基本信息·出版社：电子工业出版社 ·页码：766 页 ·出版日期：2009年04月 ·ISBN：7121085348/9787121085345 ·条形码：9787121085345 ·版本：第1版 · ...
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离散数学(第7版)(英文版) |
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离散数学(第7版)(英文版) |
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基本信息·出版社：电子工业出版社
·页码：766 页
·出版日期：2009年04月
·ISBN：7121085348/9787121085345
·条形码：9787121085345
·版本：第1版
·装帧：平装
·开本：16
·正文语种：英语
·丛书名：国外计算机科学教材系列
·外文书名：Discrete Mathematics,Seventh Edition
内容简介 《离散数学(第7版)(英文版)》从算法分析和问题求解的角度，全面系统地介绍了离散数学的基础概念及相关知识，并在其前一版的基础上进行了修改与扩展。书中通过大量实例，深入浅出地讲解了数理逻辑、组合算法、图论、布尔代数、网络模型、形式语言与自动机理论等与计算机科学密切相关的前沿课题，既着重于各部分内容之间的紧密联系，又深入探讨了相关的概念、理论、算法和实际应用。《离散数学(第7版)(英文版)》内容叙述严谨、推演详尽，各章配有相当数量的习题与书后的提示和答案，为读者迅速掌握相关知识提供了有效的帮助。
编辑推荐 《离散数学(第7版)(英文版)》为电子工业出版社出版发行。
目录 Preface XI
1 Sets and Logic
1.1 Sets
1.2 Propositions
1.3 Conditional Propositions and Logical Equivalence
1.4 Arguments and Rules of Inference
1.5 Quantifiers
1.6 Nested Quantifiers
Problem-Solving Corner: Quantifiers
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
2 Proofs
2.1 Mathematical Systems, Direct Proofs, and Counterexamples
2.2 More Methods of Proof
Problem-Solving Corner: Proving Some Properties of Real Numbers
2.3 Resolution Proofst
2.4 Mathematical Induction
Problem-Solving Corner: Mathematical Induction
2.5 Strong Form of Induction and the Well-Ordering Property
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
3 Functions,Sequences,and Relations
3.1 Functions
Problem-Solving Corner: Functions
3.2 Sequences and Strings
3.3 Relations
3.4 Equivalence Relations
Problem-Solving Corner: Equivalence Relations
3.5 Matrices of Relations
3.6 Relational Databases
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
4 Algorithms
4.1 Introduction
4.2 Examples of Algorithms
4.3 Analysis of Algorithms
Problem-Solving Corner: Design and Analysis of an Algorithm
4.4 Recursive Algorithms
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
5 Introduction to Number Theory
5.1 Divisors
5.2 Representations of Integers and Integer Algorithms
5.3 The Euclidean Algorithm
Problem-Solving Corner: Making Postage
5.4 The RSA Public-Key Cryptosystem
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
6 Counting Methods and the Pigeonhole Principle
6.1 Basic Principles
Problem-Solving Corner: Counting
6.2 Permutations and Combinations
Problem-Solving Comer:. Combinations
6.3 Generalized Permutations and Combinations
6.4 Algorithms for Generating Permutations and Combinations
6.5 Introduction to Discrete Probabilityt
6.6 Discrete Probability Theoryt
6.7 Binomial Coefficients and Combinatorial Identities
6.8 The Pigeonhole Principle
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
7 Recurrence Relations
7.1 Introduction
7.2 Solving Recurrence Relations
Problem-Solving Corner: Recurrence Relations
7.3 Applications to the Analysis of Algorithms ..
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
8 Graph Theory
8.1 Introduction
8.2 Paths and Cycles
Problem-Solving Corner: Graphs
8.3 Hamiltonian Cycles and the Traveling Salesperson Problem
8.4 A Shortest-Path Algorithm
8.5 Representations of Graphs
8.6 Isomorphisms of Graphs
8.7 Planar Graphs
8.8 Instant Insanityt
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
9 Trees
9.1 Introduction
9.2 Terminology and Characterizations of Trees
Problem-Solving Corner: Trees
9.3 Spanning Trees
9.4 Minimal Spanning Trees
9.5 Binary Trees
9.6 Tree Traversals
9.7 Decision Trees and the Minimum Time for Sorting
9.8 Isomorphisms of Trees
9.9 Game Treest
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
10 Network Models
10.1 Introduction
10.2 A Maximal Flow Algorithm
10.3 The Max Flow, Min Cut Theorem
10.4 Matching
Problem-Solving Corner: Matching
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
11 Boolean Algebras and Combinatorial Circuits
11.1 Combinatorial Circuits
11.2 Properties of Combinatorial Circuits
11.3 Boolean Algebras
Problem-Solving Corner: Boolean Algebras
11.4 Boolean Functions and Synthesis of Circuits
11.5 Applications
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
12 Automata,Grammars,and Languages
12.1 Sequential Circuits and Finite-State Machines
12.2 Finite-State Automata
12.3 Languages and Grammars
12.4 Nondeterministic Finite-State Automata
12.5 Relationships Between Languages and Automata
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
13 Computational Geometry
13.1 The Closest-Pair Problem
13.2 An Algorithm to Compute the Convex Hull
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
Appendix
A Matrices
B Algebra Review
C Pseudocode
References
Hints and Solutions to Selected Exercises
Index
……
序言 This updated edition is intended for a one- or two-term introductory course in discrete mathematics, based on my experience in teaching this course over many years and requests from users of previous editions. Formal mathematics prerequisites are minimal; calculus is not required. There are no computer science prerequisites. The book includes examples, exercises, figures, tables, sections on problem-solving, sections containing problem-solving tips, section reviews, notes, chapter reviews, self-tests, and computer exercises to help the reader master introductory discrete mathematics. In addition, an Instructor's Guide and website are available.
In the early 1980s there were few textbooks appropriate for an introductory course in discrete mathematics. However, there was a need for a course that extended students' mathematical maturity and ability to deal with abstraction, which also included useful topics such as combinatorics, algorithms, and graphs. The original edition of thishook （1984） addressed this need and significantly influenced the development of discrete mathematics courses. Subsequently, discrete mathematics courses were endorsed by many groups for several different audiences, including mathematics and computer science majors. A panel of the Mathematical Association of America （MAA） endorsed a year-long course in discrete mathematics. The Educational Activities Board of the Institute of Electrical and Electronics Engineers （IEEE） recommended a freshman discrete mathematics course. The Association for Computing Machinery （ACM） and IEEE accreditation guidelines mandated a discrete mathematics course. This edition, like its predecessors, includes topics such as algorithms, combinatorics, sets, functions, and mathematical induction endorsed by these groups. It also addresses understanding and constructing proofs and, generally, expanding mathematical maturity.
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