离散数学及其应用

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

end-of-chaptermaterial-

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

end-of-chaptermaterial

3 algorithms

3.1 algorithms

3.2 the growth of functions

3.3 complexity of algofithms

end-of-chapter material

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

end-of-chapter material

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

end-of-chapter material

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

end-of-chapter material

7 discrete probability

7.1 an introduction to discrete probability

7.2 probability theory

7.3 bayes'theorem

7.4 expected value and variance

end-of-chapter material

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

end-of-chapter material

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

end-of-chapter material

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

end-of-chapter material

12 boolean algebra

12.1 boolean functions

12.2 representing boolean functions

12.3 logic gates

12.4 minimization of circuits

end-of-chapter material

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

《离散数学及其应用（英文版）（第7版）》是介绍离散数学理论和方法的经典教材，已经成为采用率最高的离散数学教材，被美国众多名校用作教材，获得了极大的成功。《离散数学及其应用（英文版）（第7版）》中文版也已被国内大学广泛采用为教材。作者参考用书教师和学生的反馈，并结合自身对教育的洞察，在第7版中做了大量的改进，使其成为更有效的教学工具。《离散数学及其应用（英文版）（第7版）》可作为1～2个学期的离散数学课程教材，适用于数学、计算机科学、计算机工程、信息技术等专业的学生。