Concrete Mathematics

MATH 544 Spring 2006 course policies

Instructor: Dr. André Kündgen
Email: akundgen@csusm.edu
Office: 339 Science Hall II
Office phone: (760) 750-8070
Office hours: TBA

The easiest way to make an appointment or reach me in general is by email.

Lectures: Tuesday, Thursday 16:00-17:15 (308 Science Hall 2).
CRN: 21672
Webpage: http://courses.csusm.edu/math544ak/

The course webpage contains useful information, like the homework assignments, general announcements, and clarifications regarding the homework. You should check it at least once a week.

Required Textbook

D.B. West, The Art of Combinatorics, excerpts from Chapters 0,3,7,8,9.

We will follow this textbook, and homework will come from it as well. Handwritten lecture notes will also be available on WebCT.

Prerequisites

A certain amount of mathematical maturity is necessary for this course. MATH 350, MATH 370 or a similar discrete mathematics course that stresses the ability to understand and write proofs is required. It is also sufficient, and probably helpful, if you have already taken a more advanced course in discrete mathematics like MATH 472, MATH 474, MATH 540 or MATH 542.

The course is open to upper level undergraduate students as well as graduate students. No knowledge in graph theory or combinatorics is required, since we will develop everything we need from first principles.

Grading Policies

The numerical scores of all exams and assignments will be used in computing final score that will determine your final letter grade:

Homework 20%
Midterm Exam 25%
Presentation 25%
Final Exam 30%
Letter grade Numerical grade
A 85-100
B 70-84
C 60-69
D 50-59
F 00-49
There will be around 5 homework assignments and a detailed homework policy can be found on the web.

Important Dates

January 17: First day of classes
March 7: Midterm Exam
March 27-31: Spring break (no class)
May 4: Last day of classes
May 11: Final Exam, 16:00-18:00

Course content

Suppose you want to color the countries on a map so that any two countries that share a boundary receive a different color. How many colors will you need. If you have an island with three countries that are all mutually adjacent then you will need 4 colors (1 for the ocean and 1 for each of the countries). Are there maps that need more colors?

The goal of this course is to tackle a wide variety of questions of this type: Can we color a structure with respect to certain constraints and how many colors will we need?

More specifically, we will try to cover a list of major theorems from graph theory concerning graph coloring, topological graph theory, and the theory of graph minors. A draft of this list can be found on the course webpage. This list will be updated as we go along. We will also cover open questions that can readily lead to research problems that are accessible to graduate students and advanced undergraduates.

Learning outcomes

Students in this course are expected to solve problems independently, and to develop mathematical proofs in the area of graph theory and then to communicate their ideas orally and in writing. Connections to related areas of mathematics and other disciplines are also developed.