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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Discrete Mathematics 2

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Code Completion Credits Range Language
01DIM2 Z 2 2+0 Czech
Lecturer:
Zuzana Masáková (guarantor)
Tutor:
Zuzana Masáková (guarantor), Kateřina Medková
Supervisor:
Department of Mathematics
Synopsis:

The seminar is devoted to recurrence relations. It includes individual problem solving.

Requirements:

Knowledge of grammer school mathematics is assumed. Also knowledge of FNSPE courses 01MA1, 01LA1 is needed.

Syllabus of lectures:

1. Recurrence relations: Linear difference equations, some types of non-linear recurrences, inverting formula.

2. Josephus problem.

3. Fibonacci numbers and Wythoff's game.

4. Integer coefficient polynomials and their rational roots, Viete relations.

5. Finite groups.

Syllabus of tutorials:
Study Objective:

Acquired knowledge: Students learn to solve linear recurrence relations with constant coefficients and some other types of difference equations.

Acquired skills: The emphasis is put on correct formulation of mathematical ideas and logic process.

Study materials:

Ronald L. Graham, Donald E. Knuth, Oren Patashnik, Concrete Mathematics: A Foundation for Computer Science, Reading, Massachusetts: Addison-Wesley, 1994

P. Cull, M. Flahive, R. Robson, Difference Equations, Springer, 2005.

J. Herman, R. Kučera, J. Šimša,

Equations and Inequalities: Elementary Problems and Theorems in Algebra and Number Theory. 1. vyd. New York : Springer-Verlag,

2000. 355 s. Canadian Mathematical Society Books in Math.

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 2019-09-21
For updated information see http://bilakniha.cvut.cz/en/predmet11339105.html