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.
Zeichnung

News:

The current draft of the script is available here. If anyone of you wants to contribute, just write it in the overleaf chat. You can then be included in the corresponding whatsapp group if you want.

General:

The lectures will be on Tuesdays and Thursdays. at 10am on zoom in this virtual room: lecture
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.

Contents:

Combinatorics is a branch of pure mathematics concerning the study of mostly finite objects. It is related to many other areas of mathematics, such as algebra, probability theory and geometry, as well as to applied subjects in computer science and statistical physics. Typical combinatorial questions are: Does a set with certain properties exist at all? If yes, how many are there? How do I find them? Combinatorics abounds with beautiful problems that are easily understood, but very often a real challenge to solve.

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:
  1. Basic Counting
  2. Generating Functions
  3. Combinatorics of Finite Sets
  4. Posets
  5. Duality Theorems
  6. Polya Theory
  7. Design Theory
  8. Graphs and Chromatic Number
  9. Gray Codes and De Brujin Sequences
  10. Catalan Families

Tutorials:

The tutorials are directed by Felix Schröder. There will be two tutorials a week, one in English, the other in German.
Questions? Ask
fschroed(at)math.tu-berlin.de

Problem sets

PrePractice sheet [pdf]
This sheet is optional. However, we recommend thinking about the problems.
  1. Practice sheet [pdf]
  2. Practice sheet [pdf]
  3. Practice sheet [pdf]
  4. Practice sheet [pdf]
  5. Practice sheet [pdf]
  6. Practice sheet [pdf]
  7. Practice sheet [pdf]
  8. Practice sheet [pdf]
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  10. Practice sheet [pdf]
  11. Practice sheet [pdf]
  12. Practice sheet [pdf]
  13. Practice sheet [pdf]

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

Terms to receive a certificate / credit-points:

At the beginning of every tutorial every participant has to mark in a list, which exercises of the current sheet she/he solved and is able to present. If somebody marks an exercise she/he is not able to present in a satisfying way, ALL exercises of this sheet will be disregarded and therefore not counted (also, each exercise is only counted once, even if presented in both tutorials). We expect a better presentation and solutions of master- and BMS students, compared to the ones acceptable from bachelor students. To receive a certificate for the tutorials (Schein), you have to solve at least 50% of the exercises.
To complete the Modul, participants have to pass an oral exam.

References:

Last modified April 2021