Discrete Mathematics 1
Code  Completion  Credits  Range  Language 

818DIM1  Z  2  2+0  Czech 
 Lecturer:
 Kateřina Horaisová (guarantor)
 Tutor:
 Kateřina Horaisová (guarantor)
 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: AddisonWesley, 1994
[2] 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.
Recommended literature:
[3] P. Erdös, J. Surányi, Topics in the Theory of Numbers, SpringerVerlag, 2001.
[4] M. Křížek, F. Luca, L. Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, CMS Books in Mathematics, vol. 9, SpringerVerlag, New York, 2001.
 Note:
 Timetable for winter semester 2020/2021:
 Timetable is not available yet
 Timetable for summer semester 2020/2021:
 Timetable is not available yet
 The course is a part of the following study plans: