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COURSE CATALOGUE FOR INCOMING ERASMUS STUDENTS

(IN ENGLISH)

LIST OF COURSES Semester: winter

COURSE COURSE COORDINATOR L E S ECTS

Vector Spaces I Neven Grbac 30 30 0 5

Measure and Integral Neven Grbac 30 30 0 7

Permutation groups Vedrana Mikulić Crnković 30 0 15 6

Statistics Nermina Mujaković 30 30 0 6

Introduction to design theory Sanja Rukavina 30 15 15 6

LIST OF COURSES Semester: summer

COURSE COURSE COORDINATOR L E S ECTS

Vector Spaces II Neven Grbac 30 30 0 6

Graph theory Dean Crnković 30 15 15 6Design and analysis of experiment

Dean CrnkovićSanja Rukavina 30 15 15 6

Probability Theory Nermina Mujaković 30 30 0 6

Harmonic analysis Neven Grbac 30 0 15 6

Coding Theory and Criptography Vedrana Mikulić Crnković 30 0 15 6

Course description

General informationLecturer Neven Grbac

Course title Vector spaces ICredit values and modes of instruction

ECTS credits / student workload 5Hours (L+E+S) 30 + 30 + 0

1. COURSE DESCRIPTION1.1. Course objectives

Main course objective is to get students acquainted with basic concepts of vector space theory. For that purpose it is necessary within the course to:

- define vector space and describe characteristic examples of vector spaces- define linear operators and analyse their properties- analyse matrix representation of a linear operator- define and analyse invariant subspaces and operator eigenvalues- describe reduction of operator on finite dimensional vector spaces- define unitary spaces and analyse Gram-Schmidt method of orthogonalization

1.2. Course prerequisite

None.

1.3. Expected outcomes for the course

After completing this course students should be able to:- know basic examples of vector spaces and linear operators

argumentedly solve problems related to the calculation of the rank - minimal polynomial and operator eigenvalues - argumentedly apply procedure of reduction of an operator on finite dimensional vector spaces in concrete

problems - know bacis examples of unitary spaces - mathematically prove foundation of procedures and formulas which they use within the course

1.4. Course contentThe notion of a vector space. Linear dependence. Subspace. Direct sum of subspaces. Quotient space. Basis of a vector space. Linear operators. The space (X,Y). Matrix of an operator in the given basis. Dependence of the matrix of an operator on the given basis. Limit in the space (X,Y). The notion of an algebra. Minimal polynomial. Invertible operator. Resolvent. Adjoint space and adjoint operator. Rank of an operator. Determinant and trace of an operator. Invariant subspaces and eigenvalues. Nilpotent operator. Reduction of operators on finite dimensional vector spaces. Jordan matrix of an operator. Operator functions. Unitary spaces. Gram-Schmidt method of ortogonalization.

1.5. Modes of instruction

X lectures X seminars and workshops X exercises

e-learning field work practice practicum

X independent work multimedia and the internet laboratory project strategies tutorials

X consultations other ___________________

1.6. Comments

1.7. Student requirementsStudents' work will be evaluated and assessed during the semester and in the final exam. Total number of points student can achieve during the semester is 70 (to assess the activities listed in the table), while in the final exam student can achieve 30 points.The detailed work out of monitoring and evaluation of students' work will appear in the executive program.

1.8. Evaluation and assessment1

Class attendance & class participation 1.1 Seminar paper Experiment Written exam 2 Oral exam 1.3 Essay Research work

1 IMPORTANT: Fill in the appropriate number of points for each of the chosen categories so that the sum of the allocated points corresponds to the course credit value. Add new categories, if necessary.

Project Continuous assessment 0.6 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have 5 ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.

1.9. Assessment and evaluation of students' work during the semester and in the final examStudents' work will be evaluated and assessed during the semester and in the final exam. Total number of points student can achieve during the semester is 70 (to assess the activities listed in the table), while in the final exam student can achieve 30 points.The detailed work out of monitoring and evaluation of students' work will appear in the executive program.

