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| preface 1 sets and logic 1.1 sets 1.2 propositions 1.3 conditional propositions and logical equivalence 1.4 arguments and rules of inference 1.5 quantifiers 1.6 nested quantifiers problem-solving corner: quantifiers notes chapter review chapter self-test computer exercises 2 proofs 2.1 mathematical systems, direct proofs, and counterexamples 2.2 more methods of proof problem-solving corner: proving some properties of real numbers 2.3 resolution proofst 2.4 mathematical induction problem-solving corner: mathematical induction 2.5 strong form of induction and the well-ordering property notes chapter review chapter self-test computer exercises 3 functions, sequences, and relations 3.1 functions problem-solving corner: functions 3.2 sequences and strings 3.3 relations 3.4 equivalence relations problem-solving corner: equivalence relations 3.5 matrices of relations 3.6 relational databasest notes chapter review chapter self-test computer exercises 4 algorithms 4.1 introduction 4.2 examples of algorithms 4.3 analysis of algorithms problem-solving corner: design and analysis of an algorithm 4.4 recursive algorithms notes chapter review chapter self-test computer exercises 5 introduction to number theory 5.1 divisors 5.2 representations of integers and integer algorithms 5.3 the euclidean algorithm problem-solving corner: making postage 5.4 the rsa public-key cryptosystem notes chapter review chapter self-test computer exercises 6 counting methods and the pigeonhole principle 6.1 basic principles 265 problem-solving corner: counting …… 7 recurence relations 8 graph theory 9 trees 10 network models 11 boolean algebras and combinatorial circuits 12 automata, grammars, and languages 13 computational geometry a matrices b algebra review c pesudocode references hints and solutions to selected exercises index |
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