离散数学结构(第三版)--英文

ISBN: 9787302027669

作者: [加拿大]科尔曼

出版社: 清华大学出版社

出版年: 1997-12

页数: 524

定价: 32.00

装帧: 平装

内容简介

用于计算机科学的离散数学是大学一、二年级?难教又难学的一门课程。本书深

入浅出，由简及繁，将定义和理论抽象压缩到最低限度。除仍像前两版那样以关系

和有向图作为中心外，本书增加了较大的灵活性和模块性。本书11章分别为：基础；

逻辑；计数；关系和有向图；函数；图论问题；有序关系及结构；树；半群和群；语

言和有限状态机；群和编码。除新增一章图论外，还增加了一些新的小节如：数学结

构，谓词演算，递归关系，用于计算机科学的函数，函数的序，最小生成树。附录B离散

数学实验是新增加的；此外，有关递归、逻辑及验证也引入了更多的新材料，排列和组

合的表达形式有了扩展，每章都增加了编码练习。本书既可作数学也可作计算机科学或

计算机工程课的教材。

作者简介

Bernard Kolman received his B.S. (summa cum laude with honors in mathemat-

ics and physics) from Brooklyn College in 1954, his Sc.M. from Brown University

in 1956, and his Ph.D. from the University of Pennsylvania in 1965, all in mathe-

matics. During the summers of 1955 and 1956 he worked as a mathematician for

the U.S. Navy, and IBM, respectively, in areas of numerical analysis and simula-

tion. From 1957-1964, he was employed as a mathematician by the UNIVAC

Division of Sperry Rand Corporation, working in the areas of operations

research, numerical analysis, and discrete mathematics. He also had extensive

experience as.a consultant to industry in operations research. Since 1964, he has

been a member of the Mathematics Department at Drexel University, where he

also served as Acting Head of this department. Since 1964, his research activities

have been in the areas of Lie algebras and operations research.

Professor Kolman is the author of numerous papers, primarily in Lie alge-

bras, and has organized several conferences on Lie algebras. He is also well

known as the author of many mathematics textbooks that are used worldwide

and have been translated into several other languages. He belongs to a number

of professional associations and is a member of Phi Beta Kappa, Pi Mu Epsi'.on,

and Sigma Xi.

Robert C. Busby received his B.S. in Physics from Drexel University in 1963 and

his A.M. in 1964 and Ph.D. in 1966, both in mathematics from the University of

Pennsylvania. From September 1967 to May 1969 he was a member of the math-

ematics department at Oakland University in Rochester, Michigan. Since 1969 he

has been a faculty member at Drexel University, in what is now the Department

of Mathematics and Computer Science. He has consulted in applied mathemat-

ics in industry and government. This includes a period of three years as a consul-

tant to the Office of Emergency Preparedness, Executive Office of the President,

specializing in applications of mathematics to economic problems. He has had

extensive experience developing computer implementations of a variety of math-

ematical applications.

Professor Busby has written two books and has numerous research papers

in operator algebras, group representations, operator continued fractions, and the

applications of probability and statistics to mathematical demography.

Sharon Cutler Ross received an S.B. in mathematics from the Massachusetts

Institute of Technology (1965), an M.A.T. in secondary mathematics from

Harvard University (1966), and a Ph.D. also in mathematics from Emory

University (1976). In addition, she is a graduate of the Institute for Retraining in

Computer Science (1984). She has taught junior high, high school, and college

mathematics. She has also taught computer science at the collegiate level. Since

1974, she has been a member of the Department of Mathematics at DeKalb

College. Her current professional interests are in the areas of undergraduate

mathematics education reform and alternative forms of assessment.

Professor Ross is the co-author of two other mathematics textbooks. She is

well known for her activities with the Mathematical Association of America, the

American Mathematical Association of Two -Year Colleges, and UME Trends. In

addition, she is a full member of Sigma Xi and of numerous other professional

associations.

CONTENTS
Preface
Fundamentals
1.1 Sets and Subsets
1.2 Operations on Sets
1.3 Sequences
1.4 Division in the Integers
1.5 Matrices
1.6 Mathematical Structures
Logic
2.1 Propositions and Logical Operations
2.2 Conditional Statements
2.3 Methods of Proof
2.4 Mathematical Induction
Counting
3.1 Permutations
3.2 Combinations
3.3 The Pigeonhole Principle
3.4 Elements of Probability
3.5 Recurrence Relations
Relations and Digraphs
4.1 Product Sets and Partitions
4.2 Relations and Digraphs
4.3 Paths in Relations and Digraphs
4.4 Properties of Relations
4.5 Equivalence Relations
4.6 Computer Representation of Relations and Digraphs
4.7 Manipulation of Relations
4.8 Transitive Closure and Warshall's Algorithm
Functions
5.1 Functions
5.2 Functions for Computer Science
5.3 Permutation Functions
5.4 Growth of Functions
Topics in Graph Theory
6.1 Graphs
6.2 Euler Paths and Circuits
6.3 Hamiltonian Paths and Circuits
6.4 Coloring Graphs
Order Relations and Structures
7.1 Partially Ordered Sets
7.2 Extremal Elements of Partially Ordered Sets
7.3 Lattices
7.4 Finite Boolean Algebras
7.5 Functions on Boolean Algebras
7.6 Boolean Functions as Boolean Polynomials
Trees
8.1 Trees
8.2 Labeled Trees
8.3 Tree Searehing
8.4 Undirected Trees
8.5 Minimal Spanning Trees
Semigroups and Groups
9.1 Binary Operations Revisited
9.2 Semigroups
9.3 Products and Quotients of Semigroups
9.4 Groups
9.5 Products and Quotients of Groups
Languages and Finite-State Machines
10.1 Languages
10.2 Representations of Special Languages and Grammars
10.3 Finite-State Machines 391
10.4 Semigroups, Machines, and Languages
10.5 Machines and Regular Languages
10.6 Simplification of Machines
Groups and Coding 420
11.1 Coding of Binary Information and Error Detection
11.2 Decoding and Error Correction
Appendix A Algorithms and Pseudocode
Appendix B Experiments in Discrete Mathematics
Answers to Odd-Numbered Exercises
Index

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