1. komponenta

Lecture type	Total
Lectures	45
Exercises	30

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: To introduce students to the basic concepts of combinatorial and discrete mathematics and graph theory.

COURSE DESCRIPTION AND SYLLABUS:
1. Introduction. Motivating examples.
2. Counting and enumeration. Basic principles. Enumeration of subsets. The binomial theorem and applications. Permutations. Multisets and multinomial coefficients. Set partitions. Generation of combinatorial objects. Examples of calculating probabilities of events by counting.
3. Recurrences, generating functions and the inclusion-exclusion formula. Introductory remarks. Fibonacci numbers. Linear recurrences. Generating functions. Complexity of sorting algorithms. The inclusion-exclusion formula.
4. Graph theory. Introduction and basic definitions. Trees and forests. Planarity. Eulerian and Hamiltonian graphs. Graph colouring. Applications of linear algebra in graph theory.

1. Predavanja iz Diskretne matematike, I. Nakić.
2. Vježbe iz Diskretne matematike, M. Bašić, M. Marohnić i dr..
3. Combinatorics: Topics, Techniques, Algorithms, P. J. Cameron, Cambridge University Press, 1994.
4. A first Course in Discrete Mathematics, I. Anderson, Springer Verlag, 2001.
5. Discrete Mathematics, L.Lovasz, J.Pelikan, K.L.Vesztergombi, Springer Verlag, 2003.
6. Principles and Techniques in Combinatorics, C.Chuan-Chong, K. Khee-Meng, World Scientific Publishing Company, Singapore, 1992.
7. Kombinatorika, M.Cvitković, Element, Zagreb, 1994.
8. Probability, skripta, R. Weber.

Enrollment :
Attended : Elementary mathematics
Attended : Mathematical analysis 1

Examination :
Passed : Elementary mathematics
Passed : Mathematical analysis 1

Mandatory course - Regular study - Mathematics