1.10. Required literature (when proposing the program )

1. S. Kurepa, Konačno dimenzionalni vektorski prostoi i primjene, Sveučilišna naklada Liber, Zagreb, 1976.2. H. Kraljević, Vektorski prostori, Odjel za matematiku, Sveučilište u Osijeku

1.11. Recommended literature (when proposing the program)

1. P.R.Halmos, Finite Dimensional Vector Spaces, Van Nostrand, New York, 1958.2. K.Horvatić, Linearna algebra, Golden marketing – Tehnička knjiga, Zagreb, 2004.3. S.Lang, Linear algebra, Springer Verlag, Berlin, 1987.

1.12. Number of copies of required literature in relation to the number of students currently attending classes of the course

Title Number of copies Number of students

1.13. Quality assurance which ensure acquisition of knoxledge, skills and competenciesIn the last week of the semester students will evaluate the quality of the lectures. At the end of each semester (March 1 and September 30 of the current academic year) results of the exams will be analyzed.


Course title Measure and IntegralCredit values and modes of instruction



Main course objective is to get students acquainted with basic concepts of measure and integration theory. For that purpose it is necessary within the course to:

- define measure and analyse its properties- describe the basic examples of measure spaces- define Lebesgue measure and analyse its properties- define the concept of a measurable function- definine the integral of a function on the measure space and analyse its properties- prove Lebesgue's monotone and dominated convergence theorem and Fatou's lemma- describe the construction of a product measure and prove the Fubini theorem- describe the concepts of absolute continuity and singularity of measure- prove Radon-Nikodym theorem- analyse the connection between Riemann and Lebesgue integral


None.

1.3. Expected outcomes for the course After completion of the course students should:

- be able to argumentedly use properties of measure and integral - know some examples of measures with special accent on Lebesgue measure - be able to argumentedly use the convergence theorems in problem solving - be able to argumentedly use the Fubini theorem in problem solving - know the concepts of absolute continuity and singularity of measure and relations

- know the connections and differences between Riemann and Lebesgue integral- be able to mathematicly prove the foundation of procedures and formulas which they use within the course

1.4. Course contentRing, algebra, σ-algebra of sets, Borel sets. Measure, outer measure. Lebesgue measure. Monotone and dominated convergence theorems, Fatou's lema. Product of measures. Fubini theorem. Absolute continuity and singularity of measures. Radon-Nikodym theorem. Connection between Riemann and Lebesgue integral.


X lectures seminars and workshops

X exercises e-learning field work practice practicum

X independent work X multimedia and the internet

laboratory project strategies tutorials


1.6. Comments



Class attendance & class participation 1.8 Seminar paper Experiment Written exam 2.5 Oral exam 1.8 Essay Research work Project Continuous assessment 0.9 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have 7 ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.



1. Sibe Mardešić: Matematička analiza II, Školska knjiga , Zagreb, 19772. Donald L.Cohn: Measure theory, Birkhäuser Boston, 1994

1.11. Recommended literature (when proposing the program)1. P.Halmos: Measure theory, Springer-Verlag, New York, 19742. N.Antonić, M.Vrdoljak: Mjera i integral, PMF-Matematički odjel, Zagreb, 20011.12. Number of copies of required literature in relation to the number of students currently attending classes

of the courseTitle Number of copies Number of students



Course title Vector spaces IICredit values and modes of instruction

ECTS credits / student workload 6 Hours (L+E+S) 30 + 30 + 0



- acquisition of basic notions and properties of topological vector spaces,- definition of normed space and examples,- definition and analysis of local convexity, metrizability and complete spaces,- acquisition of basic properties of linear functionals


Vector spaces I.

