FI:MB154 Discrete mathematics - Course Information
MB154 Discrete mathematics
Faculty of InformaticsAutumn 2019
The course is not taught in Autumn 2019
- Extent and Intensity
- 2/2/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jan Slovák, DrSc. (lecturer)
Mgr. Martin Panák, Ph.D. (seminar tutor)
Mgr. Michal Bulant, Ph.D. (assistant) - Guaranteed by
- prof. RNDr. Jan Slovák, DrSc.
Department of Computer Science – Faculty of Informatics
Supplier department: Faculty of Science - Prerequisites
- ! MB104 Discrete mathematics && ! MB204 Discrete mathematics B && ( MB101 Mathematics I || MB201 Linear models B || MB151 Linear models || MB102 Calculus || MB202 Calculus B || MB152 Calculus )
High school mathematics. Elementary knowledge of algebraic and combinatorial tasks. - 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
- Tho goal of this course is to introduce the basics of theory of numbers.
- Learning outcomes
- 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. Available from: https://dx.doi.org/10.5817/CZ.MUNI.O210-6308-2013. Základní učebnice matematiky pro vysokoškolské studium info
- 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
- MB141 Linear algebra and discrete mathematics
!NOW(MB151) && ( !MB151 || !MB154 )
- MB141 Linear algebra and discrete mathematics
- Enrolment Statistics (Autumn 2019, recent)
- Permalink: https://is.muni.cz/course/fi/autumn2019/MB154