This lecture is an introduction into combinatorics, a field concerned with the existence, enumeration, analysis and optimization of discrete structures. The students are taught various combinatorial techniques, which can be applied all over mathematics.

The specific topics include:

- counting and bijections,
- generating functions,
- partial orders,
- combinatorial designs.

### Lecture Notes

We offer the notes of this lecture from summer term 2015 here. The lecture will be based on these notes, but some changes are planned.

**Please note** that the exam will be based on the current lecture, that might contain parts which are not covered by these notes.

### Exercise Sheets

- Exercise Sheet 1 - Solutions Sheet 1
- Exercise Sheet 2 - Solutions Sheet 2
- Exercise Sheet 3 - Solutions Sheet 3
- Exercise Sheet 4 - Solutions Sheet 4
- Exercise Sheet 5 - Solutions Sheet 5
- Exercise Sheet 6 - Solutions Sheet 6
- Exercise Sheet 7 - Solutions Sheet 7
- Exercise Sheet 8 - Solutions Sheet 8
- Exercise Sheet 9 - Solutions Sheet 9
- Exercise Sheet 10 - Solutions Sheet 10
- Exercise Sheet 11 - Solutions Sheet 11
- Exercise Sheet 12 - Solutions Sheet 12
- Exercise Sheet 13 - Solutions Sheet 13

We will publish an exercise sheet each week on this website. You may submit written solutions in the problem class on Monday or in the blue box labeled "Combinatorics" in the math building. The solutions will be graded.

**Please grab your graded solutions in the problem class or from the box in room/balcony 1.069.**

We strongly encourage you to work on these exercises to practice solving problems and to get used to the material from the lecture. Some of the solutions will be discussed in the problem class and published on this website.

### Bonus

There is the possibility to obtain a bonus by successfully working the exercise sheets.

In order to receive the bonus you need to obtain **at least half of the total amount** of points on the **first 6 sheets, as well as on the second 6 sheets**.

The bonus will improve the grade of a **passed** exam of this lecture at the end of the semester by **one step** (0.3 or 0.4).

### Exam

The written exam will be

- on
**September 8** **9:45 - 12:45**- in the
**MTI-Hörsaal**(building 30.33, room 101, "Messtechnik").

The online registration for the exam is open between July 20 and September 1.

We will publish a seating plan few days before the exam here.

Calculators and other means are not allowed.

Solutions may be written in German or English.

### Prerequisites

Basic knowledge of linear algebra.

### Language

This lecture will be taught in English.

### References

Among others this lectures will be based on the following books:

- "
*Introductory Combinatorics*" by Richard A. Brualdi - "
*A Course in Combinatorics*" by J.H. van Lint and R.M. Wilson.