Discrete Mathematics 1

Course guarantor:

Zuzana Masáková

Lecturer:

Kateřina Horaisová

Tutor:

Kateřina Horaisová

Supervisor:

Department of Software Engineering

Synopsis:

The seminar is devoted to elementary number theory and applications. It includes individual problem solving.

Requirements:

Knowledge of grammer school mathematics is assumed.

Syllabus of lectures:

1. Divisibility, congruences, Femat's little theorem.

2. Euler's function, Moebius function, inclusion exclusion principle.

3. Perfect numbers, Mersenne's primes, Fermat's numbers.

4. Primality testing. Public key cryptographic systems: RSA, knapsack problem.

Syllabus of tutorials:

Study Objective:

Acquired knowledge:

Students learn to solve some types of elementary number theoretical problems.

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

[2] 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.

Recommended literature:

[3] P. Erdös, J. Surányi, Topics in the Theory of Numbers, Springer-Verlag, 2001.

[4] M. Křížek, F. Luca, L. Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, CMS Books in Mathematics, vol. 9, Springer-Verlag, New York, 2001.

Note:

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed
Thu	roomDC:P4 Horaisová K. 08:00–09:50 (lecture parallel1) Decin
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

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