 | 书 名: 离散数学 英文版
作 者: Richard Johnsonbaugh
出 版 社: 电子工业出版社
ISBN : 750539613
原 价: ￥58
 有一家网站低于85折正在热销 | 离散数学 英文版-图书目录:
PREFACE
1 LOGIC AND PROOFS 1
1.1 Propositions 2
1.2 Conditional Propositions and Logical Equivalence
1.3 Quantifiers 14
1.4 Proofs 29
1.5 Resolution Proofs 37
1.6 Mathematical Induction 41
Problem-Solving Comer: MathematicalInduction 49
Notes 51
Chapter Review 51
Chapter Self-Test 53
Computer Exercises 54
2 THE LANGUAGE OF MATHEMATICS 55
2.1 Sets 56
2.2 Sequences and Strings 64
2.3 Number Systems 71
2.4 Relations 77
Problem-Solving Corner: Relations 84
2.5 Equivalence Relations 85
Problem-Solving Comer: Equivalence Relations 90
2.6 Matrices of Relations 92
*2.7 Relational Databases 97
2.8 Functions 101
Notes 114
Chapter Review 114
Chapter Self-Test 116
Computer Exercises 118
3 ALGORITHMS 120
3.1 Introduction 121
3.2 Notation for Algorithms 122
3.3 The Euclidean Algorithm 128
3.4 Recursive Algorithms 132
3.5 Complexity of Algorithms 138
Problem-Solving Corner: Design and Analysis of an Algorithm 152
3.6 Analysis of the Euclidean Algorithm 154
*3.7 The RSA Public-Key Cryptosystem 157
Notes 160
Chapter Review 161
Chapter Self-Test 162
Computer Exercises 164
4 COUNTING METHDDS AND THE PIGEONHOLE PRINCIPLE 165
4.1 Basic Principles 165
Problem-Solving Corner: Counting 172
4.2 Permutations and Combinations 174
Problem-Solving Corner: Combinations 185
4.3 Algorithms for Generating Permutations and Combinations 187
*4.4 Introduction to Discrete Probability 192
*4.5 Discrete Probability Theory 195
4.6 Generalized Permutations and Combinations 206
4.7 Binomial Coefficients and Combinatorial Identities 211
4.8 The Pigeonhole Principle 216
Notes 220
Chapter Review 220
Chapter Self-Test 221
Computer Exercises 223
5 RECURRENCE RELATIONS 224
5.1 Introduction 224
5.2 Solving Recurrence Relations 235
Problem-Solving Corner: Recurrence Relations 246
5.3 Applications to the Analysis of Algorithms 249
Notes 260
Chapter Review 260
Chapter Self-Test 260
Computer Exercises 261
6
GRAPH THECIRY 263
6.1 Introduction 263
6.2 Paths and Cycles 2´74
Problem-Solving Corner: Graphs 284
6.3 Hamiltonian Cycles and the Traveling Salesperson Problem 285
6.4 A Shortest-Path Algorithm 291
6.5 Representations of Graphs 296
6.6 Isomorphisms of Graphs 301
6.7 Planar Graphs 307
*6.8 Instant Insanity 313
Notes 317
Chapter Review 317
Chapter Self-Test 319
Computer Exercises 321
7 TREES 323
7.1 Introduction 323
7.2 Terminology and Characterizations of Trees 331
Problem-Solving Corner: Trees 336
7.3 Spanning Trees 337
7.4 Minimal Spanning Trees 343
7.5 Binary Trees 349
7.6 Tree Traversals 355
7.7 Decision Trees and the Minimum Time for Sorting 361
7.8 Isomorphisms of Trees 367
*7.9 Game Trees 376
Notes 384
Chapter Review 384
Chapter Self-Test 385
Computer Exercises 389
8
NETWORK MODELS 390
8.1 Introduction 390
8.2 A Maximal Flow Algorithm 396
8.3 The Max Flow, Min Cut Theorem 404
8.4 Matching 407
Problem-Solving Comer: Matching 412
Notes 413
Chapter Review 414
Chapter Self-Test 414
Computer Exercises 415
9 BOOLEAN ALGEBRAS AND COMBINATORIAL CIRCUITS 416
9.1 Combinatorial Circuits 416
9.2 Properties of Combinatorial Circuits 423
9.3 Boolean Algebras 427
Problem-Solving Corner: Boolean Algebras 432
9.4 Boolean Functions and Synthesis of Circuits 434
9.5 Applications 439
Notes 447
Chapter Review 447
Chapter Self-Test 448
Computer Exercises 450
10 AUTOMATA,GRAMMARS,AND LANGUAGES 452
10.1 Sequential Circuits and Finite-State Machines 452
10.2 Finite-State Automata 458
10.3 Languages and Grammars 464
10.4 Nondeterministic Finite-State Automata 472
10.5 Relationships Between Languages and Automata 479
Notes 484
Chapter Review 485
Chapter Self-Test 486
Computer Exercises 488
11 COMPUTATIONAL GEOMETRY 489
11.1 The Closest-Pair Problem 489
*11.2 A Lower Bound for the Closest-Pair Problem 494
11.3 An Algorithm to Compute the Convex Hull 496
Notes 503
Chapter Review 503
Chapter Self-Test 503
Computer Exercises 504
A
MATRICES 505
B
ALGEBRA REVIEW 509
REFERENCES 521
HINTS AND SOLUTIONS TO
SELECTED EXERCISES 527
iNDEX 607
离散数学 英文版-图书简介:
离散数学是现代数学的一个重要分支和计算机科学基础理论的核心课程，?涑浞置枋隽思扑慊蒲Ю肷⑿缘奶氐悖撬孀偶扑慊蒲У姆⒄苟鸩浇⑵鹄吹男滦说幕⌒匝Э啤１臼槟谌莘岣弧⑷嫦低场⒔峁骨逦⑼ㄋ滓锥⒆⒅厥涤茫瓤梢宰魑扑慊蒲Ш图扑闶У茸ㄒ档谋究朴胙芯可滩模挚梢宰魑こ碳际跞嗽钡牟慰际椤?
本书作为离散数学的基本教材，把握关键问题并以全新的编排方式通过精选的大量实例，深入浅出地介绍了数理逻辑、组合算法、图论、布尔代数、网络模型、形式语言与自动机理论等与计算机科学密切相关的前沿课题，既着重于各部分之间的紧密联系，又深入探讨各部分内容的概念、理论、算法和实际应用，内容叙述严谨、推演详尽。各章节配有相当数量的习题，书后的提示与答案为读者迅速掌握有关知识提供有效的帮助。
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