Skip to second half of course
Tuesday, August 28 (pdf of Notes pages 0–10)
- Material from Section 1.1 and more
- Course Introduction
Thursday, August 30 (pdf of Notes pages 11–24)
- Material from Sections 1.1 and 1.2
- Simple Counting
- Multiplication Principle
- Examples
Tuesday, September 4 (pdf of Notes pages 25–37)
- Material from Sections 1.1 - 1.3
- Counting pitfalls
- Overcounting, Counting the complement
- Bijections
Thursday, September 6 (pdf of Notes pages 38–44)
- Material from Section 1.4
Tuesday, September 11 (pdf of Notes pages 45–56)
- Material from Sections 2.1 and 2.2
- Equivalence classes
- Counting using symmetry
- Counting distributions
Thursday, September 13
Thursday, September 20 (pdf of Notes pages 57–60)
- Material from Sections 2.1-2.3
- More distributions
- The binomial theorem
- Combinatorial proofs
- Worksheet on combinatorial proofs
Thursday, September 28 (pdf of Notes pages 61–72)
- Material from Sections 2.3, 2.4, and Chapter 3
- Combinatorial proofs
- Worksheet on combinatorial proofs
Tuesday, October 2 (pdf of Notes pages 73–76)
- Material from Section 4.2
- Domino-square interpretations
Thursday, October 4
Tuesday, October 9 (pdf of Notes pages 77–85)
- Material not in the book
- Combinatorial statistics
- Permutation representations
- descent, inversion, major statistic
Thursday, October 11
Tuesday, October 16
Thursday, October 18 and Tuesday, October 23 (pdf of Notes pages 86–95)
- Material from Sections 3.3
- Introduction to generating functions
- Generating function manipulations
- Generating function worksheet
Thursday, October 25 (pdf of Notes pages 96–101)
- Material from Section 3.5
- Solving recurrence relations
- Fibonacci generating function
Tuesday, November 6
Thursday, November 8 (pdf of Notes pages 102–110) (These are the same notes that were posted before the storm.)
- Material from Sections 2.4, 3.4, and 4.4
- Integer partitions
- Integer partition bijections
Tuesday, November 13 (pdf of Notes pages 111–116) AND (117–118)
- Material from Section 3.4 PLUS additional material
- Products of generating functions
- Compositions of generating functions
- And their combinatorial interpretations
Thursday, November 15 (pdf of Notes pages 119–127)
- Material from Section 4.1 PLUS additional material
- Catalan numbers
- Catalan number interpretations
- Catalan number generating function
- (link to Stanley's Catalan Interpretations)
Tuesday, November 20 (pdf of Notes pages 128–133)
- Material from Section 6.2
- Graph Theory definitions
- Labeled trees
- Binary trees
Tuesday, November 27 (pdf of Notes pages 134–139)
- Material about q-analogs
- q-factorials, q-Binomial coefficients
- Multivariate generating functions
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