Math 461: Combinatorial Theory

Professor William McGovern 
Fall 2008


Instructor:
Monty (or William) McGovern
Office: Padelford C-450
Phone: 206-543-1149
Email: mcgovern@math.washington.edu
Office Hours: MW 1:30, or by appointment; grader office hour Th 10:30 or by appointment, Padelford C-450
Lectures:
Monday, Wednesday & Friday, 9:30-10:20 a.m., Smith Hall 305
Required Text:

Introductory Combinatorics, by Brualdi, (4th ed., Prentice Hall, 2004).

Prerequisites:
Math 308 or the equivalent. 
Grading:
Your grade will be based on weekly homework, two midterms, and a final exam, each accounting for 1/3 of the final grade. The midterms will be given on October 17 and November 14; the final exam will be given on Wednesday, December 10, at 8:30 a.m., and will be comprehensive. If you cannot complete a homework assignment on time, you can always turn it in by 4:00 on the day it is due to the grader's (Kurt Luoto's) mailbox. PLEASE turn in WHATEVER YOU CAN rather than nothing. I encourage you to work on homework in groups, though each assignment must be written up individually. In the midterms and final you may use two letter-sized pages (one sheet front and back of notes in your own handwriting).
Incompletes and Drops:
The grade of Incomplete will be given ONLY if a student has been doing satisfactory work until the end of the quarter and then misses the final exam for a documented illness, religious reason, or family emergency.
What to Expect:
I will begin by reviewing mathematical induction and the pigeonhole principle, two basic techniques to be used throughout the course. Then I will apply these techniques and others to study enumeration, existence, and extremal problems (the "three Es" of combinatorics). More precisely, I will cover most of Chapters 2 through 8 in Brualdi and some topics from Chapter 9.

             Homework

Due:
Problems:
Sep 26
show that the sum of the cubes of the first n natural numbers is the SQUARE of the sum of these numbers.
Oct 3
p. 40 #7,10,13 (counts double),16, a board problem given in class: read Chapter 2, 3.1--3.3
Oct 10
section 3.6 #4,7,9,18,28: finish Chapter 3 and start Chapter 4
Oct 17
study problems, midterm: section 3.6 #22,50; section 4.6 #8,19,20; finish Chapter 4
Oct 24
4.6 #7,8; 5.8 #11,12,33 [case of even n only; for extra credit, do odd n]: read Chapter 5
Oct 31
5.8 #19; 6.7 #1,14,16,31: read 6.1-6.4
Nov 7
6.7 #9,24; 7.8 #1,5,8: read 6.5,7.1-7.3
Nov 14
study problems: 6.7 #11,32[correction: ALL squares EXCEPT (1,1),(2,2)..,(n,1) are forbidden]; 7.8 #32,34,35: read 7.4,7.5
Nov 21
7.8 #35,45; 8.6 #1,2,34 [correction to #34: Catalan number C_n, NOT large Schroder number R_n]: finish Chapter 7, read 8.1-8.3
Dec 5
turn in problems from missing HW assignments: read 8.5,8.6 (omit 8.4), start Chapter 9


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