Welcome to the course website! The lectures on Discrete Geometry I are taught by Günter M. Ziegler. The tutorials are held by Albert Haase. If you have any questions, please ask us during class or email us!

Course Description

This is the first in a series of three courses on Discrete Geometry. We will get to know fascinating geometric structures such as configurations of points and lines, hyperplane arrangements, and in particular polytopes and polyhedra, and learn how to handle them using modern methods for computation and visualization and current analysis and proof techniques. A lot of this looks quite simple and concrete at first sight (and some of it is), but it also very quickly touches topics of current research. To follow the course, a solid background in linear algebra is necessary. Some knowledge of combinatorics and geometry is helpful.

For students with an interest in discrete mathematics and geometry, this is the starting point to specialize in discrete geometry. The topics addressed in the course supplement and deepen the understanding of discrete-geometric structures appearing in differential geometry, optimization, combinatorics, topology, and algebraic geometry.

Lectures

Contact

Tutorial and Exercises

In addition to the lectures there will be a weekly tutorial. In the tutorial, we will occasionally review topics from the lectures but mostly discuss and solve exercises. Each week every student is asked to turn in solutions to a set of three or four exercises that will appear on this website in form of an exercise sheet. The exercise sheets will be uploaded on Wednesdays and should be turned in before the second lecture on the following Wednesday. Please bring them with you to the lecture and hand them to Professor Ziegler by 10.15 AM. You will receive points for solving each exercise based on whether your solution is correct and well-written.

Course requirements are the following: (1) You must score at least 60% of the sum of the maximum number of points of all exercises. In other words, it is ok to score less than 60% on an exercise sheet as long as you reach 60% of the total points by the end of the semester. (2) You must pass an exam at the end of the semester. Details about the nature of the exam will be discussed as we go along.

Exercise Sheets