作者：(美)肯尼斯·H.罗森
页数：1604
出版社：哈尔滨工业大学出版社
出版日期：2023
ISBN：9787576706512
电子书格式：pdf/epub/txt
内容简介
本书是一部英文版的权威的数学工具书。本书呈现材料的方式可以让读者快速、轻松地找到和使用关键信息.每章都包含一个词汇表，用来对该章节中最重要的术语提供简洁的定义，单独的主题包含在每章的各个部分和小节中，每个部分都是清晰可辨的。事实被简明扼要地列出来，以便于读者查找和理解.本书还提供了连接各部分的交叉引用参考资料，希望进一步研究某个主题的读者可以查阅列出的资料。本书中材料的选择主要是因为它们的重要性与实用性.为了确保全面性，本书还添加了额外的资料，以便读者在探索中遇到离散数学中的新术语和概念时能够从本书中获得帮助。本书提供了一些例子用以说明一些关键的定义、事实和算法，读者可能会发现一些有趣的事实和谜题也包括在内.读者还将在主要章节之后找到大量传记，重点介绍了离散数学的许多重要贡献者的生平，本书的每一章都包含了一个分为印刷资源和相关网站的参考清单。
目录
1. FOUNDATIONS
1.1 Propositional and Predicate Logic – Jerrold W. Grossman
1.2 Set Theory – Jerrold W. Grossman
1.3 Functions – Jerrold W. Grossman
1.4 Relations – John G. Michaels
1.5 Proof Techniques – Susanna S. Epp
1.6 Axiomatic Program Verification – David Riley
1.7 Logic-Based Computer Programming Paradigms – Mukesh Dalal
2. COUNTING METHODS
2.1 Summary of Counting Problems – John G. Michaels
2.2 Basic Counting Techniques – Jay Yellen
2.3 Permutations and Combinations – Edward W. Packel
2.4 Inclusion/Exclusion – Robert G. Rieper
2.5 Partitions – George E. Andrews and Andrew V. Sills
2.6 Burnside/Pólya Counting Formula – Alan C. Tucker
2.7 M?bius Inversion Counting – Edward A. Bender
2.8 Young Tableaux – Bruce E. Sagan
3. SEQUENCES
3.1 Special Sequences – Thomas A. Dowling and Douglas R. Shier
3.2 Generating Functions – Ralph P. Grimaldi
3.3 Recurrence Relations – Ralph P. Grimaldi
3.4 Finite Differences – Jay Yellen
3.5 Finite Sums and Summation – Victor S. Miller
3.6 Asymptotics of Sequences – Edward A. Bender and Juanjo Rué
3.7 Mechanical Summation Procedures – Kenneth H. Rosen
4. NUMBER THEORY
4.1 Basic Concepts – Kenneth H. Rosen
4.2 Greatest Common Divisors – Kenneth H. Rosen
4.3 Congruences – Kenneth H. Rosen
4.4 Prime Numbers – Jon F. Grantham and Carl Pomerance
4.5 Factorization – Jon F. Grantham and Carl Pomerance
4.6 Arithmetic Functions – Kenneth H. Rosen
4.7 Primitive Roots and Quadratic Residues – Kenneth H. Rosen
4.8 Diophantine Equations – Bart E. Goddard
4.9 Diophantine Approximation – Jeff Shalit
4.10 Algebraic Number Theory – Lawrence C. Washington
4.11 Elliptic Curves – Lawrence C. Washington
5. ALGEBRAIC STRUCTURES – John G. Michaels
5.1 Algebraic Models
5.2 Groups
5.3 Permutation Groups
5.4 Rings
5.5 Polynomial Rings
5.6 Fields
5.7 Lattices
5.8 Boolean Algebras
6. LINEAR ALGEBRA
6.1 Vector Spaces – Joel V. Brawley
6.2 Linear Transformations – Joel V. Brawley
6.3 Matrix Algebra – Peter R. Turner
1.1 Propositional and Predicate Logic – Jerrold W. Grossman
1.2 Set Theory – Jerrold W. Grossman
1.3 Functions – Jerrold W. Grossman
1.4 Relations – John G. Michaels
1.5 Proof Techniques – Susanna S. Epp
1.6 Axiomatic Program Verification – David Riley
1.7 Logic-Based Computer Programming Paradigms – Mukesh Dalal
2. COUNTING METHODS
2.1 Summary of Counting Problems – John G. Michaels
2.2 Basic Counting Techniques – Jay Yellen
2.3 Permutations and Combinations – Edward W. Packel
2.4 Inclusion/Exclusion – Robert G. Rieper
2.5 Partitions – George E. Andrews and Andrew V. Sills
2.6 Burnside/Pólya Counting Formula – Alan C. Tucker
2.7 M?bius Inversion Counting – Edward A. Bender
2.8 Young Tableaux – Bruce E. Sagan
3. SEQUENCES
3.1 Special Sequences – Thomas A. Dowling and Douglas R. Shier
3.2 Generating Functions – Ralph P. Grimaldi
3.3 Recurrence Relations – Ralph P. Grimaldi
3.4 Finite Differences – Jay Yellen
3.5 Finite Sums and Summation – Victor S. Miller
3.6 Asymptotics of Sequences – Edward A. Bender and Juanjo Rué
3.7 Mechanical Summation Procedures – Kenneth H. Rosen
4. NUMBER THEORY
4.1 Basic Concepts – Kenneth H. Rosen
4.2 Greatest Common Divisors – Kenneth H. Rosen
4.3 Congruences – Kenneth H. Rosen
4.4 Prime Numbers – Jon F. Grantham and Carl Pomerance
4.5 Factorization – Jon F. Grantham and Carl Pomerance
4.6 Arithmetic Functions – Kenneth H. Rosen
4.7 Primitive Roots and Quadratic Residues – Kenneth H. Rosen
4.8 Diophantine Equations – Bart E. Goddard
4.9 Diophantine Approximation – Jeff Shalit
4.10 Algebraic Number Theory – Lawrence C. Washington
4.11 Elliptic Curves – Lawrence C. Washington
5. ALGEBRAIC STRUCTURES – John G. Michaels
5.1 Algebraic Models
5.2 Groups
5.3 Permutation Groups
5.4 Rings
5.5 Polynomial Rings
5.6 Fields
5.7 Lattices
5.8 Boolean Algebras
6. LINEAR ALGEBRA
6.1 Vector Spaces – Joel V. Brawley
6.2 Linear Transformations – Joel V. Brawley
6.3 Matrix Algebra – Peter R. Turner
