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.