1.3. Expected outcomes for the course After completing this course students should be able to:

- describe various examples of topological vector spaces,- understand basic relationships between mathematical objects that will be elaborated in this course,- understand the relationship between topological and linear structure in topological vector spaces

1.4. Course contentTopological vector spaces. Normed vector space. Local convexity. Metrizability. Completeness. Linear functionals and the Hahn-Banach theorem. Weak topologies. Dual spaces.


lectures seminars and workshops exercises e-learning field work practise practicum

independent work multimedia and the internet laboratory project strategies tutorials consultations other ___________________

1.6. Comments



Class attendance & class participation 1.8 Seminar paper Experiment Written exam 2 Oral exam 1.4 Essay Research work

Project Continuous assessment 0.8 Presentation Practical work

Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have 6 ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.10. Required literature (when proposing the program )1. S. Kurepa: Funkcionalna analiza, Školska knjiga, Zagreb, 19842. W. Rudin: Functional analysis, McGraw-Hill,1972


1. K. Yosida: Functional analysis, Springer-Verlag, New York, 1985.




1.13. Quality assurance which ensure acquisition of knoxledge, skills and competencies In the last week of the semester students will evaluate the quality of the lectures. At the end of each semester (March 1 and September 30 of the current academic year) results of the exams will be analyzed.

General informationLecturer Nermina Mujaković

Course title Probability theoryCredit values and modes of instruction



Main course objective is to get students acquainted with basic concepts of probability theory. For that purpose it is necessary within the course to:

- define random variables and analyse their basic properties- define distribution functions and describe the classification of random variables- define mathematical expectation and prove limit theorems for mathematical expectation- define variance and moments of random variables- prove basic inequalities in probability- describe basic types of convergence of random variables and their relations- prove weak and strong laws od large numbers- describe convergence of series of random variables- define notion of characteristic function of random variable and analyse basic properties of characteristic

functions- prove inversion and continuity theorems for characteristic functions- describe weak convergence of sequences of distribution functions - prove central limit theorem


None.


- argumentedly use random variables and their properties in problem solving - know the classification of random variables - argumentedly apply limit theorems for mathematical expectation - argumentedly apply basic probability inequalities - know basic types of convergence of random variables and their relations- know weak and strong laws of large numbers - know convergence of series of random variables - argumentedly apply properties of characteristic functions - know inversion and continuity theorems for characteristic functions - know concept of weak convergence of sequences of distribution functions - argumentedly apply central limit theorem - mathematically prove foundation of procedures and formulas which they use within the course

1.4. Course content

Random variables. Distribution functions. Classification of random variables. Mathematical expectation. Limit theorems for the mathematical expectation. Variance and moments. Important inequalities in probability. Convergence of random variables. Independence of random variables. Laws of large numbers. Convergence of series of random variables. Characteristic functions. Inversion theorem. Weak convergence. Continuity theorem. Central limit theorems.


X lectures seminars and workshops X exercises X e-learning

field work



practice practicum


1.6. Comments

1.7. Student requirementsStudents must satisfy requirements for obtaining the signature (listed in the executive program) from the course Probability theory and pass the final exam.



1.9. Assessment and evaluation of students' work during the semester and in the final examStudents' work will be evaluated and assessed during the semester and in the final exam. Total number of points student can achieve during the semester is 70 (the activities listed in the table will be assessed), while in the final exam student can achieve 30 points.The detailed work out of monitoring and evaluation of students' work will appear in the executive program.

1.10. Required literature (when proposing the program )1. N.Sarapa, Teorija vjerojatnosti, Školska knjiga, Zagreb, 2002.

2. Ž.Pauše, Vjerojatnost – Informacija – Stohastički procesi, Školska knjiga, Zagreb, 2003.


