apply the mathematical concepts and expertise acquired in the program; students are particularly encouraged to explore a deeper understanding of one of these disciplines by means of a Minor program of study. The emphasis on Applied and Industrial mathematics is reflected in the wide range of courses focused on the applications of mathematics (e.g., Differential Equations, Mathematical Modelling, Optimization, Computational Science, Partial Differential Equations, and Industrial Mathematics). Moreover, many of the basic core topics for a comprehensive pure mathematics education are also covered in the courses Discrete Mathematics, Real and Complex Analysis, Algebraic Structures and Applied Functional Analysis. We expect the graduates of our program will be fully qualified to be admitted to graduate studies in any reputable applied mathematics program worldwide. The students’ knowledge will be sufficiently broad to also allow them admission into a pure mathematics graduate program. A mandatory fourth-year undergraduate thesis project will introduce the students to the practice of research in the mathematical sciences. Through the thesis project, students will develop independent research skills, including reading historical and current literature, and writing and communicating technical ideas. Among the other objectives of the thesis are synthesizing mathematical theories and techniques and their relevance to solving scientific or industrial problems, implementing a practical solution to a tractable problem and identifying open research problems.



In addition, the proposed program:

• complements the interdisciplinary focus of the Faculty of Science in its other program offerings, and the courses in the proposed program are expected to be attractive electives for students in these programs.

• provides a range of courses for students in the Concurrent Education program who wish to satisfy the requirements for a first or second “teachable” in Mathematics.

• provides a synergy with the existing Computational Science secondary specialization, and with the Computing Science program

• provides an undergraduate “feeder stream” for the proposed MSc program in Modelling and Computational Science

Learning takes place in classroom lectures, tutorials, laboratories, computer simulations, and through independent and group research as well as multidimensional projects. Admission Requirements Admission requirements and requirements for promotion and graduation are exactly the same as those in place for the existing approved programs in the Faculty of Science. Research and Work Placements The primary and secondary areas of specialization give students good opportunities to undertake research outside the University and to participate in work placements, particularly in the upper years of their program of study. It is envisaged that informal opportunities will be made available for internships in the upper years of the program. Career Opportunities A graduate from the Applied and Industrial Mathematics program will be well-equipped to fill positions that require the quantitative skills acquired in the program, and to participate as a member of interdisciplinary teams in a wide range of organizations, including the computer software industry, electronics and computer manufacturers, the financial services industry, communication service providers, pharmaceutical, chemical and petroleum companies, research organizations, consulting firms, and government agencies. By combining this program with the university's Bachelor of Education degree in a Concurrent Education program, students can help to fill the need for mathematics teachers in Ontario's secondary schools. The program also provides an excellent preparation for entrance to graduate programs in applied mathematics; by taking appropriate courses specializing in an area of science, graduate program opportunities are also available in other areas.



4. Program Map - BSc in Applied and Industrial Mathematics

Year-Sem. Subject Subject Subject Subject Subject

1-1 Chemistry I CHEM1010U

Biology I BIOL1010U

Physics I PHY1010U

Calculus I MATH 1010U

Scientific Computing Tools

CSCI1000U

1-2 Chemistry II CHEM1020U

Biology II BIOL1020U

Physics II PHY1020U

Calculus II MATH1020U

Fundamentals of Programming CSCI1020U

2-1 Discrete

Mathematics** MATH2080U

Advanced Calculus I

MATH2010U

Linear Algebra MATH2050U

Statistics and Probability for

Physical Science STAT2010U

Elective*

2-2 Computational

Science I MATH2072U

Advanced Calculus II

MATH2020U

Differential Equations

MATH2060U Elective* Elective*

3-1 Real Analysis MATH3020U

Optimization MATH3040U Elective* Elective* Elective*

3-2 Mathematical

Modeling MATH3050U

Complex AnalysisMATH3060U

Algebraic Structures

MATH3070U Elective* Elective*

4-1 Dynamical

Systems and Chaos

MATH4010U

Computational Science II

MATH4020U

Topics in Applied Mathematics MATH4041U or Elective***

Industrial Mathematics MATH4060U

Elective*

4-2 Partial Differential

Equations MATH4050U

Applied Functional Analysis

MATH4030U

Topics in Applied Mathematics MATH4042U or Elective***

Thesis Project MATH4400U Elective*

*Students are required to take 5 science electives and 6 liberal studies electives, including Collaborative Leadership BUSI2000U ** Cross-listed with Discrete Structures in Computer Science, CSCI1010U *** At least one of these must be either Topics in Applied Mathematics I MATH4041U or Topics in Applied Mathematics II MATH4042U • Courses with no colour are unchanged from existing courses in the Physical Science:

mathematics specialization • Lightly shaded courses are modifications of courses already existing in the Physical

Science: mathematics specialization; darkly shaded courses are new; see the Appendix 1 for outlines of the shaded courses.



