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Tom Roby's Math 5020 Home Page (Fall 2008)
Combinatorics
Questions or Comments?
Class InformationCOORDINATES: Classes meet Tuesdays and Thursdays 9:30-10:45 in MSB 118. The registrar calls this Section 001, #9939. TEXT: Richard Stanley: Enumerative Combinatorics.. We'll start with Chapter 1 (2nd ed.) then probably move on to Volume 2. WEBPAGE: The homepage for this course is http://www.math.uconn.edu/~troby/Math5020S09/. GRADING:Grading will be based on homework, which will be assigned fortnightly. (See schedule below.) CONTENT: Combinatorics is related to the word "combinations", and much of the field deals with counting problems ("enumeration"). More broadly, combinatorics considers discrete structures, such as graphs, partially ordered sets, polytopes, and Young tableaux, and questions that go beyond simple enumeration. With the advent of computers in the second half of the last century, such questions have become increasingly important in applications as well as more managable to solve. Combinatorics has forged stronger connections with other areas of mathematics, including representation theory (counting dimensions of irreducible representations), and algebraic geometry (via polytopes and posets that represent the intersection of hyperplanes or algebraic varieties).
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