Discrete Mathematics and Its Applications
8th Edition
By Kenneth Rosen
ISBN10: 125967651X
ISBN13: 9781259676512
Copyright: 2019
1 The Foundations: Logic and Proofs
1.1 Propositional Logic
1.2 Applications of Propositional Logic.
1.3 Propositional Equivalences
1.4 Predicates and Quantifiers
1.5 Nested Quantifiers
1.6 Rules of Inference.
1.7 Introduction to Proofs
1.8 Proof Methods and Strategy
End-of-Chapter Material
2 Basic Structures: Sets, Functions, Sequences, Sums,
and Matrices
2.1 Sets
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations
2.5 Cardinality of Sets
2.6 Matrices
End-of-Chapter Material
3 Algorithms
3.1 Algorithms.
3.2 The Growth of Functions
3.3 Complexity of Algorithms
End-of-Chapter Material
4 Number Theory and Cryptography
4.1 Divisibility and Modular Arithmetic
4.2 Integer Representations and Algorithms
4.3 Primes and Greatest Common Divisors
4.4 Solving Congruences.
4.5 Applications of Congruences
4.6 Cryptography
End-of-Chapter Material
5 Induction and Recursion
5.1 Mathematical Induction
5.2 Strong Induction and Well-Ordering
5.3 Recursive Definitions and Structural Induction
5.4 Recursive Algorithms
5.5 Program Correctness
End-of-Chapter Material
6 Counting
6.1 The Basics of Counting.
6.2 The Pigeonhole Principle
6.3 Permutations and Combinations
6.4 Binomial Coefficients and Identities
6.5 Generalized Permutations and Combinations
6.6 Generating Permutations and Combinations
End-of-Chapter Material
7 Discrete Probability
7.1 An Introduction to Discrete Probability
7.2 Probability Theory
7.3 Bayes’ Theorem
7.4 Expected Value and Variance
End-of-Chapter Material
8 Advanced Counting Techniques
8.1 Applications of Recurrence Relations
8.2 Solving Linear Recurrence Relations
8.3 Divide-and-Conquer Algorithms and Recurrence Relations
8.4 Generating Functions
8.5 Inclusion–Exclusion
8.6 Applications of Inclusion–Exclusion
End-of-Chapter Material
9 Relations.
9.1 Relations and Their Properties
9.2 n-ary Relations and Their Applications.
9.3 Representing Relations
9.4 Closures of Relations
9.5 Equivalence Relations
9.6 Partial Orderings
End-of-Chapter Material
Contents v
10 Graphs
10.1 Graphs and Graph Models
10.2 Graph Terminology and Special Types of Graphs
10.3 Representing Graphs and Graph Isomorphism
10.4 Connectivity
10.5 Euler and Hamilton Paths
10.6 Shortest-Path Problems.
10.7 Planar Graphs
10.8 Graph Coloring
End-of-Chapter Material
11 Trees
11.1 Introduction to Trees
11.2 Applications of Trees
11.3 Tree Traversal
11.4 Spanning Trees
11.5 Minimum Spanning Trees
End-of-Chapter Material
12 Boolean Algebra
12.1 Boolean Functions
12.2 Representing Boolean Functions
12.3 Logic Gates
12.4 Minimization of Circuits
End-of-Chapter Material
13 Modeling Computation
13.1 Languages and Grammars
13.2 Finite-State Machines with Output.
13.3 Finite-State Machines with No Output
13.4 Language Recognition
13.5 Turing Machines.
End-of-Chapter Material
Appendices
1 Axioms for the Real Numbers and the Positive Integers
2 Exponential and Logarithmic Functions
3 Pseudocode
1 基础：逻辑和证明
1.1 命题逻辑
1.2 命题逻辑的应用
1.3 命题等价
1.4 谓词和量词
1.5 嵌套量词
1.6 推理规则。
1.7 证明简介
1.8 证明方法和策略
章末材料
2 基本结构：集合、函数、序列、求和、
和矩阵
2.1 套
2.2 集合运算
2.3 函数
2.4 序列和召唤
2.5 集合的基数
2.6 矩阵
章末材料
3 算法
3.1 算法。
3.2 函数的增长
3.3 算法的复杂性
章末材料
4 数论与密码学
4.1 可除性和模运算
4.2 整数表示和算法
4.3 素数和最大公约数
4.4 求解全等。
4.5 全等的应用
4.6 密码学
章末材料
5 归纳和递归
5.1 数学归纳法
5.2 强归纳和良序
5.3 递归定义与结构归纳
5.4 递归算法
5.5 程序正确性
章末材料
6 计数
6.1 计数的基础知识。
6.2 鸽子洞原理
6.3 排列和组合
6.4 二项式系数和恒等式
6.5 广义排列和组合
6.6 生成排列和组合
章末材料
7 离散概率
7.1 离散概率简介
7.2 概率论
7.3 贝叶斯定理
7.4 期望值和方差
章末材料
8 种高级计数技术
8.1 递归关系的应用
8.2 求解线性递归关系
8.3 分而治之算法与递归关系
8.4 生成函数
8.5 包含-排除
8.6 包容-排除的应用
章末材料
9 关系。
9.1 关系及其性质
9.2 n元关系及其应用。
9.3 表示关系
9.4 关系的结束
9.5 等价关系
9.6 部分排序
章末材料
目录 v
10 图表
10.1 图和图模型
10.2 图术语和特殊类型的图谱
10.3 表示图和图同构
10.4 连接性
10.5 欧拉和汉密尔顿路径
10.6 最短路径问题。
10.7 平面图
10.8 图形着色
章末材料
11 树
11.1 树简介
11.2 树木的应用
11.3 树遍历
11.4 生成树
11.5 最小生成树
章末材料
12 布尔代数
12.1 布尔函数
12.2 表示布尔函数
12.3 逻辑门
12.4 电路最小化
章末材料
13 建模计算
13.1 语言和语法
13.2 带输出的有限状态机。
13.3 没有输出的有限状态机
13.4 语言识别
13.5 图灵机。
章末材料
附录
1 实数和正整数的公理
2 指数和对数函数
3 伪代码
『Discrete Mathematics and Its Applications』离散数学及其应用学习笔记. https://blog.csdn.net/liteng607/article/details/104649755
Discrete Mathematics and Its Applications. https://www.mheducation.com/highered/product/discrete-mathematics-applications-rosen/M9781259676512.html
bing翻译. https://cn.bing.com/translator