5. Program Learning Outcomes

Program Level Learning Outcomes Program requirement(s), or segments of requirements, that contribute to this outcome

Apply knowledge and understanding of the basic concepts, theories, and principles of mathematics and the related physical and biological sciences to theoretical and practical problems in these areas

Calculus I and II, Chemistry I and II, Biology I and Biology II, Physics I and II, Discrete Mathematics, Advanced Calculus I, Advanced Calculus II, Linear Algebra I, Differential Equations, Statistics and Probability for Physical Science, Mechanics I (elective)

explore the current state of knowledge in mathematics and investigate innovative solutions to significant related scientific problems

Real Analysis, Complex Analysis, Optimization, Mathematical Modelling, Algebraic Structures, Dynamical Systems and Chaos, Partial Differential Equations, Topics in Applied Mathematics, Industrial Mathematics, Applied Functional Analysis, Thesis Project

utilize knowledge to analyze, evaluate, and apply the concepts, techniques or processes needed in the study and application of mathematics

Any course with written reports meets these requirements. Computational Science I and II, Statistics and Probability for Physical Science, Industrial Mathematics

communicate effectively in written, spoken and visual format with both technical experts and members of the general public on science issues

Collaborative Leadership.

All courses with discussion components, reports, cooperative learning activities, and oral presentations will contribute to this learning outcome. Written analyses, essays, reports, and tests will require students to use written communication skills regularly. This is applicable to all required science electives, as well as non-science electives.

Understand and utilize contemporary laboratory and measurement techniques, procedures, safety protocols and equipment necessary for conduct of work in physical science

Chemistry I and II, Physics I and II, Biology I and II

plan and implement experiments and investigations, critically examine the results and draw valid conclusions

Statistics and Probability for Physical Science, Industrial Mathematics, Thesis Project.




apply to scientific study, an appreciation for the level of uncertainty in experimental results and theoretical predictions

Most laboratory experiments will give students experience with variability in data and present an opportunity to evaluate and explain the variation. Statistics and Probability for Physical Science

apply relevant numerical skills including statistical analysis as necessary for physical sciences

Statistics and Probability for Physical Science, Computational Science I and II, Industrial Mathematics, Topics in Applied Mathematics.

use current Information Technology to access, store and retrieve information, to acquire and process data, and to analyze and solve problems

All students in UOIT will be supplied with a laptop computer and will access, store and retrieve information on a daily basis in every course. Scientific Computing Tools, Computational Science I and II, Industrial Mathematics.

contribute as effective participant in multidisciplinary and multi-cultural teams, in both membership and leadership roles

Collaborative Leadership, BUSI2000U

The population of the geographic region from which the students of UOIT will come is very culturally diverse. Thus the student population of UOIT will be diverse. Daily experience in labs, tutorials, group work and student life activities will prepare students for participation in varied roles.

This is applicable to all required and science electives, as well as non-science electives.

recognize and value the alternative outlooks that people from various social, ethnic and religious backgrounds may bring to scientific endeavours

Collaborative Leadership, BUSI2000U Due to the diverse student population and exposure to representatives from business and industry through field visits and guest presentations, this is also applicable to all required and science electives, as well as non-science electives.




have well-developed strategies to update knowledge, maintain and enhance learning

Collaborative Leadership, BUSI2000U Learning enhancement with a laptop computer will continually update students relative to a vast array of knowledge. This is also applicable to all courses in which students are required to utilize various resources and conduct research to prepare for discussions, reports, assignments or presentations.

6. Similar or Complementary Programs Elsewhere in Ontario

While many Ontario universities offer a traditional B.Sc. in Mathematics, in some cases allowing for a specialization in Applied Mathematics, several Ontario universities have now started to offer B.Sc. degrees in Applied Mathematics, some with an industrial specialization. York University

York University offers a B.Sc. and B.Sc. (Honours) in Applied Mathematics. In addition, they have recently added a B.Sc. in Computational Mathematics; Applied and Industrial Mathematics is one of the available areas of specialization within the new degree.

