Combinatorics by Michael Tait

Overview & Synopsis

This PDF covers the
following topics related to Combinatorics, Introduction, Enumeration,
Sequences and the Multiplication Principle, Permutations and Combinations,
Bijections and Double Counting, Estimation, InclusionExclusion, 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, Lovasz Local Lemma,
Extremal Graph Theory, Turans Theorem, Projective planes, Sidon sets,
Constructing C4free graphs, Ramsey numbers, Combinatorial Number Theory,
Erd osKoRado Theorem, Spectral graph theory, Linear Algebra Preliminaries,
The adjacency matrix, Short proofs of old results using spectral graph
theory, The GrahamPollak Theorem, The ExpanderMixing Lemma, The
HoffmanSingleton Theorem.