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Discrete mathematics

Code: 36904
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Marcela Hanzer - Lectures
doc. dr. sc. Tomislav Pejković - Lectures
Lecturers: Karmen Grizelj, mag. math. - Exercises
doc. dr. sc. Tomislav Pejković - Exercises
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: It serves as an introduction to basic combinatorics, discrete mathematics and graph teory.

COURSE DESCRIPTION AND SYLLABUS:
1. Combinatorial enumeration. Enumeration of sets, functions, injections, bijections. Binomial formula and binomial coefficients.
2. Some recursive problems. Fibonacci numbers, Catalan numbers, Linear reccurences.
3. Inclusion-exclusion principle. Principle and applications.
4. Generating functions. Basic ideas, examples and applications.
5. Introduction to graphs. Paths, cycles, trees, walk on graphs. Graph colorings. Planar graphs. Matchings in graphs.
Literature:
  1. I. Nakić: Predavanja iz Diskretne matematike
  2. P. J. Cameron: Combinatorics: Topics, Techniques, Algorithms
  3. I. Anderson: A first Course in Discrete Mathematics
  4. L.Lovasz, J.Pelikan, K.L.Vesztergombi: Discrete Mathematics
  5. B. Bašić, M. Marohnić i dr.: Vježbe iz Diskretne matematike. Dvostruko prebrojavanje
  6. C.Chuan-Chong, K. Khee-Meng: Principles and Techniques in Combinatorics
  7. M.Cvitković: Kombinatorika
Prerequisit for:
Enrollment :
Passed : Elementary mathematics 1
Passed : Mathematical analysis 1
3. semester
Mandatory course - Regular study - Mathematics
Consultations schedule:

Content

Link to the course web page: https://web.math.pmf.unizg.hr/nastava/komb/