离散数学及其应用（英文版·第7版） pdf epub mobi txt 电子书 下载 2025

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[美] 罗森 著

图书标签:

• 离散数学
• 数学
• 计算机科学
• 算法
• 图论
• 逻辑
• 集合论
• 组合数学
• 数学基础
• 高等教育

店铺： 华心图书专营店

出版社： 机械工业出版社

ISBN：9787111385509

商品编码：28401049035

开本：16

出版时间：2012-09-01

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，andmatrices 

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 recurrencerelations 

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 

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