1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2022/2023
4. WMIiE - oferta ERASMUS - Program Erasmus
5. Combinatorial Analysis

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Combinatorial Analysis - opis przedmiotu

Cel przedmiotu

Introducing students to basic definitions, theorems and methods of combinatorial analysis and examples of applications of them.

Wymagania wstępne

Zapisz zmiany

Completed courses of mathematical analysis, linear algebra and discrete mathematics.

Zakres tematyczny

Lecture
1. The binomial coefficients (4 h)
2. Rook polynomials (4 h)
3. Latin squares (4 h)
4. Van der Waerden’s Theorem, Schur’s Theorem (4 h)
5. Map-colourings, Four – Colour Theorem (4 h)
6. Minimax theorems (4 h)
7. Combinatorial designs (2 h)
8. Perfect codes, Hadamard’s matrices (4 h)
 

Class
1. Proving combinatorial identities (2 h)
2. Applications of rook polynomials (4 h)
3. Making latin squares; proving properties of latin squares (4 h)
4. Applications of van der Waerden’s and Schur’s Theorems (4 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 (4 h)
7. Constructing of perfect codes (4 h)
Test (2 h)

Metody kształcenia

Traditional lecture, discussion exercises, work in groups.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

1. Tests 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.

Literatura podstawowa

1. V. Bryant, Aspects of Combinatorics. A wide-ranging introduction, Cambridge University Press, 1993.
3. J. Matoušek, Lectures on Discrete Geometry, Springer, New York, 2002.

Literatura uzupełniająca

2. R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics - A foundation for computer science, Oren, 1994.
 

Uwagi

Zmodyfikowane przez dr Magdalena Łysakowska (ostatnia modyfikacja: 19-04-2022 09:12)