česky | **in English**

Spring 2019

**Extent and Intensity**- 2/2/0. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
**Teacher(s)**- prof. RNDr. Jan Slovák, DrSc. (lecturer)

Mgr. Jana Bartoňová (seminar tutor)

Mgr. Jonatan Kolegar (seminar tutor)

Mgr. Martin Panák, Ph.D. (seminar tutor)

Mgr. Radka Penčevová (seminar tutor)

Mgr. Mária Šimková (seminar tutor)

Mgr. Michal Bulant, Ph.D. (assistant)

doc. Lukáš Vokřínek, PhD. (assistant) **Supervisor**- prof. RNDr. Jan Slovák, DrSc.

Faculty of Informatics

Supplier department: Faculty of Science **Prerequisites**- !
**MB204**Discrete mathematics B && ! NOW (**MB204**Discrete mathematics B )

High school mathematics. Elementary knowledge of algebraic and combinatorial tasks (in the extent of MB101 or MB102). **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**Fields of study the course is directly associated with**- there are 16 fields of study the course is directly associated with, display
**Course objectives**- At the end of this course, students should be able to:
understand and use methods of number theory to solve simple tasks;
understand approximately how results of number theory are applied in cryptography:
understand basic computational context;

model and solve simple combinatorial problems. **Syllabus**- Number theory:
- divisiblity (gcd, extended Euclid algorithm, Bezout); numerics of big numbers (gcd, modular exponential); prime numbers (properties, basic theorems of arithmetics, factorization, prime number testing (Rabin-Miller, Mersenneho prime numbers); congruences (basic properties, small Fermat theorem; Euler theorem; linear congruences; binomial congruences a primitiv roots; discrete logarithm;
- Number theory applications:
- short introduction to asymetric cryptography (RSA, DH, ElGamal, DSA, ECC); basic coding theory (linear and polynomial codes);
- Combinatorics:
- reminder of basics of combinatorics; generalized binomial theorem; combinatorial identities; Catalan numbers; formal power series; (ordinary) generating functions; exponential generating functions; probabilistic generating functions; solving combinatorial problems with the help of generating functions; solving basic reccurences (Fibonacci).

**Literature**- SLOVÁK, Jan, Martin PANÁK and Michal BULANT.
*Matematika drsně a svižně (Brisk Guide to Mathematics)*. 1. vyd. Brno: Masarykova univerzita, 2013. 773 pp. ISBN 978-80-210-6307-5. doi:10.5817/CZ.MUNI.O210-6308-2013.*Základní učebnice matematiky pro vysokoškolské studium*info

- SLOVÁK, Jan, Martin PANÁK and Michal BULANT.
**Bookmarks**- https://is.muni.cz/ln/tag/FI:MB104!
**Teaching methods**- There are standard two-hour lectures and standard tutorial.
**Assessment methods**- During the semester, two obligatory mid-term exams are evaluated (each for max 10 points). In the seminar groups there are tests during the semester being written. The seminars are evaluated in total by max 5 points. The final practical written test for max 20 points. For successful examination (the grade at least E) the student needs to obtain 20 points or more.
**Language of instruction**- Czech
**Further Comments**- The course is taught annually.

The course is taught: every week. **Listed among pre-requisites of other courses****MB204**Discrete mathematics B

!MB104 && !NOW(MB104)

- Enrolment Statistics (Spring 2019, recent)
- Permalink: https://is.muni.cz/course/fi/spring2019/MB104

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