This PDF covers the
following topics related to Combinatorics : Introduction, Enumeration,
Sequences and the Multiplication Principle, Permutations and Combinations,
Bijections and Double Counting, Estimation, Inclusion-Exclusion, Generating
Functions, Formal Power Series, Generating Functions Redux, Change making,
Compositions, Counting Subsets, Counting Strings, The Probabilistic Method,
Preliminaries, The first moment method, Linearity of expectation,
Alterations, Markov and Chebyshev, Chernoff Bound, Lov´asz Local Lemma,
Extremal Graph Theory, Tur´an’s Theorem, Projective planes, Sidon sets,
Constructing C4-free graphs, Ramsey numbers, Combinatorial Number Theory,
Erd os-Ko-Rado Theorem, Spectral graph theory, Linear Algebra Preliminaries,
The adjacency matrix, Short proofs of old results using spectral graph
theory, The Graham-Pollak Theorem, The Expander-Mixing Lemma, The
Hoffman-Singleton Theorem.

**Author(s):** Michael Tait, Carnegie Mellon University

103**Pages**