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离散数学暨组合数学(影印版)

离散数学暨组合数学(影印版)

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作者: 安德森著

出版社: 清华大学出版社

出版时间: 2004-01

版次: 1

ISBN: 9787302077893

定价: 79.00

装帧: 平装

开本: 其他

纸张: 胶版纸

页数: 807页

分类: 自然科学

11人买过

本书结构严谨、简洁易懂、逻辑性强，其内容涵盖了离散数学各种基础主题，每个主题的概念都与计算机工程和数学的实际应用相结合。本书不仅介绍了很多的基本概念，而且还讨论了一些扩展主题，如逻辑、集合、图、树、迭代、代数、计算理论和组合数学，并有大量实例，以帮助学生巩固所学知识。

  全书讨论严谨，实例、习题多，是一本有关计算机基础数学理论的很好教材。 preface

1 Truth Tables,Logic,and Proofs

  1.1 Statements and Connectives

  1.2 Conditional Statements

  1.3 Equivalent Statements

  1.4 Axiomatic Systems:Arguments and Proofs

  1.5 Completeness in Propositional Logic

  1.6 Karnaugh Maps

  1.7 Circuit Diagrams

2 Set Theory

  2.1 Introduction to Sets

  2.2 Set Operations

  2.3 Venn Diagrams

  2.4 Boolean Algebras

  2.5 Relations

  2.6 Partially Ordered Sets

  2.7 Equivalence Relations

3 Logic,Integers,and Proofs

  3.1 Predicate Calculus

  3.2 Basic Concepts of Proofs and the Structure of Integers

  3.3 Mathematical Induction

  3.4 Divisibility

  3.5 Prime Integers

  3.6 Congruence Relations

4 Functions and Matrices

  4.1 Functions

  4.2 Special Functions

  4.3 Matrices

  4.4 Cardinality

  4.5 Cardinals Continued

5 Algorithms and Recursion

  5.1 The “for” Procedure and Algorithms for Matrices

  5.2 Recursive Functions and Algorithms

  5.3 Complexity of Algorithms

  5.4 Sorting Algorithms

  5.5 Prefix and Suffix Notation

  5.6 Binary and Hexadecimal Numbers

  5.7 Signed Numbers

  5.8 Matrices Continued

6 Graphs,Directed Graphs,and Trees

  6.1 Graphs

  6.2 Directed Graphs

  6.3 Trees

  6.4 Instant Insanity

  6.5 Euler Paths and Cycles

  6.6 Incidence and Adjacency Matrices

  6.7 Hypercubes and Gray Code

7 Number Theory

  7.1 Sieve of Eratosthenes

  7.2 Fermat's Factorization Method

  7.3 The Division and Euclidean Algorithms

  7.4 Continued Fractions

  7.5 Convergents

8 Counting and Probability

  8.1 Basic Counting Principles

  8.2 Inclusion-Exclusion Introduced

  8.3 Permutations and Combinations

  8.4 Generating Permutations and Combinations

  8.5 Probability Introduced

  8.6 Generalized Permutations and Combinations

  8.7 Permutations and Combinations with Repeition

  8.8 Pigeonhole Principle

  8.9 Probability Revisited

  8.10 Bayes' Theorem

  8.11 Markov Chains

9 Algebraic Structures

10 Number Theory Revisited

11 Recursion Revisited

12 Counting Continued

13 Generating Functions

14 Graphs Revisited

15 Trees

16 Networks

17 Theory of Computation

18 Theory of Codes

19 Enumeration of Colors

20 Rings,Integral Domains,and Fields

21 Group and Semigroup Characters

22 Applications of Number Theory

Bibliography

Hints and Solutions to Selected Exercises

Index
内容简介:
本书结构严谨、简洁易懂、逻辑性强，其内容涵盖了离散数学各种基础主题，每个主题的概念都与计算机工程和数学的实际应用相结合。本书不仅介绍了很多的基本概念，而且还讨论了一些扩展主题，如逻辑、集合、图、树、迭代、代数、计算理论和组合数学，并有大量实例，以帮助学生巩固所学知识。

全书讨论严谨，实例、习题多，是一本有关计算机基础数学理论的很好教材。
目录:
preface

1 Truth Tables,Logic,and Proofs

  1.1 Statements and Connectives

  1.2 Conditional Statements

  1.3 Equivalent Statements

  1.4 Axiomatic Systems:Arguments and Proofs

  1.5 Completeness in Propositional Logic

  1.6 Karnaugh Maps

  1.7 Circuit Diagrams

2 Set Theory

  2.1 Introduction to Sets

  2.2 Set Operations

  2.3 Venn Diagrams

  2.4 Boolean Algebras

  2.5 Relations

  2.6 Partially Ordered Sets

  2.7 Equivalence Relations

3 Logic,Integers,and Proofs

  3.1 Predicate Calculus

  3.2 Basic Concepts of Proofs and the Structure of Integers

  3.3 Mathematical Induction

  3.4 Divisibility

  3.5 Prime Integers

  3.6 Congruence Relations

4 Functions and Matrices

  4.1 Functions

  4.2 Special Functions

  4.3 Matrices

  4.4 Cardinality

  4.5 Cardinals Continued

5 Algorithms and Recursion

  5.1 The “for” Procedure and Algorithms for Matrices

  5.2 Recursive Functions and Algorithms

  5.3 Complexity of Algorithms

  5.4 Sorting Algorithms

  5.5 Prefix and Suffix Notation

  5.6 Binary and Hexadecimal Numbers

  5.7 Signed Numbers

  5.8 Matrices Continued

6 Graphs,Directed Graphs,and Trees

  6.1 Graphs

  6.2 Directed Graphs

  6.3 Trees

  6.4 Instant Insanity

  6.5 Euler Paths and Cycles

  6.6 Incidence and Adjacency Matrices

  6.7 Hypercubes and Gray Code

7 Number Theory

  7.1 Sieve of Eratosthenes

  7.2 Fermat's Factorization Method

  7.3 The Division and Euclidean Algorithms

  7.4 Continued Fractions

  7.5 Convergents

8 Counting and Probability

  8.1 Basic Counting Principles

  8.2 Inclusion-Exclusion Introduced

  8.3 Permutations and Combinations

  8.4 Generating Permutations and Combinations

  8.5 Probability Introduced

  8.6 Generalized Permutations and Combinations

  8.7 Permutations and Combinations with Repeition

  8.8 Pigeonhole Principle

  8.9 Probability Revisited

  8.10 Bayes' Theorem

  8.11 Markov Chains

9 Algebraic Structures

10 Number Theory Revisited

11 Recursion Revisited

12 Counting Continued

13 Generating Functions

14 Graphs Revisited

15 Trees

16 Networks

17 Theory of Computation

18 Theory of Codes

19 Enumeration of Colors

20 Rings,Integral Domains,and Fields

21 Group and Semigroup Characters

22 Applications of Number Theory

Bibliography

Hints and Solutions to Selected Exercises

Index

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