Math 370 - Schedule

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# Schedule

### Schedule of topics: Math 370

Date Chapter       Description
Jan 20              Introduction and orientation
Jan 22 3.1-3.2 Elementary counting problems

Jan 25 3.3-3.4, 4.1 Elementary counting: bijective method
Jan 27 4.1 Binomials and lattice paths
Jan 29 4.2, 5.1 Multinomials, compositions

Feb 1 5.2-5.3 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: 1-line 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; Inclusion-Exclusion
Feb 19 Exam 1 (in class)

Feb 22 7.1 Inclusion-Exclusion formula; Euler characteristic
Feb 24 7.2 Inclusion-Exclusion 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 8.1.2-8.1.3 Application: odd partitions; Compositions
Mar 17 8.2.1-8.2.2 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 Erdős-Szekeres Theorem

Apr 12 15.1-15.2 The probabilistic method and a Ramsey lower bound
Apr 14 15.3 Independence and Bayes' Theorem
Apr 16 The Erdős-Ko-Rado 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)

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