Combinatorics BMS Basic Course -- Diskrete Strukturen I Summer Term 2021 Sommersemester 2021 Prof. Stefan Felsner LV-Nr.: 3236 L 149 The lecture is scheduled at 10am every Tuesday and Thursday during the semester. |

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https://tu-berlin.zoom.us/j/66095399876?pwd=SnBudXdYVGpMVUJITGEzZUpWS2pydz09

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

According to the Corona regulations of TU Berlin the course will be given in a distance learning scheme.

This is the first course of the course series (Studienschwerpunkt) Diskrete Strukturen. It will be continued by Graphentheorie/Graph Theory (Diskrete Strukturen II), winter term 21/22, and a more specialized course Diskrete Strukturen III in the summer term 2022.

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, [zoom] (Kenncode 006171)
- Thursday 16:15 - 17:45 [zoom] (Kenncode 075428)

Questions? Ask

fschroed(at)math.tu-berlin.de

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]
- Practice sheet [pdf]

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

To complete the Modul, participants have to pass an oral exam.

- M.Aigner: A Course in Enumeration;

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

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

Springer, 2001. - J.H.van Lint and R.M.Wilson: A Course in Combinatorics (2nd ed.);

Cambridge Univ. Press, 2001. - R.Stanley: Enumerative Combinatorics, Volume I;

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

Cambridge Univ. Press, 1999. - D.B.West: Combinatorial Mathematics;

Cambridge Univ. Press, 2021.

Last modified April 2021