SylabUZ
Course name | Combinatorial Analysis |
Course ID | 11.1-WK-MATD-AK-W-S14_pNadGenT0E38 |
Faculty | Faculty of Mathematics, Computer Science and Econometrics |
Field of study | Mathematics |
Education profile | academic |
Level of studies | Second-cycle studies leading to MS degree |
Beginning semester | winter term 2020/2021 |
Semester | 4 |
ECTS credits to win | 5 |
Course type | optional |
Teaching language | polish |
Author of syllabus |
|
The class form | Hours per semester (full-time) | Hours per week (full-time) | Hours per semester (part-time) | Hours per week (part-time) | Form of assignment |
Lecture | 30 | 2 | - | - | Credit with grade |
Class | 30 | 2 | - | - | Credit with grade |
Introducing students to basic definitions, theorems and methods of combinatorial analysis and examples of applications of them.
Completed courses of mathematical analysis, linear algebra and discrete mathematics.
Lecture
1. The binomial coefficients (2 h)
2. Rook polynomials (2 h)
3. Latin squares (2 h)
4. Van der Waerden’s Theorem, Schur’s Theorem (2 h)
5. Map-colourings, Four – Colour Theorem (3 h)
6. Minimax theorems (4 h)
7. Combinatorial designs (2 h)
8. Perfect codes, Hadamard’s matrices (5 h)
9. Sperner’s Lemma (3 h)
10. Minkowski’s Theorem, Radon’s Theorem, Helly’s Theorem, Tverberg’s Theorem (5 h)
Class
1. Proving combinatorial identities (2 h)
2. Applications of rook polynomials (3 h)
3. Making latin squares; proving properties of latin squares (3 h)
4. Applications of van der Waerden’s and Schur’s Theorems (2 h)
Test (2 h)
5. Applications of Four - Colour Theorem and minimax theorems (4 h)
6. Proving properties of combinatorial designs; applications of combinatorial designs (3 h)
7. Constructing of perfect codes (3 h)
8. Applications of Sperner’s Lemma and basic theorems of combinatorial geometry (6 h)
Test (2 h)
Traditional lecture, discussion exercises, work in groups.
Outcome description | Outcome symbols | Methods of verification | The class form |
1. Checking of preparedness of students and their activity during exercise
2. Colloquiums with tasks of different difficulty, allowing to evaluate whether the students have achieved specified learning outcomes in minimal level
3. Written exam
The grade of the module is the arithmetic mean of the exercise grade and the exam grade. The prerequisite of the exam is to get a positive assessment of the exercise. The condition to obtain a positive evaluation of the module is the positive evaluation of the exam.
1. W. Lipski, W. Marek, Analiza kombinatoryczna, PWN, Warszawa,1986.
2. K. A. Rybnikow (red.), Analiza kombinatoryczna w zadaniach, PWN, Warszawa, 1988.
3. J. Matoušek, Lectures on Discrete Geometry, Springer, New York, 2002.
1. Z. Palka, A. Ruciński, Wykłady z kombinatoryki, WNT, Warszawa, 1998.
2. R. L. Graham, D. E. Knuth, O. Patashnik, Matematyka konkretna, PWN, Warszawa, 2011.
3. V. Bryant, Aspekty kombinatoryki, WNT, Warszawa, 1997.
Modified by dr Alina Szelecka (last modification: 18-09-2020 13:46)