Discrete mathematicsTopics

The main features of discrete and continuous sets, their differences and areas of application are studied in the subject. union, intersection, difference, and cartesian product operations on sets are explained. the concept of fuzzy set, membership function and differences from classical sets are also explored.

In the subject, the concept of relation, the essence of binary relations and the construction of sets are studied. representation of binary relations through sets of pairs, tables, graphs and matrices is explained. also, basic properties of relations and their application in discrete mathematics problems are investigated.

In the topic, the concept of functional relationship and its special place in binary relationships are studied. the concept of function is explained based on the condition that only one image matches against each element. also, the domain of the functional relation, the set of values ​​and the graphical representation are investigated.

In the subject, the relation of equivalence, its determination on the basis of properties of reflexivity, symmetry and transitivity is studied. the ordering relation, the main properties of partially and completely ordered sets are explained. also, the concept of a lattice set and the definition of upper and lower boundary elements are investigated.

In the subject, the basic principles of combinatorics and the rules of selecting objects by different methods are studied. the application of addition and multiplication rules and the differences between ordered and unordered samples are explained. the use of the concepts of permutation, arrangement and combination in problem solving is also investigated.

Methods of counting combinatorial objects and calculating combinatorial numbers are studied in the subject. the correct counting of elements in intersecting sets is explained by the method of insertion and removal. also, the application of these methods in issues related to division, remainders and number theory is investigated.

In the subject, the concept of reasoning, its evaluation as true or false, and the structure of logical expressions are studied. basic logical operations such as negation, conjunction, disjunction, implication and equivalence are explained on reasoning. it also examines the pricing of complex reasoning through truth tables.

In the subject, the concept of formula in the logic of reasoning and the rules of building formulas are studied. determining the truth values ​​of complex logical expressions is explained. also, verification of equivalence formulas by means of truth tables and logical laws is investigated.

In the subject, the concept of the bul function, its arguments and values ​​are studied only 0 and 1. the elementary boolean functions of negation, conjunction, disjunction, implication, and equivalence are explained. also, the application of bul functions through truth tables and construction of logical expressions is investigated.

In the topic, the separation of bul functions on separate variables and the role of this method in the analysis of the function are studied. simplification of boolean functions through equivalence transformations and replacement by equivalent expressions is explained. also, the rules for bringing functions into disjunctive and conjunctive normal forms are investigated.

In the subject, the application of functions of logic algebra in the fields of mathematical logic, discrete mathematics and informatics is studied. the use of boolean functions in the construction of electronic circuits, in the description of the logical structure of algorithms and in decision-making models is explained. also, the simplification of logical expressions and their application in solving practical problems are investigated.

In the topic, the concept of graph, the main elements of graphs and actions performed on them are studied. matrix, list, and graphical representation methods of graphs are explained, as well as the concepts of route, chain, and path. also, connected graphs and methods for partitioning a graph into strongly connected subgraphs are investigated.

In the topic, the nature of extremal problems in graph theory and their practical applications are studied. the structure of shortest path, minimal spanning tree, maximal flow and similar optimization problems is explained. also, the main algorithmic approaches used to solve these problems are investigated.

In the topic, the concept of tree in graph theory, its main properties and areas of application are studied. the concept of a network, its vertices, edges, cuts and flow capacities are explained. also, basic principles of flow construction and flow-cross-section relationship are investigated in the network.