Discrete Mathematics 2

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Software Engineering

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.

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:

Compulsory literature:

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

Recommended literature:

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

[3] 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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: