離散數學及其應用(英文版原書第8版)/經典原版書庫
內容大鋼
本書是介紹離散數學理論和方法的經典教材，被全球數百所高校採用，獲得了極大的成功。第8版做了與時俱進的更新，添加了多重集、字元串匹配演算法、同態加密、數據挖掘中的關聯規則、語義網路等內容，同時更新了配套教輔資源，成為更加實用的教學工具。本書可作為1?2個學期的離散數學課程教材，適用於數學、電腦科學、電腦工程、信息技術等專業的學生。
本書特色：
例題：共800多道例題，用於闡明概念、建立不同主題之間的關聯以及介紹實際應用。
應用：涉及的領域包括電腦科學、數據網路、心理學、化學、工程學、語言學、生物學、商業和網際網路等，展示了離散數學的實用性。
演算法：每一章都介紹了一些關鍵演算法，提供偽代碼，並簡要分析其計算複雜度。
歷史資料：給出了89位數學家和電腦科學家的簡短傳記，幫助讀者了解不同技術的歷史背景和發展軌跡。
練習、複習題和補充練習：共有4200多道難度各異的練習題，可以滿足不同層次學生的需求。此外，還有一些研究性題目，幫助學生通過計算來探索新知識和新想法。
作者介紹
(美)肯尼思·H.羅森|責編:曲熠
肯尼思·H.羅森（Kenneth H.Rosen），于1972年獲密歇根大學安娜堡分校數學學士學位，1976年獲麻省理工學院數學博士學位。Rosen曾就職于科羅拉多大學、俄亥俄州立大學、緬因大學和蒙茅斯大學，教授離散數學、演算法設計和電腦安全方面的課程；他還曾加盟貝爾實驗室，並且是AT&T貝爾實驗室的傑出技術人員。他的著作《初等數論及其應用》和《離散數學及其應用》均被翻譯成多種語言，在全球數百所大學中廣為採用。
目錄
1 The Foundations: Logic and Proofs
1.1 Propositional Logic
1.2 Applications of Propositional Logic
1.3 Propositional Equivalences
1.4 Predicates and Quantifiers
1.5 Nested Quantifiers
1.6 Rules of Inference
1.7 Introduction to Proofs
1.8 Proof Methods and Strategy
End-of-Chapter Material
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-Chapter Material
3 Algorithms
3.1 Algorithms
3.2 The Growth of Functions
3.3 Complexity of Algorithms
End-of-Chapter Material
4 Number Theory and Cryptography
4.1 Divisibility and Modular Arithmetic
4.2 Integer Representations and Algorithms
4.3 Primes and 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 The Basics of Counting
6.2 The Pigeonhole Principle
6.3 Permutations and Combinations
6.4 Binomial Coefficients and Identifies
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 Counting Techniques
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 Their Applications
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 and Graph Models
10.2 Graph Terminology and Special Types of Graphs
10.3 Representing Graphs and Graph Isomorphism
10.4 Connectivity
10.5 Euler and Hamilton Paths
10.6 Shortest-Path Problems
10.7 Planar Graphs
10.8 Graph Coloring
End-of-Chapter Material
11 Trees
11.1 Introduction to Trees
11.2 Applications of Trees
11.3 Tree Traversal
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 Computation
13.1 Languages and Grammars
13.2 Finite-State Machines with Output
13.3 Finite-State Machines with No Output
13.4 Language Recognition
13.5 Turing Machines
End-of-Chapter Material
Appendices
1 Axioms for the Real Numbers and the Positive Integers
2 Exponential and Logarithmic Functions
3 Pseudocode
Suggested Readings B-1
Answers to Odd-Numbered Exercises S-1
Index of Biographies I-1
Index I-2
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