# 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

[Teaching Top]

okamotoy@uec.ac.jp