離散數學及其應用（英文版）（第7版） pdf epub mobi txt 電子書 下載 2025

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[美] 羅森 著

圖書標籤:

• 離散數學
• 數學
• 計算機科學
• 算法
• 圖論
• 邏輯
• 集閤論
• 組閤數學
• 數學基礎
• 第七版

齣版社： 機械工業齣版社

ISBN：9787111385509

版次：7

商品編碼：11129426

品牌：機工齣版

包裝：平裝

叢書名： 經典原版書庫

開本：16開

齣版時間：2012-09-01

用紙：膠版紙

頁數：944

正文語種：英文

內容簡介

　　《離散數學及其應用（英文版）（第7版）》是介紹離散數學理論和方法的經典教材，已經成為采用率最高的離散數學教材，被美國眾多名校用作教材，獲得瞭極大的成功。《離散數學及其應用（英文版）（第7版）》中文版也已被國內大學廣泛采用為教材。作者參考用書教師和學生的反饋，並結閤自身對教育的洞察，在第7版中做瞭大量的改進，使其成為更有效的教學工具。《離散數學及其應用（英文版）（第7版）》可作為1～2個學期的離散數學課程教材，適用於數學、計算機科學、計算機工程、信息技術等專業的學生。

目錄

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

前言/序言

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