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Lecture Slides (Fall 2015)
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Lecture 1 – Motivating Questions
Lecture 2 – Enumeration Basics
Lecture 3 – Binomial Coefficients, Lattice Paths, & Recurrences
Lecture 4 – Mathematical Induction & the Euclidean Algorithm
Lecture 5 – Multinomial Theorem, Pigeonhole Principle, & Complexity
Lecture 6 – Induction Examples & Introduction to Graph Theory
Lecture 7 – More Graph Theory Basics: Trees & Euler Circuits
Lecture 8 – Hamiltonian Graphs, Complexity, & Chromatic Number
Lecture 9 – Chromatic Number vs. Clique Number & Girth
Lecture 10 – Perfect Graphs, Interval Graphs, & Coloring Algorithms
Lecture 11 – Planar Graphs & Euler’s Formula
Lecture 12 – More on Coloring & Planarity
Lecture 13 – Introduction to Posets
Lecture 14 – Posets: Mirsky’s & Dilworth’s Theorems
Lecture 15 – Cover Graphs, Comparability Graphs, & Transitive Orientations
Lecture 16 – Interval Order & Interval Graph Algorithms
Lecture 17 – Subset Lattices
Lecture 18 – Inclusion/Exclusion
Lecture 19 – Generating Functions
Lecture 20 – Solving Recurrence Equations
Lecture 21- More on Recurrence Equations
Lecture 22
Lecture 23
Lecture 24
Lecture 25
Lecture 26 – Probability
Lecture 27 – Ramsey Numbers & Markov Chains
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