离散数学及其应用（英文版·原书第8版）
| 作者 |
| [美]肯尼思·H. 罗森（Kenneth H. Rosen） |
| 丛书名 |
| 经典原版书库 |
| 出版社 |
| 机械工业出版社 |
| ISBN |
| 9787111645306 |
| 简要 |
| 简介 |
| 内容简介书籍计算机书籍 本书是经典的离散数学教材，被全球数百所大学广为采用。书中全面而系统地介绍了离散数学的理论和方法，主要包括：逻辑和证明，集合、函数、序列、求和与矩阵，算法，数论和密码学，归纳与递归，计数，离散概率，关系，图，树，布尔代数，计算模型。全书取材广泛，除包括定义、定理的严格陈述外，还配备大量的例题、图表、应用实例和练习。第8版做了与时俱进的更新，成为更加实用的教学工具。本书可作为高等院校数学、计算机科学和计算机工程等专业的教材，也可作为科技领域从业人员的参考书。 |
| 目录 |
| 1 The Foundations: Logic and Proofs....................................1 1.1 Propositional Logic........................................1 1.2 Applications of Propositional Logic........................................17 1.3 Propositional Equivalences........................................26 1.4 Predicates and Quantifiers........................................40 1.5 Nested Quantifiers........................................60 1.6 Rules of Inference........................................73 1.7 Introduction to Proofs........................................84 1.8 Proof Methods and Strategy........................................96 End-of-Chapter Material........................................115 2 Basic Structures: Sets, Functions, Sequences, Sums, and atrices....................................121 2.1 Sets........................................121 2.2 Set Operations........................................133 2.3 Functions........................................147 2.4 Sequences and Summations........................................165 2.5 Cardinality of Sets........................................179 2.6 Matrices........................................188 End-of-Chapter Material........................................195 3 Algorithms........................................201 3.1 Algorithms........................................201 3.2 The Growth of Functions........................................216 3.3 Complexity of Algorithms........................................231 End-of-Chapter Materia........................................244 4 Number Theory and Cryptography..................................251 4.1 Divisibility and Modular Arithmetic........................................251 4.2 Integer Representations and Algorithms........................................260 4.3 Primes and Greatest Common Divisors........................................271 4.4 Solving Congruences........................................290 4.5 Applications of Congruences........................................303 4.6 Cryptography........................................310 End-of-Chapter Materia........................................324 5 Induction and Recursion........................................331 5.1 Mathematical Induction........................................331 5.2 Strong Induction and Well-Ordering........................................354 5.3 Recursive Definitions and Structural Induction..................................365 5.4 Recursive Algorithms........................................381 5.5 Program Correctness........................................393 End-of-Chapter Materia........................................398 6 Counting........................................405 6.1 The Basics of Counting........................................405 6.2 The Pigeonhole Principle........................................420 6.3 Permutations and Combinations........................................428 6.4 Binomial Coeficients and Identities........................................437 6.5 Generalized Permutations and Combinations...................................445 6.6 Generating Permutations and Combinations....................................457 End-of-Chapter Materia........................................461 7 Discrete Probability........................................469 7.1 An Introduction to Discrete Probability........................................469 7.2 Probability Theory........................................477 7.3 Bayes’Theorem........................................494 7.4 Expected Valueand Variance........................................503 End-of-Chapter Materia........................................520 8 Advanced Counting Techniques.....................................527 8.1 Applications of Recurrence Relations........................................527 8.2 Solving Linear Recurrence Relations........................................540 8.3 Divide-and-Conquer Algorithms and Recurrence Relations......................553 8.4 Generating Functions........................................563 8.5 Inclusion–Exclusion........................................579 8.6 Applications of Inclusion–Exclusion........................................585 End-of-Chapter Materia........................................592 9 Relations........................................599 9.1 Relations and Their Properties........................................599 9.2 n-ary Relations and Their Applications........................................611 9.3 Representing Relations........................................621 9.4 Closures of Relations........................................628 9.5 Equivalence Relations........................................638 9.6 Partial Orderings........................................650 End-of-Chapter Materia........................................665 10 Graphs........................................673 10.1 Graphs and Graph Models........................................673 10.2 Graph Terminology and Special Types of Graphs...............................685 10.3 Representing Graphs and Graph Isomorphism..................................703 10.4 Connectivity........................................714 10.5 Euler and Hamilton Paths........................................728 10.6 Shortest-Path Problems........................................743 10.7 Planar Graphs........................................753 10.8 Graph Coloring........................................762 End-of-Chapter Materia........................................771 11 Trees........................................781 11.1 Introduction to Trees........................................781 11.2 Applications of Trees........................................793 11.3 Tree Traversal........................................808 11.4 Spanning Trees........................................821 11.5 Minimum Spanning Trees........................................835 End-of-Chapter Materia........................................841 12 Boolean Algebra........................................847 12.1 Boolean Functions........................................847 12.2 Representing Boolean Functions........................................855 12.3 Logic Gates........................................858 12.4 Minimization of Circuits........................................864 End-of-Chapter Materia........................................879 13 Modeling Computation ........................................885 13.1 Languages and Grammars........................................885 13.2 Finite-State Machines with Output........................................897 13.3 Finite-State Machines with NoOutput........................................904 13.4 Language Recognition........................................917 13.5 Turing Machines........................................927 End-of-Chapter Materia........................................938 Appendices........................................A-1 1 Axioms for the Real Numbers and the Positive Integers..........................A-1 2 Exponential and Logarithmic Functions........................................A-7 3 Pseudocode........................................A-11 Suggested ReadingsB-1 Answers to Odd-Numbered Exercises S-1 Index of BiographiesI-1 IndexI-2 |
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