1. W.Feller, An Introduction to Probability Theory and Aplication, J.Wiley, New York, 1966.2. J.Malešić, Zbirka zadataka iz teorije verovatnoće sa primenama, Građevinska knjiga, Beograd, 1989.3. N.Sarapa, Vjerojatnost i statistika, II dio, Školska knjiga, Zagreb, 1996.4. B.V.Gnedenko, Kurs teorije vjerojatnosti, Nauka, Moskva, 1969.5. R.Durrett, Probability: theory and examples, Duxbury Press, Belmont, 1996



1.13. Quality assurance wich ensure acquisition of knoxledge, skills and competenciesIn the last week of the semester students will evaluate the quality of the lectures. At the end of each semester (March 1 and September 30 of the current academic year) results of the exams will be analyzed.


Course title Harmonic analysisCredit values and modes of instruction

ECTS credits / student workload 6 Hours (L+E+S) 30 + 0 +15


Main course objective is to get students acquainted with basic ideas and concepts of harmonic analysis, elements of functional analysis and their application. For that purpose it is necessary within the course to:

- Define Hilbert spaces and analyse their structure and properties- Determine orthonormal systems in Hilbert space and analyse their completness- Calculate and analyse Fourier series, compare them with the initial functions


- Analyse the consequences of the Banach-Steinhaus theorem and the open mapping theorem related to Fourier series

- Calculate and analyse Fourier transforms- Analyse the inversion theorem and compare Fourier transform with the initial function- Analyse Plancherel theorem and its consequences- Compare Fourier transform with other integral transforms: for example Laplace, Mellin, discrete Fourier transform- Calculate and analyse those other integral transforms


None.

1.3. Expected outcomes for the course Students will adopt basic terms, ideas and concepts of harmonic analysis. After finishing this course students should be able to:

- Argumentedly determine the properties of Hilbert spaces, analyse linear independence, orthogonality, orthonormality, completness of the sets in them

- Argumentedly calculate Fourier series and analyse their connection with the initial functions - Argumentedly apply the above mentioned theorems about the Banach spaces and analyse their consequences

related to Fourier series - Argumentedly calculate Fourier transformtion - Analyse the inversion theorem and compare Fourier transform with the initial function- Analyse and argumentedly apply Plancherel theorem - Argumentedly calculate and apply other integral transforms

1.4. Course contentHilbert space. Orthonormal sets. Fourier series. Banach-Steinhaus theorem. The open mapping theorem. Fourier transform. The inversion theorem. Plancherel teorem and Parseval’s formula. Examples of other integral transformations and applications.


X lectures X seminars and workshops X exercises

e-learning field work practice practicum

X independent work multimedia and the internet laboratory

X project strategies X tutorials X consultations

other ___________________

1.6. Comments

1.7. Student requirements

Homeworks, tests, continuous written and oral assessment.


Class attendance & class participation 1 Seminar paper 1 Experiment Written exam 1.5 Oral exam Essay Research work Project Continuous assessment 2.5 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have 6 ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.



1. W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1987.2. Anton Deitmar: A First Course in Harmonic Analysis, 2nd edition, Springer, 2005


1. Allan Pinkus, Samy Zafrany, Fourier Series and Integral Transforms, Cambridge University Press, 1997





General informationLecturer Vedrana Mikulić Crnković

Course title Coding theory and cryptographyCredit values and modes of instruction



Main course objective is to get students acquainted with basic cryptography systems and basic methods in coding theory. For that purpose it is necessary within the course to:

- describe, compare and apply different cryptography systems,- analyse the basic principles of cryptanalysis,- analyse the basic principles of coding theory,- define, differentiate and apply coding methods,- analyse error detection methods in coding,- describe methods of correcting errors in coding.


None.


After completing this course students should be able to:- differentiate and analyse cryptography systems and argumentedly apply adequate procedure in problem solving, - analyse and differentiate type codes and argumentedly apply adequate procedure in problem solving ,- differentiate ways of detecting errors in data transfer with particular coding method and analyse the conditions

under which it is possible to correct this error, - mathematically prove foundation of procedures and statements which they use within the course.

