M501/2 Combinatorics I, Fall 2005
Dr. A. Betten, room 207, Weber building
When and where:
M W F 2:10 - 3:00 ENGRG E106
M502: van Lint / Wilson: Combinatorics, Cambridge
M501: Richard P. Stanley: Enumerative Combinatorics, Volume I, Cambridge Studies in Advanced Mathematics 49, Cambridge
Topics (M502, Spring 06):
Topics (M501 Fall 05):
This is an introductory course on Combinatorics at the graduate level.
The student who wishes to study discrete structures (like graphs, codes, designs, geometries etc.) needs two basic ingredients. He needs a strong background in fundamental counting techniques and he should also aquire a good understanding of algebraic concepts.
This course is about the first of these, the fundamental counting techniques. The textbook by Stanley (Enumerative Combinatorics) gives an overwhelming amount of seemingly different but essentially connected counting results. Getting through this book is already an achievement, and it can only be done by picking a good collection of samples. This is what we shall do in the course.
The core topics are chapters 1-3 in the book, covering for example:
Apart from that, we may choose further topics from chapters 4 and 5. In particular, we will discuss the transfer matrix method, which is concerned with counting paths in directed graphs (in a similar but more sophisticated fashion as in the usual Computer Science Algorithms class).
The course will be continued in Spring 05. Then we will deepen our understanding of essential counting methods and we will study further applications. It would be helpful if people who wish to continue the sequence take M566 in Fall 05 in order to be prepared for a more algebraic approach to combinatorics in Spring 06 (unless, of course, they already feel strong enough on their algebra side).
Class participation and homework are essential, as is the final exam. I expect that course participants present small subject topics towards the end of the semester. The mix is: final / subject topic presentation / homework / class participation as to 30 / 30 / 30 / 10.
For further information:
Please contact A. Betten:
or visit the course webpage at
http://www.math.colostate.edu/ betten/courses/M501/FA05/index.html. http://www.math.colostate.edu/~betten/courses/M501/FA05/index.html