Date | Chapter | Description |
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Jan 20 | | Introduction and orientation |
Jan 22 | 3.1-3.2 | Elementary counting problems |
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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 |
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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 |
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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 |
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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) |
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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 |
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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) |
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Mar 8 | | Spring Break! (no class) |
Mar 10 | | Spring Break! (no class) |
Mar 12 | | Spring Break! (no class) |
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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 |
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Mar 22 | 11.1 | Coloring graphs, bipartite graphs |
Mar 24 | 11.2 | Bipartite graph bounds |
Mar 26 | Exam 2 (in class) |
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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 |
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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 |
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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 |
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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 |
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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 |
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May 12 | Final exam (1:00 pm - 3:00 pm) |