1.4. Course contentIntroduction in cryptography. Classic cryptography. Data Encryption Standard. International Data Encrpytion Algorithm. Advanced Encryption Standard. Public-key cryptography. RSA and applications. Introduction in coding theory. Golay codes. Cyclic codes. BCH codes. Hadamard codes. Reed-Solomon codes and CD.


X lectures X seminars and workshops

exercises X e-learning

field work practice practicum


laboratory X project strategies X tutorials X consultations

other ___________________

1.6. Comments




Class attendance & class participation 1.5 Seminar paper 1.5 Experiment Written exam 0.5 Oral exam 1 Essay Research work Project Continuous assessment 1.5 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have 6 ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.



1. Dujella: Kriptografija (online: http://web.math.hr/~duje/kript/kriptografija.html )2. J.I. Hall, Notes on Coding Theory, 2010 (online: http://www.math.msu.edu/~jhall/classes/codenotes/coding-notes.html)

1.11. Recommended literature (when proposing the program)1. Assmus, J.D. Key, Designs and their codes, Cambridge University Press, London, 1992.2. Dujella, M. Maretić, Kriptografija, Element, Zagreb, 2007.3. N. Koblitz, A Course in Number Theory and Cryptography, Springer Verlag, New York, 1994.4. J.H. van Lint, Introduction to Coding Theory, Springer-Verlag, Berlin, 1982.5. F.J. MacWilliams, N.J.A. Sloane, The theory of error-correcting codes, North-Holland, 1977.6. B.Schneiner, Applied Cryptography, Wiley, NY 1995.7. J. Seberry, J. Pieprzyk, Cryptography: an introduction to computer security, Prentice-Hall, 1989.8. D.R.Stinson, Cryptography. Theory and Practice, CRC Press, Boca Raton, 1996.9. D. Welsh, Codes and cryptography, Oxford: Clarendon Press, 1988.1.12. Number of copies of required literature in relation to the number of students currently attending classes

of the courseTitle Number of copies Number of students


General informationLecturer Vedrana Mikulić Crnković

Course title Permutation groupsCredit values and modes of instruction



Main course objective is to get students acquainted with advanced theory of permutation groups. For that purpose it is necessary within the course to:

- define action of a group on a set, differentiate actions of a group on a set and analyse their properties,- define a permutation group, differentiate examples of permutation groups and analyse their properties,- define basic concepts of character theory and analyse the application of the theory on permutation groups,- define coherent configurations and differentiate examples of such configurations and analyse their properties,- declare and prove O'Nan-Scott theorem and analyse its consequences,- create brief introduction to the theory of finite simple groups


None.


- differentiate and analyse actions of a group on a set and argumentedly apply adequate procedure in problem solving

http://www.math.msu.edu/~jhall/classes/codenotes/coding-notes.html

http://web.math.hr/~duje/kript/kriptografija.html

- differentiate and analyse examples of permutation groups and argumentedly apply adequate procedure in problem solving

- define basic concepts of character theory and apply theory in solving problems related to permutation groups - differentiate and analyse examples of coherent configurations and argumentedly apply adequate procedure in

problem solving - argumentedly apply O'Nan-Scott theorem and its consequences - classify finite simple groups - mathematically prove foundation of procedures and statements which they use within the course

1.4. Course contentTransitive and k-transitive groups. Regular groups. Primitive groups. Character theory and applications. Coherent configurations and examples. O'Nan-Scott theorem and consequences. Simple groups.


X lectures X seminars and workshops

exercises X e-learning




other ___________________

1.6. Comments

1.7. Student requirementsStudents must satisfy requirements for obtaining the Signature (listed in the executive program) from the course Statistics and pass the final exam.


Class attendance & class participation 1.5 Seminar paper 1.5 Experiment Written exam 0.5 Oral exam 1 Essay Research work Project Continuous assessment 1.5 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have 6 ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.



