Combinatorial and Discrete Geometry course information

Code: BMETE94MM02 (3/1/0/V/5);
Semester: 2025/26/1;
Language: English;
Instructor: Dr. Péter Vrana (E0 course)

Attendance requirements

For the signature, students are required to attend at least 70% of the lectures.

Grading

The grade is determined based on an oral exam. Please note that a signature is required in order to be eligible for taking an exam.

Schedule

Wednesdays 12:15–13:45 and 14:00–15:30

Planned topics: (to be updated as the semester progresses)

  • September 10, Affine subspaces and convex sets
  • September 17, Polytopes and polyhedral sets
  • September 24, Algebra of convex sets, valuations, Euler characteristic
  • October 1, Face structure
  • October 8, Graphs of polytopes
  • October 15, Incidence problems
  • October 22, Arrangements
  • October 29
  • November 5
  • November 12
  • November 19, no class, Students' Scientific Association Conference (TDK)
  • November 26
  • December 3
  • December 10

Lectures

The latest version of the lecture notes may be found here. (Updated: October 6)

Consultation

By appointment.

Recommended literature

  1. The lecture notes for the convex geometry course contain additional details on some of the topics (including many proofs omitted in this course).
  2. Alexander Barvinok: A Course in Convexity, Graduate Studies in Mathematics 54, AMS, Providence RI, USA, 2002.
  3. Jiří Matoušek: Lectures on Discrete Geometry, Graduate Texts in Mathematics 212, Springer-Verlag, New York NY, USA, 2002.
  4. Günter M. Ziegler: Lectures on Polytopes, Graduate Texts in Mathematics 152, Springer-Verlag, New York NY, USA, 1998.
  5. Jiří Matoušek: Using the Borsuk-Ulam Theorem, Lectures on Topological Methods in Combinatorics and Geometry, Springer-Verlag, New York NY, USA, 2003.
  6. Szabó László: Konvex geometria. egyetemi jegyzet. ELTE TTK, Budapest, 1996. (in Hungarian)
  7. G. Horváth Ákos, Lángi Zsolt: Kombinatorikus geometria, egyetemi jegyzet, Polygon, Szeged, 2012. (in Hungarian)