The Specialized Honours B.Sc. in Computational Mathematics is a new program introduced in Fall 2002. It is designed to introduce students to the full process of the application of mathematics, with emphasis on core mathematical subjects, mathematical modelling, and diverse computational methodologies for analyzing these models. Some examples of applications include controlling heat flow in manufacturing processes, pricing a stock option, and assessing risks associated with insurance policies.

In addition to taking core courses in mathematics, statistics, and computer science, each student chooses one of the following three areas of specialization: Applied and Industrial Mathematics (with an emphasis in numerical analysis and differential equations); Financial Mathematics (applications to business and the financial industry, with additional courses in operations research and economics); or Actuarial Mathematics (applications in the insurance industry, with additional courses in probability and statistics).



University of Waterloo University of Waterloo offers a BMath in Applied Mathematics, which may be taken alone, or in combination with a specialization in a related discipline (such as physics, scientific computation, economics, or engineering). In addition, the university offers BMath degrees in Combinatorics and Optimization, as well as Computational Mathematics. In their first two years, all Applied Mathematics students take the same core courses as are taken by other Mathematics students, in order to acquire a sound mathematical background. At the same time, since the application of analytical reasoning to a wide variety of problems is the essence of Applied Mathematics, there is room for courses in scientific disciplines which are heavy users of mathematics, such as Physics or Engineering. In the upper years, the focus is on courses more specifically related to their chosen area of specialization. The University of Western Ontario The university offers both a regular B.Sc. degree in Applied Mathematics, as well as an Honours B.Sc. degrees in Applied Mathematics; the latter features a variety of specializations (“options”), one of which is Mathematical and Computational methods. In addition, Applied Mathematics is offered as a joint program in combination with other disciplines (computer science, statistics, geophysics, environmetrics). This Honors Program has the Applied Mathematics Program 3 part structure of combining "analytical" math courses (like calculus, differential equations and linear algebra) with numerical and computational courses and with courses in an area where you will apply the ideas and techniques you learn to important and interesting problems of "the real world". Overall Observations Several Ontario universities are starting to address the need for highly trained individuals with strong interdisciplinary problem-solving capability and extensive skills in model formulation, development, implementation and analysis to solve practical problems arising in various settings. In addition, programs in Applied Mathematics address the substantial demand for qualified mathematics educators; such a degree prepares teacher-candidates by developing an expertise in problem-solving, mathematical modelling, and the use of mathematical software which are all integral components of the new Ontario mathematics curriculum. The Applied and Industrial Mathematics program at the University of Ontario Institute of Technology will provide students with a strong foundation in mathematics, while senior courses will allow students to focus on applications of mathematics, and the opportunity to explore “real-world” problems. The university’s mobile learning environment will greatly enhance this learning experience by providing students with extensive opportunities to utilize the latest mathematical software throughout the problem-solving process.



7. Resource Requirements Faculty

The proposed changes will not introduce any additional new faculty requirements above those already planned for the existing Physical Science: Mathematics specialization, and for delivering the courses in the first two years of the program, which are required courses in other existing or planned programs. The exact requirements will depend on overall enrolments in mathematics courses in various programs in subsequent faculty resource requirement planning cycles. Preliminary estimates at this time, based upon filling the currently authorized 1 new position in mathematics/statistics in 2005/2006, indicate that the requirements will be 2 additional faculty for 2006/2007 and 1 for 2007/2008. The expertise of these faculty will be oriented towards the teaching requirements of the 11 specialist courses (plus the thesis supervision requirements) in the third and fourth years of the program, and towards the continuing goal of enhancing interdisciplinary collaborations both internal and external to the Faculty of Science.

Computers

The student laptops will be sufficient for most course-related computing requirements; the Computational Science and Visualization laboratory may be used for upper-level project and thesis courses

Other Resources

The proposed program does not require any new library resources or classroom and laboratory space. It will be adequately served by those resources already in place for the Faculty’s existing programs.

8. Applicant Acknowledgement and Agreement Form

The Applicant Acknowledgement and Agreement form, signed by the President and Vice-Chancellor of the University, is included on the pages that follow.

