Fall 2013, MATH 149

Discrete Geometry

Instructor:              Lenny Fukshansky
Time and Place:     MW 12:00-1:10 pm, RN 105
Office:                   Adams 218
Office hours:          (tentatively) MW 9:30 - 11:00 am or by appointment
Phone:                   (909) 607 - 0014
Email:                    lenny@cmc.edu
Class webpage:      http://math.cmc.edu/lenny/classes/fall_2013/m149/fall_2013_m149.html


Course Announcement: PDF
Lecture notes: PDF -- the lecture notes may be periodically updated as we proceed
Midterm: PDF or LaTeX -- due in class on Wednesday, 10/30/13 (Class average = 69.5 out of 100)

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 geometry of numbers, shortest vector problem, reduction algorithms, LLL algorithm, and connections to computational complexity and theoretical computer science.  Additional topics may include an introduction to optimization questions, such as packing and covering problems, kissing number, integer knapsack, etc.

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

Course policies

Attendance in this course is crucial. There will be one midterm exam, the time of which will be specified in advance. Homework problems will be suggested and discussed during the regular discussion sessions; attendance and participation in the discussion sessions is required. Instead of the final exam, students will do a final project and 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. No text is required, but I will post lecture notes on the class webpage as we progress.

Discussion sessions

TA: Xun Sun
Time: Every Monday at 7:00 pm
Place: RN 102

Students will work on the homework problems (suggested in class and found in the lecture notes). These problems will then be discussed during the discussion sessions. Students should be prepared to present these problems at the board.

Grade breakdown

Discussion sessions = 20%
Midterm exam = 40%
Final project and presentation = 40%


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