Fall 2008, MATH 149

Discrete Geometry

Instructor:              Lenny Fukshansky
Time and Place:     MW 12:00-1:10 pm, BC 22
Office:                   Adams 218
Office hours:          (tentatively) MW 1:30 - 3:00 pm or by appointment
Phone:                   (909) 607 - 0014
Email:                    lenny@cmc.edu
Class webpage:      http://math.cmc.edu/lenny/classes/fall_2008/m149/fall_2008_m149.html

Handouts

Course Announcement: PDF
Lecture notes (last updated 12/3/08): PDF
Take home midterm (due 11/5/08, in class): PDF
Midterm solutions: PDF

Final Projects

Group 1: Max, Lindsay, Tejas; Pick's Theorem and Erhart's Theorem; First meeting -- Tuesday, 11/25/08, 2:00 pm
Group 2: Dwayne, Maria, Jake; The LLL Algorithm; First meeting -- Tuesday, 11/25/08, 4:30 pm
Group 3: Camila, Andy, Patrick; The Kissing Number Problem; First meeting -- Tuesday, 11/25/08, 5:00 pm
Group 4: Ellie, Emily, Tara; The Frobenius Coin Exchange Problem; First meeting -- Friday, 11/21/08, 3:00 pm

Course Description

The goal of this course is to introduce students to the basics of discrete and convex geometry. Topics covered will include convex bodies, lattices, quadratic forms, and interactions between them, such as the fundamentals of Minkowski’s theory, shortest vector problem, reduction algorithms, LLL, and connections to computational complexity and theoretical computer science.  Additional topics may include an introduction to optimization questions, such as tiling, packing, and covering problems.

Prerequisites: Multivariable Calculus (MATH 32) and Linear Algebra (MATH 60)

Course policies

Attendance in this course is crucial. There will be one take-home midterm exam, the time of which will be specified in advance. Homework problems will be suggested, but not collected; I will, however, be happy to discuss these problems with anyone interested, and the midterm problems may be based on these homework excercises.  Instead of the final exam, students will prepare presentations on topics related to the class material to be given towards the end of the semester; I will discuss presentation topics individually with students in the second half of the semester. The midterm and the final project will be worth 50% of the grade each. No text is required, but I will post lecture notes on this webpage as we progress.

Announcements

Midterm average: 60.3 out of 100

All printed handouts and web-materials are protected by US Copyright Laws. No multiple copies can be made without written permission by the instructor.