METHODS Basic methods When we add and when we subtract When we multiply When we divide Applications of basic counting principles The pigeonhole principle Notes Chapter review Exercises Solutions to exercises Supplementary exercises Applications of basic methods Multisets and compositions Set partitions Partitions of integers The inclusion-exclusion principle The twelvefold way Notes Chapter review Exercises Solutions to exercises Supplementary exercises Generating functions Power series Warming up: Solving recurrence relations Products of generating functions Compositions of generating functions A different type of generating functions Notes Chapter review Exercises Solutions to exercises Supplementary exercises TOPICS Counting permutations Eulerian numbers The cycle structure of permutations Cycle structure and exponential generating functions Inversions Advanced applications of generating functions to permutation enumeration Notes Chapter review Exercises Solutions to exercises Supplementary exercises Counting graphs Trees and forests Graphs and functions When the vertices are not freely labeled Graphs on colored vertices Graphs and generating functions Notes Chapter review Exercises Solutions to exercises Supplementary exercises Extremal combinatorics Extremal graph theory Hypergraphs Something is more than nothing: Existence proofs Notes Chapter review Exercises Solutions to exercises Supplementary exercises AN ADVANCED METHOD Analytic combinatorics Exponential growth rates Polynomial precision More precise asymptotics Notes Chapter review Exercises Solutions to exercises Supplementary exercises SPECIAL TOPICS Symmetric structures Designs Finite projective planes Error-correcting codes Counting symmetric structures Notes Chapter review Exercises Solutions to exercises Supplementary exercises Sequences in combinatorics Unimodality Log-concavity The real zeros property Notes Chapter review Exercises Solutions to exercises Supplementary exercises Counting magic squares and magic cubes A distribution problem Magic squares of fixed size Magic squares of fixed line sum Why magic cubes are different Notes Chapter review Exercises Solutions to exercises Supplementary exercises Appendix: The method of mathematical induction Weak induction Strong induction t;B> Exercises Solutions to exercises Supplementary exercises Generating functions Power series Warming up: Solving recurrence relations Products of generating functions Compositions of generating functions A different type of generating functions Notes Chapter review Exercises Solutions to exercises Supplementary exercises TOPICS Counting permutations Eulerian numbers The cycle structure of permutations Cycle structure and exponential generating functions Inversions Advanced applications of generating functions to permutation enumeration Notes Chapter review Exercises Solutions to exercises Supplementary exercises Counting graphs Trees and forests Graphs and functions When the vertices are not freely labeled Graphs on colored vertices Graphs and generating functions Notes Chapter review Exercises Solutions to exercises Supplementary exercises Extremal combinatorics Extremal graph theory Hypergraphs Something is more than nothing: Existence proofs Notes Chapter review Exercises Solutions to exercises Supplementary exercises AN ADVANCED METHOD Analytic combinatorics Exponential growth rates Polynomial precision More precise asymptotics Notes Chapter review Exercises Solutions to exercises Supplementary exercises SPECIAL TOPICS Symmetric structures Designs Finite projective planes Error-correcting codes Counting symmetric structures Notes Chapter review Exercises Solutions to exercises Supplementary exercises Sequences in combinatorics Unimodality Log-concavity The real zeros property Notes Chapter review Exercises Solutions to exercises Supplementary exercises Counting magic squares and magic cubes A distribution problem Magic squares of fixed size Magic squares of fixed line sum Why magic cubes are different Notes Chapter review Exercises Solutions to exercises Supplementary exercises Appendix: The method of mathematical induction Weak induction Strong induction BR>Inversions Advanced applications of generating functions to permutation enumeration Notes Chapter review Exercises Solutions to exercises Supplementary exercises Counting graphs Trees and forests Graphs and functions When the vertices are not freely labeled Graphs on colored vertices Graphs and generating functions Notes Chapter review Exercises Solutions to exercises Supplementary exercises Extremal combinatorics Extremal graph theory Hypergraphs Something is more than nothing: Existence proofs Notes Chapter review Exercises Solutions to exercises Supplementary exercises AN ADVANCED METHOD Analytic combinatorics Exponential growth rates Polynomial precision More precise asymptotics Notes Chapter review Exercises Solutions to exercises Supplementary exercises SPECIAL TOPICS Symmetric structures Designs Finite projective planes Error-correcting codes Counting symmetric structures Notes Chapter review Exercises Solutions to exercises Supplementary exercises Sequences in combinatorics Unimodality Log-concavity The real zeros property Notes Chapter review Exercises Solutions to exercises Supplementary exercises Counting magic squares and magic cubes A distribution problem Magic squares of fixed size Magic squares of fixed line sum Why magic cubes are different Notes Chapter review Exercises Solutions to exercises Supplementary exercises Appendix: The method of mathematical induction Weak induction Strong induction ;lt;B> Hypergraphs Something is more than nothing: Existence proofs Notes Chapter review Exercises Solutions to exercises Supplementary exercises AN ADVANCED METHOD Analytic combinatorics Exponential growth rates Polynomial precision More precise asymptotics Notes Chapter review Exercises Solutions to exercises Supplementary exercises SPECIAL TOPICS Symmetric structures Designs Finite projective planes Error-correcting codes Counting symmetric structures Notes Chapter review Exercises Solutions to exercises Supplementary exercises Sequences in combinatorics Unimodality Log-concavity The real zeros property Notes Chapter review Exercises Solutions to exercises Supplementary exercises Counting magic squares and magic cubes A distribution problem Magic squares of fixed size Magic squares of fixed line sum Why magic cubes are different Notes Chapter review Exercises Solutions to exercises Supplementary exercises Appendix: The method of mathematical induction Weak induction Strong induction cting codes Counting symmetric structures Notes Chapter review Exercises Solut.