Date  Chapter  Description 

Jan 20   Introduction and orientation 
Jan 22  3.13.2  Elementary counting problems 

Jan 25  3.33.4, 4.1  Elementary counting: bijective method 
Jan 27  4.1  Binomials and lattice paths 
Jan 29  4.2, 5.1  Multinomials, compositions 

Feb 1  5.25.3  Set partitions and Stirling numbers; integer partitions 
Feb 3  5.3  Lattice paths below the diagonal; integer partitions 
Feb 5  5.3,6.1  Relationship between integer and set partitions; Permutation groups 

Feb 8  6.1  Permutation groups: 1line and cycle structure 
Feb 10  6.1  Stirling numbers of the 1st kind 
Feb 12  6.1  Stirling numbers and duality 

Feb 15  6.2  Permutations with special cycle structure 
Feb 17  6.2, 7.1  Special cycle structure; InclusionExclusion 
Feb 19  Exam 1 (in class) 

Feb 22  7.1  InclusionExclusion formula; Euler characteristic 
Feb 24  7.2  InclusionExclusion applications 
Feb 26   Moebius inversion  Boolean algebra and number theory 

Mar 1  8.1.1  A generating function for the Fibonacci numbers 
Mar 3   Simplicial complexes and join 
Mar 5  8.1.2  Convolution formula, a generating function for p(n) 

Mar 8   Spring Break! (no class) 
Mar 10   Spring Break! (no class) 
Mar 12   Spring Break! (no class) 

Mar 15  8.1.28.1.3  Application: odd partitions; Compositions 
Mar 17  8.2.18.2.2  Exponential generating functions, Bell numbers 
Mar 19  8.2.3  Composing exponential generating functions; Graphs 

Mar 22  11.1  Coloring graphs, bipartite graphs 
Mar 24  11.2  Bipartite graph bounds 
Mar 26  Exam 2 (in class) 

Mar 29  11.3  Matchings and graph simplicial complexes 
Mar 31  11.3  Hall's Marriage Theorem 
Apr 2  11.3  Augmenting paths, Turan's Theorem 

Apr 5  13.1  Ramsey's Theorem, and some Ramsey numbers 
Apr 7  13.2  Multicolor and Hypergraph Ramsey numbers 
Apr 9  13.2  Hypergraph Ramsey numbers and the ErdősSzekeres Theorem 

Apr 12  15.115.2  The probabilistic method and a Ramsey lower bound 
Apr 14  15.3  Independence and Bayes' Theorem 
Apr 16   The ErdősKoRado Theorem, extensions 

Apr 19  15.4  Linearity of expectation, the LYM inequality 
Apr 21  16.1  The LYM inequality and Sperner's Theorem, Posets 
Apr 23  16.1  Chains, antichains, and Dilworth's Theorem 

Apr 26  16.2  Dilworth's Theorem, Poset Möbius inversion 
Apr 28  16.2  Möbius inversion through algebra and topology 
Apr 30  16.2  Möbius inversion and applications 

May 12  Final exam (1:00 pm  3:00 pm) 