Discrete Mathematics 2
Code  Completion  Credits  Range  Language 

801DIM2  Z  2  2+0  Czech 
 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 nonlinear 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: AddisonWesley, 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 : SpringerVerlag,
2000. 355 s. Canadian Mathematical Society Books in Math.
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Applications of Informatics in Natural Sciences (compulsory course in the program)