1. P. J. Cameron, Permutation groups, Cambridge University Press, 1999.


1. J. D. Dixon, B. Mortimer, Permutation groups, Springer, New York, 1996.


Title Number of copies Number of studentsP. J. Cameron, Permutation groups, Cambridge University Press, 1999. 0


General informationLecturer Nermina Mujaković

Course title StatisticsECTS credits / student workload 6


Credit values and modes of instruction Hours (L+E+S) 30 + 30 + 0


Main course objective is to get students acquainted with basic ideas and concepts of mathematical statistics. For that purpose it is necessary within the course to:

- demonstrate basic ways of presentation of statistical data- describe the classification of statistical variables- define parametres of sequence of statistical data- define estimators and define their properties- describe methods of moments and maximum likelihood- define confidence intervals- describe and analyse method of least squares within the linear corelation- describe and analyse statistical hypothesis testing- describe methods of hypothesis testing


None.


- present statistical data in tabular and graphical form - know the classification of statistical variables - argumentedly use estimators and their properties within the specific statistical models - argumentedly apply method of least squares in estimating parameters - argumentedly apply methods of moments and maximum likelihood - argumentedly apply methods of statistical data analysis - argumentedly construct confidence intervals - perform procedure testing statistical hypothesis - know Neyman-Pearson lemma - mathematically prove foundation of procedures and formulas which they use within the course

1.4. Course contentStatistical data. Concept and classification of statistical variables. Grouped data. Parameters of sequence of statistical data. Statistical data of two-dimensional properties. Regression function. Covariance and correlation coefficient. Population and sample. Sampling method. Point estimation. Method of moments and maximum likelihood method. Interval estimation. Confidence intervals. Statistical hypothesis testing. Errors in testing. Neyman-Pearson lemma. Tests about parameters of a normal population. Regression analysis.


X lectures seminars and workshops X exercises X e-learning





1.6. Comments Some parts of course content will be performed on the computers.

1.7. Student requirementsStudents must satisfy requirements for obtaining the Signature (listed in the executive program) from the course Statistics and pass the final exam.



1.9. Assessment and evaluation of students' work during the semester and in the final exam


Students' work will be evaluated and assessed during the semester and in the final exam. Total number of points student can achieve during the semester is 70 (to assess the activities listed in the table), while in the final exam student can achieve 30 points.The detailed work out of monitoring and evaluation of students' work will appear in the executive program.

1.10. Required literature (when proposing the program )1. Ž.Pauše, Uvod u matematičku statistiku, Školska knjiga, Zagreb, 1993.

2. F.Daly, D.J.Hand, M.C.Jones, A.D.Lunn, K.J.McConway, Elements of Statistics, Addison Wesley, 1995.

1.11. Recommended literature (when proposing the program)1. N.Sarapa, Vjerojatnost i statsistika, II dio, Školska knjiga, Zagreb, 1996.2. R.C.Mittelhammer, Mathematical statistics for economics and business, Springer Verlag, New York, 1996.

3. J.E.Freund, Mathematical Statistics, Prentice Hall, New York, 1992. 4. D.Williams, Weighing the Odds, Cambridge University Press, 2001.

5. R.B.Ash, Lectures on Statistics, University of Illinois, 2007. (http://www.math.uiuc.edu/~r-ash/Stat.html)



1.13. Quality assurance wich ensure acquisition of knoxledge, skills and competenciesIn the last week of the semester students will evaluate the quality of the lectures. At the end of each semester (March 1 and September 30 of the current academic year) results of the exams will be analyzed.

General informationLecturer Sanja Rukavina

Course title Introduction to design theoryCredit values and modes of instruction



Main course objectives are:- acquaint students with basic definitions, concepts, procedures and theorems of the design theory- indicate the relation between different combinatorial structures, link designs with codes, graphs, differential sets,

latin square- acquaint with basic application combinatorial design in coding theory, at the input scheme, visual cryptography

and group testing.


None.


After completing this course students should be able to:- define basic concepts of design theory and argumentedly apply basic procedures in design theory - know and prove basic theorems of design - construct examples for block designes and related combinatorial structures - apply the design theory in the elementary problems of coding, input scheme, visual cryptography and group

testing

1.4. Course contentBasic definitions and properties of combinatorial designes; incidence matrix, isomorfism and automorfism, Fisher's inequality. Symmetric designs; differential sets, construction of differential sets, residual and derived designs, Hadamard matrix and designs, Bruck-Ryser-Chowla theorem. Resolvable designs; Affine plane, projective plane, Boas inequality, Affine designs. Steiner triple system; quasigroups, Boas construction, The Skolem construction, cyclic Steiner triple system. Orthogonal latin squares; mutually orthogonal latin squares, orthogonal array and transversal designs.

http://www.math.uiuc.edu/~r-%20%20ash/Stat.html

Applications of combinatoral designs; codes, threshold scheme, visual cryptography, group testing


X lectures seminars and workshops

X exercises X e-learning

field work practice

X practicum



other ___________________

1.6. Comments

1.7. Student requirementsRegular attendance, making homework and project assignment, and performance of all obligations in accordance with the executive program.


Class attendance & class participation 1.5 Seminar paper Experiment Written exam Oral exam 1.3 Essay Research work Project 1.5 Continuous assessment 1.7 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have 6 ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.


1.10. Required literature (when proposing the program )1. D.R. Stinson: Combinatorial Designs with Selected Applications, Lecture Notes

(www.cacr.math.uwaterloo.ca/~dstinson/papers/designnotes.ps)


1. Anderson, I. Honkala: A Short Course in Combinatorial Designs, Internet Edition, 1997. (www.utu.fi/~honkala/designs.ps)


Title Number of copies Number of studentsLiterature is available to students on-line (also in the e-course).



Sveučilište u Rijeci • University of RijekaTrg braće Mažuranića 10 • 51 000 Rijeka • Croatia

T: +385 (0)51 406 500 • F: +385 (0)51 406 588W: www.uniri.hr • E: [email protected]

General informationLecturer Dean Crnković

Course title Graph theoryCredit values and modes of instruction



Main course objective is to get students acquainted with basic ideas and concepts of graph theory and the application of graph theory. For that purpose it is necessary within the course to:

- define basic concepts of graph theory and describe their basic properties- define Euler's and Hamilton's graph, prove some of their properties and describe the applications- define the concept of graph connectivity, analyse the properties of connected graphs and application in

constructing reliable communication networks- define matching and perfect matching in graphs, elaborate statements and applications connected to those terms- define basic concepts of Ramsey theory for graphs- define basic concepts of theory of directed graphs, elaborate basic properties and some applications- analyse and compare certain algorithms


None.




After finishing this course students should be able to:- differentiate the before mentioned concepts and properties of graphs and argumentedly apply

appropriate properties and statements in solving the assignments - analyse problems of graph connectivity and related properties - analyse Euler's and Hamilton's graphs and argumentedly apply definitions and properties in solving assignments - solve problems which come down to matching in graphs - apply statements and algorithms elaborated within this course - mathematicly prove foundation of all procedures and formulas they use within this course

1.4. Course contentConcept and basic properties of graphs. Euler's tours and Hamilton's cycles. Chinese postman problem and Fleury's algorithm. Traveling salesman problem. Graph connectivity. Reliable communication networks. Matching in graphs. Perfect matchings. Employment problem and Hungarian matching algorithm. Optimal employment problem and Kuhn-Munkres algorithm. Independent sets, covers and cliques. Ramsey theory for graphs. Directed graphs. Application on ranking the tournament players. Application on one-way street trafic. Transport networks. Ford-Fulkerson algorithm for marking. Topological sorting.


X lectures X seminars and workshops X exercises X e-learning




other ___________________

1.6. Comments



Class attendance 0.2 Class participation 0.3 Seminar paper 0.7 Experiment Written exam 2.0 Oral exam 1.8 Essay Research work Project Continuous assessment 1.0 Presentation Practical work Portfolio Comment: ECTS distribution from above is made for studies and/or modules with courses which have 6 ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.



1. D.Veljan: Kombinatorika i diskretna matematika, Algoritam, Zagreb, 2001.2. D.Veljan: Kombinatorika s teorijom grafova, Školska knjiga, Zagreb, 1989.


1. N.Biggs: Discrete Mathematics, Clarendon Press, Oxford, 1989.2. R.Diestel: Graph Theory, Fourth edition, Springer-Verlag, New York, 2010.3. R.Balakrishnan, K.Ranganathan: A Textbook of Graph Theory, Springer-Verlag, Heidelberg, 2000.4. R.Balakrishnan: Schaum's outline of Graph Theory: Included Hundreds of Solved Problems, McGraw-Hill, New

York, 1997.






D.Veljan: Kombinatorika i diskretna matematika, Algoritam, Zagreb, 2001. 5 20-25

D.Veljan: Kombinatorika s teorijom grafova, Školska knjiga, Zagreb, 1989. 5 20-25


Basic descriptionCourse coordinator Dean Crnković, Sanja Rukavina

Course title Design and analysis of experiment

ECTS credits and teaching

ECTS student ‘s workload coefficient 6Number of hours (L+E+S) 30 + 15 + 15

1.COURSE DESCRIPTION1.1. Course objectives

The main objective of this course is get students acquainted with procedures of designing and analysing of experiments and enable them to carry out these procedures in specific situations.


Attended courses Statistics and Introduction to design theory.


After finishing this course students should be able to:- define basic concepts in the field of design and analysis of experiments and argumentedly implement appropriate

procedures in this area - self-rule on choosing the correct procedure to solve concrete problems in the areas of design and analysis of

experiments - use software package Statistica for solving problems in this area.

1.4. Course content

Basic principles and techniques, replication, blocking, and randomization. Experimental design; checklist, some standard experimental designs. Designs with one source of variation, randomization, the model of completely randomized design. Single factor analysis of variance. Sample size. Checking the model assumptions; strategies for checking model assumptions. Experiments with two or more crossed factors; sense of interaction, models with two crossed factors, checking the model assumption. Complete block designs, analysis of randomized complete block design, analysis of general complete block design, checking the model assumption. Random effects and variance components.


X lectures X seminars and workshops X exercises X e-learning

field work practice

X practicum



other ___________________

1.6. Comments

1.7. Student requirements

Regular class attendance, doing homework and project assignment and performance of all obligations in accordance with the detailed elaboration in the executive program of the course.





Class attendance & class participation Seminar paper 1 Experiment

Written exam

1 Oral exam 1 Essay Written exam

Project 1.5 Continuous assessment 1.5 Presentation ProjectPortfolio

Comment: ECTS distribution from above is made for studies and/or modules with courses which have 6 ECTS. For studies and/or modules with different number of total ECTS the distribution should be used for calculating percentages.

1.9. Assessment and evaluation of students' work during the semester and in the final exam

Students' work will be evaluated and assessed during the semester and in the final exam. Total number of points student can achieve during the semester is 70 (to assess the activities listed in the table), while in the final exam student can achieve 30 points.The detailed work out of monitoring and evaluation of students' work will appear in the executive program.

1.10. Required literature (when proposing the program )1. A. Dean, D. Voss: Design and Analysis of Experiments, Springer, 1999.2. D.C. Montgomery, Design and Analysis of Experiments, 5th Edn. J. Wiley., 2004.


1. Tanenbaum A., M. V. Steen , Distributed Systems: Principles and Paradigms, Prentice Hall, 2002.2. Silberschatz A., Galvin P. B., Operating system concepts, Addison Wesley, 1989.




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