Discrete mathematics

Description

The subject provides students with the formation of theoretical knowledge and analytical skills on the fundamental concepts and methods of discrete mathematics. within the subject, mathematical logic and logic of predicates, sets and relations, boolean algebra, basics of combinatorics and graph theory are studied. principles of correct formulation of mathematical concepts, logical analysis of reasoning and application of various proof methods are considered. bul functions, their separations, concepts of completeness and closure, multivalued functions, operations on graphs, paths and chains in graphs, connectivity, and other basic graph concepts are explored. within the scope of the subject, the application of discrete mathematics methods in computing technologies, automata theory, coding, information transfer and processing, development of algorithms and optimal software solutions is considered. special attention is also paid to the application of graph theory in the fields of network security and cyber forensics. the subject is aimed at developing students' abilities to analyze mathematical texts, make logical judgments, apply theoretical knowledge to solving practical problems, and model computing and information security problems using discrete structures.

Course learning outcomes

1. 1

   CLO 1: Must have knowledge of elementary functions of logic algebra and their properties. formulas, expression of functions with formulas, should be able to work with formulas of the same structure. must have knowledge of tautology and false formulas of identity, equivalence of formulas.

2. 2

   CLO 2: A dual function must have knowledge of the principle of duality. logic should be able to construct separation of algebraic functions by variables, perfect disjunctive forms, and perfect normal forms.

3. 3

   CLO 3: Must know bul functions and their simple applications in modeling digital circuits and cryptographic primitives.

4. 4

   CLO 4: Must know the essential elements of number theory used in public-key cryptography and their applications in appropriate cryptographic algorithms.

5. 5

   CLO 5: Must know the basic elements of finite squares and be aware of examples of their application in cryptographic algorithms.

6. 6

   CLO 6: Must know graph description methods and algorithms for finding shortest paths in weighted graphs and be able to apply them in network modeling (ospf).