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### Math 21-228 Fall 2016 Combinatorics Course Calendar

Updated 1 December 2016

This calendar is subject to revision throughout the term.
• Monday, 29 August: Introduction: What is Discrete Mathematics? Counting subsets. Sections 1.1-1.3
• Wednesday, 31 August: Sequences, permutations, and ordered subsets. Sections 1.5-1.7
• Friday, 2 September: Meet the binomial coefficients, an enumerativist's best friend. Section 1.8, 3.1, 3.5
• Monday, 5 September: Holiday
• Wednesday, 7 September: Mathematical induction (remember that?) Section 2.1-2.2
• Friday, 9 September: Inclusion/Exclusion. Section 2.3
• Monday, 12 September: Inclusion/Exclusion, continued. Pigeonhole Principle. Sections 2.3-2.4
• Wednesday, 14 September: The binomial coefficients return, and get fancy: Multinomial Theorem and More Pascal's Triangle. Sections 3.1, 3.2-3.6
• Friday, 16 September: More Pascal. Section 3.6-3.7. Introduction to recurrences: Fibonacci numbers. Section 4.1-4.2
• Monday, 26 September: Exam 1
• Wednesday, 28 September: Intro to generating functions, continued Generatingfunctionology by Wilf, Sections 1.1,1.2.
• Friday, 30 September: Counting with generating functions: products
• Monday, 3 October: Counting with generating functions: products, continued.
• Wednesday, 5 October: Exponential generating functions Generatingfunctionology by Wilf, Section 2.3.
• Friday, 7 October: Exponential generating functions, continued.
• Monday, 10 October: Exponential generating functions, continued.
• Wednesday, 12 October: Two-variable generating functions and exponential families.
• Friday, 14 October: Two-variable generating functions and exponential families, continued.
• Monday, 17 October: Two-variable generating functions and exponential families, continued.
• Wednesday, 19 October: Graph theory basics. Sections 7.1, 7.2.
• Friday, 21 October: Holiday
• Monday, 24 October: Exam 2
• Wednesday, 26 October: Traversibility. Section 7.3.
• Friday, 28 October: Trees and Cayley's Theorem. Sections 8.1-8.3.
• Monday, 31 October: Trees meet traversibility: Traveling Salesman and related problems. Chapter 9.
• Wednesday, 2 November: Traveling Salesman and related problems, continued.
• Friday, 4 November: Bipartite graphs and matchings. Section 10.1, 10.2.
• Monday, 7 November: Hall's Theorem. Section 10.3.
• Wednesday, 9 November: Finding perfect matchings with augmenting paths. Section 10.4.
• Friday, 11 November: Finding perfect matchings, continued.
• Monday, 14 November: Combinatorial Geometry, introduction. Section 11.1.
• Wednesday, 16 November: Counting regions and convex polygons, Section 11.2-3.
• Friday, 18 November: Graph embeddings and planarity, introduction. Euler's Formula. Section 12.1.
• Monday, 21 November: Exam 3
• Wednesday, 23 November: Holiday
• Friday, 25 November:Holiday
• Monday, 28 November: Euler's formula and embedding graphs in other surfaces. Notes
• Wednesday, 30 November: Kuratowski's Theorem. Section 12.2 and supplementary notes
• Friday, 2 December: Kuratowski's Theorem, continued from supplementary notes.
• Monday, 5 December: Coloring bipartite graphs. Section 13.1, 13.2.
• Wednesday, 7 December: Coloring. Section 13.3.
• Friday, 9 December: The Four-Color Theorem: coloring meets planarity. Section 13.4.