Winter Term 2013/2014 - BMS Advanced Course
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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 them during class or send an email us! |
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Those of you who were not registered with Campus Management for DG I can now pick up their "Scheine" (course certificates) in Elke Pose's office at Arnimallee 2. |
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Course DescriptionThis 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. The material will beFor 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. To follow the course, a solid background in linear algebra is necessary. Some knowledge of combinatorics and geometry is helpful. We will cover a selection of the following topics: Basic structures in discrete geometry
Combinatorial geometry / Geometric combinatorics
Polytope theory
Examples, examples, examples
Geometry of linear programming
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 for discrete-geometric structures appearing in differential geometry, optimization, combinatorics, topology, and algebraic geometry.
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Contact
Lectures
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Lectures
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Lecture Notes Etc.Bear in mind that these lecture notes are 'preliminary'. There are no guarantees. If you find errors, please email us. | |||||||||||||||||||||
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Tutorials and Problems
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Tutorial and Exercises
In addition to the lectures there will be a weekly tutorialtwo weekly (identical) tutorials. Please choose one and attend regularly. In the tutorialtutorials, we will occasionally review topics from the lectures but mostly discuss examples and solutions to problems. You are encouraged to pitch in by presenting a solution every once in a while. Every week each student is required to solve problems and hand them in. The sheets containing the problems 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 solutions should be turned in before the second lecture on in the following Wednesdayweek. Please bring them with you to the lecture on Wednesday and hand them to Professor Ziegler by 10.:15 AM. You will receive points for solving each exercise your solutions based on whether your solution is solutions are correct and well-written. Course requirements are the following: (1) You must score at least 60% 50% of the total points of the sum of the maximum number of points of all exercises. In other words, problems assigned in each half of the semester. There will be 7 problem sheets in the first half of the semester. A sheet will have problems worth roughly 20 points. Note that it is ok to score less than 60% 50% on an exercise a sheet as long as you reach 60% 50% of the total points by the end of the first respective second half of the semester. (2) You must pass an a written exam at the end of the semester . Details about the nature of the exam will be discussed as we go along. Exercisewhich alone will determine the grade that you get for this course. Problem Sheets
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