@ ontario Ministry of Training,Colleges and Universities

Applicant Acknowledgement and Agreement(To accompany eveny application for ministerial consent under the

Post-secondary Education Choice and Excellence Act, 2000)

This form must be completed by a representat ive of the appl icantwho is authorizedto bindthe appl icant, and must be includedwith the materials accompanying an application to the Minister for a consent under the Post-secondary Education Choice andExcellence Act. 2000.

Name of appl icant: Ll.nive .s i* o{ Onfo.r i o tn st itr^-t e of lech n o I oInsert name of onganization

Purpose of application:Insert name of degree and program (e.9., Bachelor of Science in physics)

! Please indicate if this application relates to use of the lerm university.

1. The applicant hereby acknowled$es that, in makingthis application, it understands that:

1.1 The granting of a consent by the Minister of TraininE,Col leges and Universi t ies underthe act is a pr iv i le$e,not a right.

1.2 A consent bythe Ministen of Training, Col leges and Uni-versities under the act is normally granted for a speci-f ied period of t ime and remains in force only duringthat specified period.

1.3 A Minister 's consent does not include any express orimpl ied ent i t lement to:. a renewal of such consent; or. a consent for additional or different activities

reBulated by the act.

1.4 A Minister 's consent does not ent i t le the consentholder to any funding from the Government of 0ntario,including but not limited to operatin$, capital, orresearch funding.

1.5 A private organization from outside 0ntario will betneated no less favourably, in l ike circumstances, thana private organization from 0ntario.

1.6 A private organization, whether from Ontario or fromoutside the province, is not entitled to treatment that isno less favourable, in like circumstances, than thetreatment accorded by the Ministen to a public

institution.

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A Minister's consent is not transferable, directly orindirectly, to a third party.

lf the applicant fails to comply with any le6islativerequirements or with the terms and conditions of theconsent, the Minister may amend or chan$e the termsand conditions of the consent or suspend or revokethe consent.

A Minister's consent does not make the consentholder's students eligible to apply for $overnmentfinancial assistance, grants, or awards that are pro-vided direct lyto students (e.€., assistance undertheOntario Student Assistance Program). Approval oforganizations and programs forthe purposes of0ntario student loans is established pursuant to theMinistry of TraininB, Colleges and Universities Act andregulations thereunder, as amended from time tot ime.

The Minister's criteria and policy statements related tothe review of applications for a ministerial consentmay change from t ime to t ime.

All information provided to the Minister or the Postsec-ondany Educat ion Qual i ty Assessment Board in appl ica-tions and related documentation may be subject todisclosure underthe Freedom of Information and Pro-tection of Privacy Act.

bontinued)

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No consent shal l take effect unt i l the appl icant pro-vides confirmation, in a written form approved by theMinister, that the appl icant understands and agrees tocomply with al l of the terms and condit ions attachedto the consent.

Should the Minister grant a consent, the consentholder wi l l be required t0 ensure that the fol lowinSstatement appears on promotional and other mater i-als, in any media, that relate to the prognam offeredunder the consent:

This program is offered under the written consent ofthe Minister of Training, Colleges and Universities forthe period from (daylmonth/year) fo (day/month/year)

Prospective students are responsible for satisfyingthemselves that the progrom and the degree will beappropriote to their needs (e.9., acceptable t0 plten-

tial employers, professional licensing bodies, or othereducatio nal i n stitution9.

The consent holden has a posit ive obl igat ion under thePost-secondany Educat ion Choice and Excel lence Act,2000, to not i fy the Minister of Training, Col leSes andUniversi t ies promptly i f the consent holder has reasonto bel ieve that not al l of the terms and condit ions of aconsent mav be met.

2. The appl icant hereby agrees to provide the Ministen orthe Postsecondary Educat ion Qual i ty Assessment Board withany addit ional mater ial required by the Minister or theboard to assess the appl icat ion.

5. The appl icant hereby conf irms and warrants that:

3.1 Al l information and representat ions provided by theappl icant as part of this appl icat ion, including informa-t ion given in the 0r$anizat ion Review Submission andthe ProSram Qual i ty Assessment Submission, ane true.

