MATH 580 / CS 571
COMBINATORIAL MATHEMATICS, Fall 2007
This is a graduate-level introduction to the fundamental ideas and
results of combinatorics. The course moves quickly but does not assume prior
study in combinatorics. It is intended for graduate students from mathematics
or related areas wanting a good one-semester background in fundamental and
applicable discrete mathematics. It also provides solid preparation
for advanced combinatorics courses and for various courses in computer science.
Roughly the first third of the course discusses elementary enumeration,
covering the material of Math 413 (and beyond) at a more sophisticated level.
The middle third discusses graph theory, presenting the main results of Math
412. The remainder touches on topics that are explored more fully in later
courses (581, 582, 583, 584), including Ramsey theory, partially ordered sets,
the probabilistic method, and combinatorial designs.
NOTE: The FALL 2008 edition of the text will be available at TIS Bookstore
(707 S. 6th St.), probably for between $40 and $50. It is 15% shorter than
last year's text due to deletion of some material we don't cover in the text
and hence is being printed only in one piece.
The course meets MWF at 2pm in 441 Altgeld Hall.
Resources in html
- List of known TYPOS in Fall 2008
pre-publication printing of text (typos and other comments welcome).
- Books on reserve
- SUMMARY of lectures in Fall 2008
- Drawing pictures with gpic: discussion,
macro package
- Archive: summary of lectures in
Fall 2007,
Fall 2006,
Fall 2005,
Fall 2004,
Fall 2003,
Fall 2002
- Archive: typos in earlier printings -
Fall 2007,
Fall 2006,
Fall 2005,
Fall 2004,
Fall 2003,
Fall 2002
Resources in postscript
- Course announcement
- Advice to students
- Fall 2008 Homework:
- Archive of problem sets from Fall 2007:
1, 2, 3,
4, 5, 6,
7, 8, 9,
10, 11, 12,
13, 14
- Archive of problem sets from Fall 2006:
1, 2, 3,
4, 5, 6,
7, 8, 9,
10, 11, 12,
13, 14
- Archive of problem sets from Fall 2005:
1, 2, 3,
4, 5, 6,
7, 8, 9,
10, 11, 12,
13, 14, 15
- Archive of problem sets from Fall 2004:
1, 2, 3,
4, 5, 6,
7, 8, 9,
10, 11, 12,
13, 14, 15
- Archive of problem sets from Fall 2003:
1, 2, 3,
4, 5, 6,
7, 8, 9,
10, 11, 12,
13, 14, 15
- Archive of problem sets from Fall 2002:
1, 2, 3,
4, 5, 6,
7, 8, 9,
10, 11, 12,
13, 14, 15