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1 The Foundations£º Logic and Proofs 1£®1 Propositional Logic 1£®2 Applications of Propositional Logic 1£®3 Propositional Equivalences 1£®4 Predicates and Quantifiers 1£®5 Nested Quantifiers 1£®6 Rules of Inference 1£®7 Introduction to Proofs 1£®8 Proof Methods and Strategy End-of Chapter Material 2 Basic Structures£º Sets£¬ Functions£¬ Sequences9 Sums£¬ and Matrices 2£®1 Sets 2£®2 Set Operations 2£®3 Functions 2£®4 Sequences and Summations 2£®5 Cardinality of Sets 2£®6 Matrices End-of Chapter Material 3 Algorithms 3£®1 Algorithms 3£®2 The Growth of Functions 3£®3 Complexity of Algorithms End-of Chapter Material 4 Number Theory and Cryptography 4£®1 Divisibility and Modular Arithmetic 4£®2 Integer Representations and Algorithms 4£®3 Primes and Greatest Common Divisors 4£®4 Solving Congruences 4£®5 Applications of Congruences 4£®6 Cryptography End-of Chapter Material ¡­¡­ 5 Induction and Recursion 6 Counting 7 Discrete Probability 8 Advanced Counting Techniques 9 Relations 10 Graphs 11 Trees 12 Boolean Algebra 13 Modeling Computation Appendices Suggested Readings B-1 Answers to Odd-Numbered Exercises S£®ie Index of Biographies I-1 Index I-2