MB154 Discrete mathematics

Faculty of Informatics
Autumn 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
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
The course is also listed under the following terms Autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (Autumn 2019, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2019/MB154