8066348|正版离散数学及其应用(英文版原书第8版)经典原版书库计算机科学理论与基础知识计算理论算法肯尼思H罗森
9787111645306
￥ 115.03 全新
库存999件
广东广州
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作者肯尼思·H.罗森(Kenneth H.Rosen)
出版社机械工业出版社
ISBN9787111645306
出版时间2020-01
装帧平装
货号613902312628
上书时间2023-07-07
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书 名: 【正版】离散数学及其应用（英文版·原书第8版）|8066348 图书定价: 139元 作 者: [美]肯尼思·H. 罗森（Kenneth H. Rosen） 出 版 社: 机械工业出版社 出版日期: 2019/12/26 0:00:00 ISBN 号: 9787111645306 开 本:16开 页 数:991 版 次:1-1 \
[美]肯尼思·H. 罗森（Kenneth H. Rosen）著：
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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。\
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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