离散数学及其应用（英文版）（原书第8版） / 经典原版书库
定价：￥139.00
作者： [美]肯尼思·H.罗森
出版时间：2020-01-07
出版社：机械工业出版社
- 机械工业出版社
- 9787111645306
- 1-7
- 47229643-3
- 16开
- 2020-01-07
- 1487
- 计算机通信类
- 本科
内容简介
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
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
