University of Connecticut College of Liberal Arts and Sciences
Department of Mathematics
Tom Roby's Math 5020 Home Page (Fall 2008) Combinatorics

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  • Homepage: http://www.math.uconn.edu/~troby
  • Offices: MBS M404 and CUE 123: phone: 860-486-4433
  • Office hours: Tuesday 1:00-1:40, Thursday 1-1:50 in MSB 404 and by appointment. You can often find me in CUE 123 on MWF 9:30-11:30 (but safest to call first). I'm happy to answer questions or schedule appointments by email, which I check frequently.

Class Information

COORDINATES: 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).

5020 LECTURE AND ASSIGNMENT SCHEDULE
Date Sections Topics
1/20 T Ch. 1.1 How to Count
1/22 R Ch. 1.1 Generating Functions HW1 (Due 2/10): EC1, Ch. 1, Do #5,8,13,19,30; Read #1,3abef,14,23,36(a-e).
1/27 T Ch. 1.2 Sets & Multisets
1/29 R Ch. 1.3 Permutation Cycles
2/3 T Class Cancelled
2/5 R Inversion table
2/10 T Cycle index, Stirling numbers(1)
2/12 R Sec. 1.4 Descents & Eulerian Polynomials HW2 (Due 2/26): EC1, Ch. 1, Do #39,51,52,94,102,110; Read #15,23,100,101.
2/17 T
2/19 R
2/24 T
2/26 R
3/2 T
3/4 R
9-13 MARCH SPRING BREAK, NO CLASS
3/17 T
3/19 R
3/24 T
3/26 R
3/31 T
4/2 R
4/7 T
4/9 R
4/14 T
4/16 R
4/21 T
4/23 R
4/28 T
4/30 R


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