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简介

离散数学及其应用

离散数学及其应用 9.1分

资源最后更新于 2020-07-26 15:38:07

作者:Kenneth H.Rosen

出版社:机械工业出版社

出版日期:2012-01

ISBN:9787111385509

文件格式: pdf

标签: 离散数学 数学 计算机科学 计算机 算法 CS 计算机基础 英文原版

简介· · · · · ·

本书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。中文版也已被国内大学广泛采用为教材。作者参考使用教师和学生的反馈,并结合自身对教育的洞察,对第7版做了大量的改进,使其成为更有效的教学工具。. 本书可作为1至2个学期的离散数学课入门教材,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。

本书特点

实例:书中有800多个实例,用于阐明概念,联系不同内容,引入各种应用。

应用:书中叙述的应用展示了离散数学在解决现实问题中的使用价值,涉及的应用领域包括计算机科学、数据网络、心理学、化学、工程、语言学、生物学、商业和互联网等。

算法:离散数学的结论常常要用算法来表示,因此本书每一章都介绍了一些关键算法。

历史资料:本书对许多主题的背景作了简要介绍,并以脚注的形式给出了83位对离散数学...

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目录

《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
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