离散数学及其应用

《离散数学及其应用(英文版第7版)》

preface iv

about theauthor xiii

the companion website xiv

to the studentxvi

list of symbols xix

1 the foundations：logic and proofs

1．1 propositional logic

1．2 applications of propositional logic

1．3 propositional equivalences

1．4 predicates andquantifiers

1．5 nested quantifiers

1．6 rules of inference

1．7 introduction to proofs

1．8 proofmethods and strategy

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2 basic structures：sets，functions，sequences，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

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3 algorithms

3．1 algorithms

3．2 the growth of functions

3．3 complexity of algofithms

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4 number theory and cryptography

4．1 divisibilitv andmodular arithmetic

4．2 integer representations andalgorithms

4．3 primesand greatest common divisors

4．4 solving congruences

4．5 applications of congruences

4．6 cryptography

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5 induction and recursion

5．1 mathematical induction

5．2 strong induction and well-ordering

5．3 recursive definitions and structural induction

5．4 recursive algorithms

5．5 program correctness

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6 counting

6．1 tlle basics of counting

6．2 the pigeonhole principle

6．3 permutations and combinations

6．4 binomial coefficients and identities

6．5 generalized permutations and combinations

6．6 generating permutations and combinations

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7 discrete probability

7．1 an introduction to discrete probability

7．2 probability theory

7．3 bayes’theorem

7．4 expected value and variance

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8 advanced counring technigues

8．1 applications of recurrence relations

8．2 solving linear recurrence relations

8．3 divide-and-conquer algorithms and recurrence relations

8．4 generating functions

8．5 inclusion-exclusion

8．6 applications of inclusion-exclusion

end—of-chapter material

9 relations

9．1 relations and their properties

9．2 n-ary relations and theirapplications

9．3 representing relations

9．4 closures of relations

9．5 equivalence relations

9．6 partial orderings

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10 graphs

10．1 graphs andgraphmodels

10．2 graph terminology and special types of graphs

10．3 representing graphs and graph isomorphism

10．4 connectivity

10．5 eulerandhamiltonpaths

10．6 shortest．pathproblems

10．7 planargraphs

10．8 graphcoloring

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11 trees

11．1 introduction to trees

11．2 applications of trees

11．3 tree travcrsal

11．4 spanning trees

11．5 minimum spanning trees

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12 boolean algebra

12．1 boolean functions

12．2 representing boolean functions

12．3 logic gates

12．4 minimization of circuits

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13 modeling cornputation

13．1 languagesand grammars

13．2 finite-state machines with output

13．3 finite-state machines with no output

13．4 languagerecognition

13．5 turing machines

end-of-chapter material

appendixes

1 axioms for the real numbers and the positive integers

2 exponential and logarithmic functions

3 pseudocode

suggestedreadings b-1

answers to odd-numbered exercises s-1

photo credits c-1

index ofbiographies i-1

index i-2

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