Discrete mathematicsSyllabus

Subject code

İF-40167y

Credits

6

Student workload

180

Semester

Autumn semester

Academic year

2025-2026

Subject type

Mandatory

Form of education

Full-time

Language of instruction

Azerbaijani

In-class hours

a) 30 saat - mühazirə b) 30 saat - seminar

Out-of-class hours

a) 72 saat sərbəst iş b) 48 saat - hazırlıq

Discrete mathematics covers the basic concepts of set theory, relations, functions, combinatorics, boolean algebra, mathematical logic, graph theory, trees and networks. the subject teaches students the mathematical foundations of discrete structures, their analysis and modeling methods, as well as their application in programming, algorithm design, data structures, and computer science. the subject serves to use theoretical knowledge in solving practical problems, to develop logical thinking and analytical thinking skills.

• lecture
• seminar
• presentations
• interactive discussion

1. 1

   CLO 1: He should know the basic concepts of mathematical logic, axiomatic methods, understanding of syntax and semantics, experience of working in formal languages.

2. 2

   CLO 2: Must have knowledge of the basics of discrete mathematics and its applications in programming.

3. 3

   CLO 3: He should learn the basic methods of discrete information processing.

4. 4

   CLO 4: Must know boolean algebra and minimization of boolean functions.

5. 5

   CLO 5: Define the elements of graph theory, types of graphs, typical properties he should learn how to present problems in the form of graphs and solve them.

6. 6

   CLO 6: Must have knowledge of flow and trees in network.

1. 1.
   Discrete sets and operations on them. uncut sets. cartesian product of sets. fuzzy sets.Lecture

   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.

2. 2.
   Theory of relations. methods of giving binary relations.Lecture

   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.

3. 3.
   Functional relationship. concept of functional relationship and function.Lecture

   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.

4. 4.
   Equivalence relation. attitude of arrangement. lattice set.Lecture

   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.

5. 5.
   Basic rules of combinatorics. rules for addition and multiplication. fixed selections. unordered selectionsLecture

   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.

6. 6.
   Methods of studying combinatorial objects and combinatorial numbers. input and output method. their application to number theoryLecture

   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.

7. 7.
   Algebra of judgments, operations on judgmentsLecture

   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.

8. 8.
   Formulas in the logic of reasoning. equivalent formulas.Lecture

   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.

9. 9.
   Elementary bul functionsLecture

   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.

10. 10.
    Separation of bul functions by variables. bringing bul functions to normal form by means of homogeneous transformations.Lecture

    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.

11. 11.
    On the application of functions of logic algebraLecture

    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.

12. 12.
    Counts and actions on them. methods of giving graphs. routes, chains, roads. determining routes. related graphs. a partition of a graph into strongly connected subgraphs.Lecture

    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.

13. 13.
    Extremal problems in graphs and their solutionsLecture

    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.

14. 14.
    Trees. basic concepts. network. cross sections of the network. stream on the netLecture

    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.

1. A. namazov, r. amirova, "discrete mathematics", azerbaijan-2025
2. A.e. huseynov, "graph theory and elements of combinatorial analysis", azerbaijan-2000(opens in a new tab)
3. Reinhard diestel, "graph theory", germany-2025(opens in a new tab)