1 The Foundations： 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： 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
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