Discrete Mathematics and Computational Structures

Summer 2009

Administrivia

Instructor: Yoshio Okamoto
Time: Thursday 10:40-12:10
Place: H114A Lecture Room, Main Bldg, Ookayama Campus

Topic

The lattice point counting in convex polytopes, Ehrhart theory.
We basically follow the book "Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra" by M. Beck and S. Robins.

Exercise Assignment

Visit the wiki page of the course.

Slides

Slides in the lectures will be available from the OCW (Tokyo Tech OpenCourseWare).

Tentative Schedule

Apr 9, 2009: Substituted by Friday's schedule
Apr 16, 2009: Lecture 1 (Introduction; Frobenius' Coin-Exchange Problem)
Apr 23, 2009: No class
Apr 30, 2009: Lecture 2 (Polytopes and Discrete Volumes)
May 7, 2009: Lecture 3 (Ehrhart Theory I)
May 14, 2009: Lecture 4 (Ehrhart Theory II)
May 21, 2009: Lecture 5 (Reciprocity)
May 28, 2009: Substituted by Tuesday's schedule
June 4, 2009: Lecture 6 (Face Numbers and the Dehn-Sommerville Relations)
June 11, 2009: Lecture 7 (Magic Squares)
June 18, 2009: Lecture 8 (Finite Fourier Analysis)
June 25, 2009: No class
July 2, 2009: Lecture 9 (Dedekind Sums)
July 9, 2009: No class
July 16, 2009: Lecture 10 (The Decomposition of a Polytope into Its Cones)
July 23, 2009: No class

Related Materials

okamotoy@uec.ac.jp