3.2 This appl icat ion was duly approved by the appl icant 'sgovenning body or by anothen representat ive dulyauthorized to bind the appl icant on

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14

Appendix 1 Course Descriptions for New/Modified Courses

Mathematical Modelling, MATH3050U Pre-requisites: MATH 2060 Differential Equations, STAT2010 Statistics and Probability for Physical Science, MATH2010 Advanced Calculus I, MATH2072 Computational Science I Year and Semester: Year 3, Semester 2 This course provides an overview of the mathematical modelling of discrete, continuous and stochastic systems. Problems arising in physics, chemistry, biology, industry, economics, and social science serve as examples to demonstrate model development, implementation, solution and analysis. The course also provides an introduction to partial differential equations. The derivation of the heat and wave equations in one, two, and three dimensions demonstrates the power of partial differential equations as a modelling tool. Methods of solution and physical interpretation of results are stressed. The Maple and MATLAB software packages are used to facilitate the modelling Dynamical Systems and Chaos, MATH4010U Pre-requisites: MATH2060U Differential Equations, MATH3020U Real Analysis Year and Semester: Year 4, Semester 1 The modern theory of differential equations studies the behaviour of solutions of nonlinear differential equations. In particular, the notion of dynamical system is crucial to the development of the theory and leads to the analysis of chaotic solutions. The course will provide the student with a rigorous treatment of the qualitative theory of ordinary differential equations, an introduction to the modern theory of dynamical systems and to elementary bifurcation theory.

Partial Differential Equations, MATH4050U Pre-requisites: MATH 3020 Real Analysis, MATH 3050U Mathematical Modeling, MATH

3060 Complex Analysis Year and Semester: Year 4, Semester 2 This course considers advanced aspects of the theory, solution and physical interpretation of first- and second-order partial differential equations in up to 4 independent variables. This includes the classification of types of equations, and the theory and examples of associated boundary-value problems. The concepts of maximum principles and Green’s functions are studied, as well as an introduction to nonlinear equations. A broad range of applications are considered.


15

Applied Functional Analysis, MATH4030U Pre-requisites: MATH 3020U Real Analysis, MATH 3060U Complex Analysis. Year and Semester: Year 4, Semester 1 This course introduces the student to the modern theory of infinite-dimensional spaces and its applications. The main topics revolve around Banach and Hilbert spaces and their applications to Fourier series, differential and integral equations. The course will focus on developing intuition and building a catalog of examples of infinite-dimensional spaces. Moreover, the course introduces the very important notions of Lebesgue measure and Lebesgue integrals. Applications will play a major role in motivating the theory. Topics in Applied Mathematics I and II, MATH4041U and MATH4042U Pre-requisite(s): MATH 2072 Computational Science I, MATH 3020 Real Analysis, MATH

3040 Optimization, MATH 3050U Mathematical Modeling Year and Semester: Year 4, Semesters 1 and 2 These courses cover various advanced topics that will enable the students to broaden their mathematical background, and allow them to explore areas in which they have particular interest. Topics in Applied Mathematics I and II will both be the same in format but will cover a different selection of topics. The topics will be chosen according to the needs and demands of the students and the availability of instructors. The list below is not exhaustive. Potential Topics:

• Stochastic processes • Advanced statistical analysis • Industrial applications of statistics • Advanced optimization (combinatoric, nonlinear, constrained, etc.) • Optimal control theory • Financial mathematics • Graph Theory • Cryptography • Artificial neural networks


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Industrial Mathematics, MATH4060U Pre-requisites: MATH 3050U Mathematical Modeling, MATH 3020 Real Analysis, MATH 2072 Computational Science I; PHYS 3060 (Fluid Mechanics) is highly recommended but not required Year and Semester: Year 4, Semester 2

Course Description and Content Outline: A case-studies approach is taken to the mathematical modelling of industrial problems and other physical problems that are relevant for industrial applications. Potential topics include:

1) Lubrication theory and slow viscous flow phenomena 2) Elasticity, plasticity, crack propagation 3) Chemical reactors and chemical kinetics 4) Heat transfer 5) Materials science modelling 6) Stability theory and vibrations of machinery 7) Semiconductor device modelling 8) Electromagnetics and inverse problems 9) Optimal design

For each topic covered, the modelling process of a specific example is followed from problem formulation to solution. Discrete, continuous, deterministic and stochastic models are used, as is a variety of solution techniques, both analytical and numerical. Both theoretical and practical issues will be considered.

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