Discrete Mathematics 1

Course guarantor:

Zuzana Masáková

Lecturer:

Lubomíra Dvořáková, Zuzana Masáková, Edita Pelantová

Tutor:

Lubomíra Dvořáková, Zuzana Masáková, Edita Pelantová

Supervisor:

Department of Mathematics

Synopsis:

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

Requirements:

Knowledge of highschool mathematics is assumed.

Syllabus of lectures:

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

2. Linear diofantic equations, linear congruences, Chinese remainder theorem.

3. Euler's function, Euler´s theorem, Moebius function, inclusion exclusion principle.

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

5. 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:

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

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.

P. Erdös, J. Surányi, Topics in the Theory of Numbers,

Springer-Verlag, 2001.

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	roomTR:101 Masáková Z. 12:00–13:50 (lecture parallel1) Trojanova 13
Tue
Wed	roomTR:101 Dvořáková L. 12:00–13:50 (lecture parallel3) Trojanova 13
Thu
Fri	roomTR:301 Pelantová E. 08:00–09:50 (lecture parallel2) Trojanova 13

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)