Discrete mathematics 1

Lecturer:

Zuzana Masáková (gar.), Tomáš Hejda, Edita Pelantová, Severin Pošta

Tutor:

Zuzana Masáková (gar.), Tomáš Hejda, Edita Pelantová, Severin Pošta

Supervisor:

Department of Mathematics

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:

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 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: