Discrete Mathematics and Applications (Paperback, 2 ed)

I Proofs Logic and Sets Statement Forms and Logical EquivalencesSet Notation Quantifiers Set Operations and IdentitiesValid Arguments Basic Proof Writing Direct Demonstration General Demonstration (Part 1) General Demonstration (Part 2) Indirect Arguments Splitting into Cases Elementary Number Theory Divisors Well-Ordering, Division, and Codes Euclid's Algorithm and Lemma Rational and Irrational Numbers Modular Arithmetic and Encryption Indexed by Integers Sequences, Indexing, and Recursion Sigma Notation Mathematical Induction, An Introduction Induction and Summations Strong Induction The Binomial TheoremRelations General Relations Special Relations on Sets Basics of Functions Special Functions General Set Constructions Cardinality II CombinatoricsBasic Counting The Multiplication Principle Permutations and Combinations Addition and Subtraction Probability Applications of Combinations Correcting for OvercountingMore Counting Inclusion-Exclusion Multinomial Coecients Generating Functions Counting Orbits Combinatorial ArgumentsBasic Graph Theory Motivation and Introduction Special GraphsMatrices Isomorphisms Invariants Directed Graphs and Markov ChainsGraph Properties Connectivity Euler CircuitsHamiltonian Cycles Planar Graphs Chromatic Number Trees and Algorithms Trees Search Trees Weighted TreesAnalysis of Algorithms (Part 1) Analysis of Algorithms (Part 2) A Assumed Properties of Z and R B Pseudocode C Answers to Selected Exercises