本书是介绍离散数学理论和方法的经典教材,已经成为采用率最高的离散数学教材。仅在美国就被600多所高校用作教材,获得了极大的成功。中文版也已被国内大学广泛采用为教材。第6版在前五版的基础上做了大量的改进,使其成为更有效的教学工具。
本书可作为1至2个学期的离散数学课入门教材,适用于数学、计算机科学、计算机工程、信息技术等专业的学生。
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书名 | 离散数学及其应用(英文版第6版)/经典原版书库 |
分类 | 科学技术-自然科学-数学 |
作者 | (美)罗森 |
出版社 | 机械工业出版社 |
下载 | ![]() |
简介 | 编辑推荐 本书是介绍离散数学理论和方法的经典教材,已经成为采用率最高的离散数学教材。仅在美国就被600多所高校用作教材,获得了极大的成功。中文版也已被国内大学广泛采用为教材。第6版在前五版的基础上做了大量的改进,使其成为更有效的教学工具。 本书可作为1至2个学期的离散数学课入门教材,适用于数学、计算机科学、计算机工程、信息技术等专业的学生。 目录 Preface fii About the Author xiv To the Student xv LIST OF SYMBOLS xviii 1 The Foundations: Logic and Proofs 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers 1.5 Rules oflnference 1.6 Introduction to Proofs 1.7 Proof Methods and Strategy End-of-Chapter Material 2 Basic Structures: Sets, Functions, Sequences, and Sums 2.1 Sets 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations End-of-Chapter Material 3 The Fundamentals: Algorithms, the Integers, and Matrices 3.1 Algorithms 3.2 The Growth of Functions 3.3 Complexity of Algorithms 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms 3.7 Applications of Number Theory 3.8 Matrices End-of-Chapter Material 4 Induction and Recursion 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering 4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms 4.5 Program Correctness End-of-Chapter Material 5 Counting 5.1 The Basics of Counting 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.4 Binomial Coefficients 5.5 Generalized Permutations and Combinations 5.6 Generating Permutations and Combinations End-of-Chapter Material 6 Discrete Probability 6.1 An Introduction to Discrete Probability 6.2 Probability Theory 6.3 Bayes' Theorem 6.4 Expected Value and Variance End-of-Chapter Material 7 Advanced Counting Techniques 7.1 Recurrence Relations 7.2 Solving Linear Recurrence Relations 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.4 Generating Functions 7.5 Inclusion-Exclusion 7.6 Applications of Inclusion-Exclusion End-of-Chapter Material 8 Relations 8.1 Relations and Their Properties 8.2 n-ary Relations and Their Applications 8.3 Representing Relations 8.4 Closures of Relations 8.5 Equivalence Relations 8.6 Partial Orderings End-of-Chapter Material 9 Graphs 9.1 Graphs and Graph Models 9.2 Graph Terminology and Special Types of Graphs 9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Paths 9.6 Shortest-Path Problems 9.7 Planar Graphs 9.8 Graph Coloring End-of-Chapter Material 10 Trees 10.1 Introduction to Trees 10.2 Applications of Trees 10.3 Tree Traversal 10.4 Spanning Trees 10.5 Minimum Spanning Trees End-of-Chapter Material 11 Boolean Algebra 11.1 Boolean Functions 11.2 Representing Boolean Functions 11.3 Logic Gates 11.4 Minimization of Circuits End-of-Chapter Material 12 Modeling Computation 12.1 Languages and Grammars 12.2 Finite-State Machines with Output 12.3 Finite-State Machines with No Output 12.4 Language Recognition 12.5 Turing Machines End-of-Chapter Material Appendixes A-1 Axioms for the Real Numbers and the Positive Integers A-2 Exponential and Logarithmic Functions A-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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