MB154 Discrete mathematics

Faculty of Informatics
Autumn 2020
Extent and Intensity
2/2/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Taught online.
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (lecturer)
Mgr. Martin Dzúrik (seminar tutor)
Mgr. Pavel Francírek, Ph.D. (seminar tutor)
Mgr. Jan Jurka (seminar tutor)
Mgr. Martin Panák, Ph.D. (seminar tutor)
Mgr. Miloslav Štěpán (seminar tutor)
Mgr. Dominik Trnka (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
Timetable
Mon 14:00–15:50 D3
  • Timetable of Seminar Groups:
MB154/01: Mon 18:00–19:50 B204, J. Jurka
MB154/02: Wed 12:00–13:50 B204, M. Štěpán
MB154/03: Thu 8:00–9:50 A320, D. Trnka
MB154/04: Thu 10:00–11:50 A320, D. Trnka
MB154/05: Thu 12:00–13:50 A320, M. Dzúrik
MB154/06: Thu 14:00–15:50 A320, M. Dzúrik
MB154/07: Wed 14:00–15:50 B204, P. Francírek
MB154/08: Wed 16:00–17:50 B204, P. Francírek
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 with its applications to cryptography, and also the basics of coding and more advanced combinatorial methods.
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 (in case of need replaced by ther distance form complemented by homework solving).
Assessment methods
During the semester, students will sit a mid-term exam, max 20 points. In the seminar groups there will be tests run, awarded in total max 20 points (13 tests per 2 points, the worst 3 results are erased; in case of the distance form, the tests will be replaced by homeworks). Out of these max 40 points, it is necessary to get at least 15 points in order to be allowed to sit the final exam in the exam period, consisting of a theoretical and a practical part, max 60 points. Altogether, it is possible to get max 100 points. For successful examination (the grade at least E) the student needs to obtain at least 50 points.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses

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