Discrete Mathematics 2

Garant předmětu:

Zuzana Masáková

Lecturer:

Zuzana Masáková, Edita Pelantová

Tutor:

Lubomíra Dvořáková, Zuzana Masáková, Edita Pelantová

Supervisor:

Department of Mathematics

Synopsis:

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

Requirements:

Knowledge of highschool mathematics is assumed. Also knowledge of FNSPE courses 01MA1, 01LA1 is needed. Knowledge of DIM1 is recommended.

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 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Aplikovaná algebra a analýza (compulsory course in the program)
• Aplikace informatiky v přírodních vědách (compulsory course in the program)
• Aplikované matematicko-stochastické metody (elective course)
• Aplikovaná informatika (compulsory course in the program)
• Fyzikální inženýrství - Fyzika plazmatu a termojaderné fúze (elective course)
• Matematické inženýrství - Matematická fyzika (elective course)
• Matematické inženýrství - Matematická informatika (PS)
• Matematické inženýrství - Matematické modelování (elective course)
• Mathematical Engineering - Mathematical Physics (elective course)
• Physical Engineering - Plasma Physics and Thermonuclear Fusion (elective course)