| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| DMML 1245 | DISCRETE MATHEMATICS AND MATHEMATICAL LOGIC | Бірінші курс | 5 | 150 | 1 | 2 | 2 |
The concept of mathematical apparatus aimed at solving applied problems, the skills of considering it as a closely related set of mathematical methods and models, languages are formed. Elements of set theory, elements of combinatorics, logic algebra functions, elements of graph theory, elements of coding theory are studied.
Computer simulation.
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narrative, exchange of ideas, discussion, problem methods.
| 1 | uses special mathematical symbols to express quantitative and qualitative relationships between objects; |
| 2 | knows the basic concepts of set theory, basic operations applied to sets and representations; |
| 3 | understands algorithmic counting (generation) of basic combinatorial objects; |
| 4 | knows the language of mathematical logic and logical operations, logic formulas, laws of logic algebra; |
| 5 | defines the types of graphs and gives their characteristics; |
| 6 | generates efficient codes used to detect and correct errors in code combinations. |
| 7 | uses the apparatus of set theory to solve applied problems and studies the properties of binary relations; |
| 8 | learns the methods of generating combinatorial problems; |
| 9 | formulates logical problems and uses mathematical logic tools to solve them; |
| 10 | master the skills of working with algorithms in graphs and methods of solving extreme problems in graphs; |
| 11 | can encode and decode information according to given algorithms. |
| Haftalık Konu | Evaluation Method | |
|---|---|---|
| 1 | Sets and operations on them | |
| 2 | Relationships and their properties | |
| 3 | Functions | |
| 4 | Combinatorial configurations. Placements. Substitutions. Dials. Binomial coefficients and their properties | |
| 5 | Partition the set. The principle of inclusion and exclusion | |
| 6 | The alphabet and formulas of the algebra of opinions. Truth functions. | |
| 7 | Normal forms and complete systems of truth functions. Types of algebraic formulas. Important tautologies. | |
| 8 | The relationship of logical consequences. Use of the language of the algebra of opinions. | |
| 9 | Calculating opinions. Formal proof and formal deduction. | |
| 10 | Predicate. Predicate algebra formulas. | |
| 11 | Graphs and similar objects. Isomorphism of graphs | |
| 12 | Types of graphs and their operations. Ways to transfer graphs | |
| 13 | Trees and their main properties. Eulerian and Hamiltonian counts | |
| 14 | Alphabetical coding. The problem of recognizing the mutual ambiguity of coding. Efficient coding. Huffman and Fano algorithms | |
| 15 | Error detection and correction codes. Hamming code |
| PÇ1 | PÇ2 | PÇ3 | PÇ4 | PÇ5 | PÇ6 | PÇ7 | PÇ8 | PÇ9 | PÇ10 | PÇ11 | PÇ12 |
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| Textbook / Material / Recommended Resources | ||
|---|---|---|
| 1 | A. Tolep, B. Yeskarayeva. Discrete mathematics. Theory and practice. -Shymkent, 2020. -132 p. | |
| 2 | A.Tolep, B. Yeskarayeva. Discrete mathematics. Tasks and exercises. Educational tool. -Turkestan, 2021. -221p. | |
| 3 | A.A. Baijumanov. Fundamentals of mathematical logic. Educational tool. -Almaty: Evero, 2023. | |
| 4 | Beisekov Zh. A methodological tool for solving logical problems in mathematics. -Shymkent, 2017. |