UIUC MATH 580, 2008. — 43 pages.
Combinatorial Arguments.
Classical Models.
Identities.
Applications.
Recurrence Relations.
Obtaining Recurrences.
Elementary Solution Methods.
Further Topics.
Generating Functions.
Ordinary Generating Functions.
Coefficients and Applications.
Exponential Generating Functions.
Partition of Integers.
Further Topics.
Principle of Inclusion-Exclusion.
Polya-Redfield Counting.
5, 6, 7 Graph Intro.
Planar Graphs.
Embeddings and Euler’s Formula.
Structure of planar Graphs.
Coloring of Planar Graphs.
Ramsey Theory.
The Pigeonhole Principle.
Ramsey’s Theorem.
Further Topics.
Partially Ordered Sets.
Structure of Posets.
Symmetric Chains and LYM.
The probabilistic Method.
Existence and Expectation.
Refinements of Basic Methods.
