# FI:MB104 Discrete mathematics - Course Information

## MB104 Discrete mathematics

**Faculty of Informatics**

Spring 2020

**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)

doc. Lukáš Vokřínek, PhD. (lecturer)

Mgr. Martin Dzúrik (seminar tutor)

Mgr. Jonatan Kolegar (seminar tutor)

Mgr. Radka Penčevová (seminar tutor)

Mgr. Tomáš Svoboda (seminar tutor)

Mgr. Mária Šimková (seminar tutor)

Mgr. Andrej Tokarčík (seminar tutor)

Mgr. Dominik Trnka (seminar tutor)

Mgr. Jana Volaříková, Ph.D. (seminar tutor)

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

doc. RNDr. Martin Čadek, CSc. (assistant)

Mgr. Martin Panák, Ph.D. (assistant) **Guaranteed by**- prof. RNDr. Jan Slovák, DrSc.

Faculty of Informatics

Supplier department: Faculty of Science **Timetable**- Mon 17. 2. to Fri 15. 5. Wed 8:00–9:50 D1
- Timetable of Seminar Groups:

*L. Vokřínek*

MB104/02: Mon 17. 2. to Fri 15. 5. Thu 8:00–9:50 A320,*J. Kolegar*

MB104/03: Mon 17. 2. to Fri 15. 5. Thu 10:00–11:50 A320,*J. Kolegar*

MB104/04: Mon 17. 2. to Fri 15. 5. Tue 12:00–13:50 B204,*T. Svoboda*

MB104/05: Mon 17. 2. to Fri 15. 5. Tue 14:00–15:50 B204,*T. Svoboda*

MB104/06: Mon 17. 2. to Fri 15. 5. Tue 18:00–19:50 B204,*M. Dzúrik*

MB104/07: Mon 17. 2. to Fri 15. 5. Wed 16:00–17:50 B204,*M. Dzúrik*

MB104/08: Mon 17. 2. to Fri 15. 5. Wed 18:00–19:50 B204,*M. Dzúrik*

MB104/09: Mon 17. 2. to Fri 15. 5. Thu 12:00–13:50 A320,*D. Trnka*

MB104/10: Mon 17. 2. to Fri 15. 5. Thu 16:00–17:50 A320,*D. Trnka*

MB104/11: Mon 17. 2. to Fri 15. 5. Thu 18:00–19:50 A320,*D. Trnka* **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 / plans the course is directly associated with**- there are 53 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)*. 1st ed. 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**- Study Materials

The course is taught annually. **Listed among pre-requisites of other courses**

- Enrolment Statistics (recent)

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