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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Discrete Mathematics 3

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Code Completion Credits Range Language
01DIM3 Z 2 2+0 Czech
Lecturer:
Tutor:
Lubomíra Dvořáková (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

The subject is devoted to elementary proofs of non-trivial combinatoriwal identities and to generating functions and their applications. In the seminar students present a problem with solution chosen from the given literature.

Requirements:

Knowledge of FNSPE courses 01MA1, 01MAA2, 01LA1, 01LAA2 is required.

Syllabus of lectures:

1. Methods of combinatorial proof.

2. Stirling, Bernoulli, Catalan and Bell numbers.

3. Ordinary, exponential and Dirichlet generating functions. 4. Evaluation of sums, solution of linear and non-linear difference equations.

5. Combinatorial interpretation of product and composition of generating functions.

6. Applications in number theory and graph theory.

Syllabus of tutorials:
Study Objective:

Students learn methods of combinatorial proof, use of generating functions for solution of difference equations and for proving combinatorial identities. Students also learn comprehension of English written mathematical text and learn to present it to others.

Study materials:

M. Aigner, G. M. Ziegler, Proofs from the Book, Springer-Verlag 2004

A. T. Benjamin, J. J. Quinn, Proofs that Really Count, The Art of Combinatorial Proof, The Mathematical Association of America, 2003.

A. M. Yaglom, I. M. Yaglom, Challenging Mathematical Problems with Elementary Solutions, Dover Publications, 1987.

H. Dörrie, 100 Great Problems of Elementary Mathematics, Dover Publications, 1965.

Kombinatorické počítání 1999 , KAM-DIMATIA Series preprint no. 451 (1999), 59 p

Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-12-11
For updated information see http://bilakniha.cvut.cz/en/predmet1594006.html