SylabUZ
| Course name | Foundation of discrete systems |
| Course ID | 11.9--INFP-FoDS-Er |
| Faculty | Faculty of Computer Science, Electrical Engineering and Automatics |
| Field of study | Computer Science |
| Education profile | academic |
| Level of studies | First-cycle Erasmus programme |
| Beginning semester | winter term 2022/2023 |
| Semester | 2 |
| ECTS credits to win | 5 |
| Course type | obligatory |
| Teaching language | english |
| Author of syllabus |
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| The class form | Hours per semester (full-time) | Hours per week (full-time) | Hours per semester (part-time) | Hours per week (part-time) | Form of assignment |
| Class | 15 | 1 | - | - | Credit with grade |
| Laboratory | 15 | 1 | - | - | Credit with grade |
| Lecture | 30 | 2 | - | - | Exam |
This is an introductory course in discrete mathematics. The main goal is to introduce students to ideas and techniques from discrete mathematics that are widely used in various areas of computer science, in particular in algorithms analysis, in modern cryptography and data analysis.
-to introduce students to the basic discrete structures algorithms, in particular, graph theory algorithms, number theory algorithms
- to introduce students to the basics of inductive and recurrent procedures used in computer science
- to teach students to think logically and mathematically,and to apply these techniques in solving typical computational problems appearing in practise
-to introduce students to the Maple/Maxima system
Mathematical Analysis Course, Linear Algebra with Analytical Geometry foudations ,Logics for Infmatics
Introduction : elementary properties of functions and sequences.Set algebra calculus , formal calculus of proposals, and the notion of abstract Bool algebra.
Basics of relation theory : the set theory notion versus digraphs notion vs matrix calculus.The equivalence and (partial ) ordering relations and their use.
Inductive and recurrent procedures:The complete mathematical induction argument and applications.Definitions and applications of recurrence definitions.Linear recurrence equations and their solutions.The notion of inductive and recurrent algorithms, examples, and their computational complexities.
Combinatorial problems and their applications : the basic definitions: permutations, combinations, variations. Applications of recurrences linear equations for solving combinatorial problems.The Dirichlet principle. Applications to elementary probability theory.
Number Theory algorithms and their applications .Modular arithmetics, liner congruency problems, and their solution. The notion of a multiplicative group, theorem and function of Euler. Small Fermat theorem. Protokol RSA and its conditional security.
Introduction to graphs theory : the basic notion .The tree type of graphs :basic properties and constructions. The Euler graphs, Hamilton path notion.Graph colouring problem.Applications in computer science problems.
traditional lectures
- computational exercises
-laboratory: computational experiments in Maple or Maxima.
| Outcome description | Outcome symbols | Methods of verification | The class form |
Lecture - the passing condition is to obtain a positive mark from the final exam in written form
Computational exercises: the passing condition is to obtain positive marks from all midterm tests
Laboratory: the passing condition is to obtain positive marks from all midterm tests
1 .Discrete Mathematics ,Ross K.A. , Wright ( 3rd edition ) Prentice Hall Inc. 1992
2. Introduction to algorithms , Cormen , T.H. , Leiserson , Ch.E , Rivest R.L .,MIT 1990
3.Discrete Mathematics and it's Applications , K.H. Rosen, (6th edition ) ,Mc Graw-Hill ,Inc.New York , 2007
"Discrete Mathematical Structures with Applications to Computer Science " , McGraw Hill , 1975
Modified by prof. dr hab. Roman Gielerak (last modification: 11-04-2022 16:54)
