Preface To the Student 1 The Foundations: Logic and Proofs 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs 1.7 Proof Methods and Strategy
End-of-Chapter Material 2 Basic Structures: Sets, Functions, Sequences and Sums 2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations
End-of-Chapter Material 3 The Fundamentals: Algorithms, the Integers, and Matrices 3.1 Algorithms 3.2 The Growth of Functions 3.3 Complexity of Algorithms 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms 3.7 Applications of Number Theory 3.8 Matrices
End-of-Chapter Material 4 Induction and Recursion 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering 4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms 4.5 Program Correctness
End-of-Chapter Material 5 Counting 5.1 The Basics of Counting 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.4 Binomial Coefficients 5.5 Generalized Permutations and Combinations 5.6 Generating Permutations and Combinations
End-of-Chapter Material 6 Discrete Probability 6.1 An Introduction to Discrete Probability 6.2 Probability Theory 6.3 Bayes’ Theorem 6.4 Expected Value and Variance
End-of-Chapter Material 7 Advanced Counting Techniques 7.1 Recurrence Relations 7.2 Solving Linear Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.4 Generating Functions 7.5 Inclusion-Exclusion 7.6 Applications of Inclusion-Exclusion
End-of-Chapter Material 8 Relations 8.1 Relations and Their Properties 8.2 n-ary Relations and Their Applications 8.3 Representing Relations 8.4 Closures of Relations 8.5 Equivalence Relations 8.6 Partial Orderings
End-of-Chapter Material 9 Graphs 9.1 Graphs and Graph Models 9.2 Graph Terminology and Special Types of Graphs 9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Paths 9.6 Shortest-Path Problems 9.7 Planar Graphs 9.8 Graph Coloring
End-of-Chapter Material 10 Trees 10.1 Introduction to Trees 10.2 Applications of Trees 10.3 Tree Traversal 10.4 Spanning Trees 10.5 Minimum Spanning Trees
End-of-Chapter Material 11 Boolean Algebra 11.1Boolean Functions 11.2 Representing Boolean Functions 11.3 Logic Gates 11.4 Minimization of Circuits
End-of-Chapter Material 12 Modeling Computation 12.1 Languages and Grammars 12.2 Finite-State Machines with Output 12.3 Finite-State Machines with No Output 12.4 Language Recognition 12.5 Turing Machines
End-of-Chapter Material Appendixes A.1 Axioms for the Real Numbers and the Positive Integers A.2 Exponential and Logarithmic Functions A.3 Pseudocode Suggested Readings Answers to Odd-Numbered Exercises Photo Credits Index of Biographies Index
2007