Combinatorics BMS basic Course -- Diskrete Strukturen I Summer Term 2019 Sommersemester 2019 Prof. Stefan Felsner Sprechstunde n.V. LV-Nr.: 3236 L 149 Di 12-14, MA 141 Fr 10-12, MA 141 |

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This is a Berlin Mathematical School (BMS) Basic Course, and will thus be taught in English.

This is also the first course of the course series Diskrete Strukturen. It will be continued by Graphentheorie/Graph Theory (Diskrete Strukturen II), winter term 19/20, and a more special course Diskrete Strukturen III in the summer term 2020.

Combinatorics is as much about problem solving as theory building, though it has developed powerful theoretical methods, especially since the later twentieth century. The goal of this course will be to provide you with a broad overview – and with a firm, concrete “working knowledge” on basic combinatorial principles, tools, methods, theories, and results.

The course will cover most of the following topics:

- Basic Counting
- Generating Functions
- Combinatorics of Finite Sets
- Posets
- Duality Theorems
- Polya Theory
- Design Theory
- Graphs and Chromatic Number
- Gray Codes and De Brujin Sequences
- Catalan Families

- Tuesday 14:15 - 15:45, MA 549,
- Thursday 10:15 - 11:45, MA 549

Questions? Ask

fschroed(at)math.tu-berlin.de, room MA 509

This sheet is optional. However, we recommend thinking about the problems.

- Practice sheet [pdf]
- Practice sheet [pdf]
- Practice sheet [pdf]
- Practice sheet [pdf]
- Practice sheet [pdf]
- Practice sheet [pdf]
- Practice sheet [pdf]
- Practice sheet [pdf]
- Practice sheet [pdf]
- Practice sheet [pdf]
- Practice sheet [pdf]
- Practice sheet [pdf] updated
- Practice sheet [pdf]

Exercises marked with a star (*) are optional and give extra points.

To complete the modul participants have to pass an additional oral exam.

- M.Aigner: A Course in Enumeration;

Springer, 2007. - R.Graham, D.Knuth, O.Patashnik: Concrete Mathematics;

Addison-Wesely, 1989. - S.Jukna: Extremal Combinatorics;

Springer, 2001. - R.Stanley: Enumerative Combinatorics, Volume I;

Cambridge Univ. Press, 1997. - R. Stanley: Enumerative Combinatorics, Volume II;

Cambridge Univ. Press, 1999. - J.H.van Lint and R.M.Wilson: A Course in Combinatorics (2nd ed.);

Cambridge Univ. Press, 2001.

Last modified April 2019