Detailed Schedule -- Combinatorics

MATH 357 -- Spring 2017, Prof. Little

This is a tentative, evolving schedule. If necessary, some topics may be added, deleted, or rearranged during the course of the semester. Any major changes will be announced in class and here. The notation [B] refers to our main course text, Beeler, How to Count: An Introduction to Combinatorics and Its Applications.

Date Class Topic Readings/Assignments
1/25 Course Introduction -- The game of SETTM (discussion)
1/27 Combinatorial problems from SETTM (discussion)
1/30 Basic combinatorial principles [B], sections 1.5,2.1,2.2
2/1 Permutations of [n], cycle decompositions [B], section 2.3
2/3 Legendre's theorem, ordered subsets of [n] [B], sections 2.4,2.5
2/6 Stirling numbers of the first kind [B], section 2.7
2/8 Unordered subsets [B], section 3.1
2/10 Poker hands [B], section 3.2
2/13 Binomial coefficients and their identities [B], section 3.3,3.4
2/15 ``Stars and Bars'' [B], section 3.5
2/17 Multinomial coefficients [B], section 3.6
2/20 Application: the German Enigma machine [B], Chapter 3.7
2/22 Spare day Review [B], chapters 1 - 3
2/24 Exam 1 [B], chapters 1 - 3
2/27 Distribution problems [B], sections 4.1,4.2
3/1 Partitions and Stirling numbers of the second kind [B], section 4.3
3/3 More on partitions [B], section 4.3
3/6,8,10 Spring Break -- no class
3/13 Preliminaries for generating functions [B], sections 5.1,5.2
3/15 The idea of a generating function [B], section 5.3
3/17 Multivariable generating functions [B], section 5.4
3/20 Recurrences [B], section 6.1 -- Notify me about Final Project choices
3/22 Solving recurrences [B], section 6.2
3/24 Linear recurrences and characteristic polynomials [B], section 6.3
3/27 Undetermined coefficients and inhomogeneous recurrences [B], section 6.5
3/29 The general inclusion-exclusion principle [B], section 7.1
3/31 [B], section 7.1
4/3 More on inclusion-exclusion [B], section 7.1
4/5 Spare day -- review for exam
4/7 Exam 2 [B], chapters 4 - 6
4/10 Group actions and counting [B], section 8.2 --Final Project Bibliographies due
4/12 Burnside's lemma [B], section 8.3
4/14,17 Easter Break -- no class
4/19 Equivalent colorings [B], section 8.4
4/21 Polya enumeration [B], section 8.5
4/24 Combinatorial designs [B], sections 10.1,10.2
4/26 Academic conference -- no class [B], section 10.3
4/28 Steiner triple systems [B], section 10.3
5/1 Final Project Presentations
5/3 Final Project Presentations
5/5 Final Project Presentations
5/8 Final Project Presentations and semester wrap-up
As explained in the course syllabus, if you do a final project paper and presentation, there will be no final exam for this course. If you opt to take a final exam, it will be given at the established time for MWF 11am classes, which is Friday, May 12 at 11:30am

Last modified: April 24, 2017