MATH 580 / CS 571

COMBINATORIAL MATHEMATICS, Fall 2009

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 2009 edition of the text is available at TIS Bookstore (707 S. 6th St.) for about $34. It is almost the same length as last year's text, with some rearrangement in a few chapters and additions to Chapters 15 and 16.

The course meets MWF at 2pm in 343 Altgeld Hall. The problem session meets Mondays 7-9pm in 141 Altgeld Hall.

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