| Lesson Code | Course Name | Class | Credit | Lesson Time | Weekly Lesson Hours (Theoretical) | Weekly Lesson Hours (Practice) | Weekly Class Hours (Laboratory) |
|---|---|---|---|---|---|---|---|
| DM 1269 | Discrete Mathematics | Бірінші курс | 5 | 150 | 15 | 30 |
The purpose of the discipline: to equip students with a mathematical apparatus aimed at solving applied problems, which can be considered as a closely related set of mathematical methods and models, languages. This course covers elements of set theory, elements of combinatorics, functions of logic algebra, elements of graph theory, elements of coding theory.
critical thinking, brainstorming, exchange of views, 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 | Functions of logic algebra. Formulas | |
| 7 | Properties of elementary functions. The principle of duality | |
| 8 | Classification of Boolean functions by variables. Fullness and tightness | |
| 9 | Important closed classes | |
| 10 | Minimization of Boolean functions | |
| 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 | PÇ13 | PÇ14 | PÇ15 |
|---|
| 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 | I. Orazov, B. Alikhanova, A. Sharipbai. Mathematical foundations of computer science. Teaching manual, -Shymkent: Alem, 2020. -192 p. | |
| 4 | Beisekov Zh. A methodological tool for solving logical problems in mathematics.-Shymkent, 2017. | |
| 5 | Kunova S.B. Discrete mathematics: Educational and methodological tool. - Almaty: 'Turan' University, 2020. -144 p. | |
| 6 | Mahmudova Sh.D., Urazgalieva A.N. Discrete mathematics: textbook. / Zapadno-Kazakhstan Agrarian and Technical University named after Jangir Khana. - Uralsk: ZKATU im. Jangir Khan, 2021. -167c. |