Conducted in terms:
Summer Semester 2006/07
Summer Semester 2007/08
Summer Semester 2008/09
Winter Semester 2009/10
Winter Semester 2010/11
Winter Semester 2011/12
Winter Semester 2012/13
Summer Semester 2013/14
Summer Semester 2014/15
Summer Semester 2015/16

ECTS credits: 4

Language: Polish

Organized by: Faculty of Computer Science

Discrete Mathematics I12016

Course content:

1. Mathematical induction. Modular arithmetics, prime numbers, division algorithm, Euler's theorem. congruentions.

2. Combinatorics; cardinality of sets, Newton's coefficients, binomial formula, computing technics, Pigeonhole principle, Stirling's numbers. Elements of asymptotics.

3. Graph theory. Computer representation of a graph. Trees and their characterizations. Cayley theorem. Euler graphs. Hamiltonian graphs. Planar graphs. Hall's theorem. Graph coloring.

4. Recurrentions. Linear recurrentions of the first and second order.

Learning outcomes: Student knows basic methods of the discrete mathematics applied in computer science

(in Polish) Rodzaj przedmiotu

(in Polish) Obowiązkowy

Course coordinators

Term 2009Z:

Joanna Karbowska-Chilińska

Term 2013L:

Term 2012Z:

Term 2008L:

Term 2010Z:

Term 2011Z:

Term 2015L:

Term 2014L:

Bibliography

a) basic references:
1. Victor Bryant, Aspekty kombinatoryki, Wydawnictwo Naukowo-Techniczne, Warszawa 1997.
2. Ronald L. Graham, Donald E. Knuth, Oren Patashnik, Matematyka konkretna, Wydawnictwo Naukowe PWN, Warszawa 1998.
3. Witold Lipski, Kombinatoryka dla programistów, Wydawnictwo Naukowo-Techniczne, Warszawa 1982.
4. Kenneth A. Ross, Charles R.B. Wright, Matematyka dyskretna, Wydawnictwo Naukowe PWN, Warszawa 2001.
5. Robin J. Wilson, Wstęp do teorii grafów, Wydawnictwo Naukowe PWN, Warszawa 1998.

b) supplementary references:
1. Martin Aigner, Gunter M. Ziegler, Dowody z Księgi, Wydawnictwo Naukowe PWN, Warszawa 2004.
2. Tadeusz Gerstenkorn, Tadeusz Śródka, Kombinatoryka i rachunek prawdopodobieństwa, PWN, Warszawa 1974.
3. Ralph P. Grimaldi, Discrete and combinatorial mathematics - An applied introduction, Addison-Wesley Publishing Company.
4. Leon Jeśmianowicz, Jerzy Łoś, Zbiór zadań z algebry, Państwowe Wydawnictwo Naukowe, Warszawa 1976.