Subjects

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Combinatorics - NUMP008

Title:	Kombinatorika
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, MC [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Antonín Slavík, Ph.D.
Class:	M Bc. DGZV M Bc. DGZV > Povinné M Bc. MZV M Bc. MZV > Povinné
Classification:	Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Incompatibility :	NMUM208
Interchangeability :	NMUM208
Is incompatible with:	NMUM208, NMUM814
Is interchangeable with:	NMUM208, NMUE011, NMUM814

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: SLAVIK (22.06.2007)

The course gives a survey on methods and results of classical combinatorics (basic and advanced combinatorial principles), helps to obtain an overview of high school mathematics.

Aim of the course -

Last update: T_KDM (19.05.2008)

This course helps to obtain theoretical background for teaching mathematics at high school.

Literature -

Last update: T_KDM (31.08.2012)

R. B. J. T. Allenby, A. Slomson: How To Count. An Introduction to Combinatorics, CRC Press, 2011.

J. M. Harris, J. L. Hirst, M. J. Mossinghoff: Combinatorics and Graph Theory, Springer, 2008.

E. Calda: Kombinatorika pro učitelské studium, Matfyzpress, 1996.

J. Matoušek, J. Nešetřil: Invitation to Discrete Mathematics, Oxford University Press, 2008.

N. Ya. Vilenkin: Combinatorics, Academic Press, 1971

R. L. Graham, D. E. Knuth, O. Patashnik: Concrete Mathematics, Addison-Wesley, 1994.

Teaching methods -

Last update: T_KDM (20.05.2008)

Lectures.

Syllabus -

Last update: T_KDM (17.05.2011)

High school combinatorics.

Inclusion - exclusion principle, derangements.

Pigeonhole principle.

Reflection method and Catalan numbers.

Distribution of distinguished and non-distinguished objects.

Rook polynomials.

Recurrent problems and their solution, Fibonacci numbers and their properties.

Generating functions and their use in solving recurrences.

Combinatorial applications of polynomials and infinite series.

Combinatorial identities.