University of Georgia Department of Mathematics

Combinatorics
Math 4670/6670
Fall 2008




Instructor: Victor Kreiman
Office: 318 Boyd Graduate Studies
Office Hours: M, W 3:45 - 4:15, Tu 12:30 - 1:30, Th 1:30 - 2:30
e-mail: vkreiman@math.uga.edu
Webpage: www.math.uga.edu/~vkreiman



Course Description
We will cover portions of chapters 2, 3, 5, 6, 7, and 8 of the textbook. Topics will include: the pigeonhole principle, basic counting principles (e.g., addition, subtraction, multiplication, and division principles), combinations and permutations of sets and multisets, the binomial and multinomial theorems, the inclusion-exclusion principle and applications, generating functions, recurrence relations, Catalan numbers, Stirling numbers. Time and interest permitting, we may examine the following additional topics: Polya counting theory, partially ordered sets, Mobius inversion, applications to number theory.

Textbook
Richard A. Brualdi, Introductory Combinatorics, Fourth Edition, Prentice Hall, 2004. Errata for this textbook can be found at http://www.math.wisc.edu/~brualdi.

Other Recommended Texts
(1) Chen Chuan-Chong and Koh Khee-Meng, Principles and Techniques in Combinatorics, World Scientific, 2007
(2) George E. Martin, Counting: The Art of Enumerative Combinatorics, Springer-Verlag, 2001
(3) V. K. Balakrishnan, Schaum's Outline of Theory and Problems of Combinatorics including concepts of Graph Theory, McGraw-Hill, 1994
(4) Kenneth P. Bogart, Enumerative Combinatorics Through Guided Discovery, available free for download at http://www.math.dartmouth.edu/archive/kpbogart/public_html

Prerequisites
(1) Linear algebra (MATH 3000 or MATH 3500 or MATH 3500H)
(2) Logic, sets, functions, induction (CSCI(MATH) 2610 or MATH 3200)

Homework
Homework will be collected regularly and graded. You are encouraged to discuss the problems with other students, but it is recommended that you first try to solve them on your own. You must write your own solutions, with no assistance, and without looking at another solution. Joint work must be acknowledged on the first page. Most of the assigned problems require proofs or explanations, and you should use clear language and correct grammar in your submitted work. Math 6670 students will be given extra problems.

Grading
Your grade will be based on homework (20%), three one-hour exams (20% each), and a comprehensive final exam (20%).

Missed work
Late homeworks will not be accepted, and there are no makeup exams.