Description:

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

Contents:

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.

Recommended literature:

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.

Keywords:

recurrence relations, difference equations, Josephus problem, Fibonacci numbers

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar