离散数学
2003-11
清华
[美]Kenneth A.Ross，Charles R.B.Wright
无
本书通过大量示例深入浅出地介绍了离散数学的主要内容，包括集合、序和函数，基础逻辑，关系，归纳与递归，计数，图与树，递归、树与算法，有向图，离散概率，布尔代数，代数结构，谓词演算与无限集等。各章节配有相当数量的练习题，书后给出了提示和答案，对教师授课和读者迅速掌握有关知识很有帮助。本书内容丰富，结构清晰、系统，讲解通俗易懂，而且注重实用性，既可作为计算机科学和计算机数学等专业的本科生和研究生的教科书，又可作为工程技术人员的参考书。
作者：(美)罗斯(Kenneth A.Ross) (美)赖特 (Charles R.B.Wright)
Preface to the Fifth EditionTo the Student Especially1 Sets, Sequences, and Functions1.1 Some Warm-up Questions1.2 Factors and MultiplesOffice Hours1.3 Some Special Sets1.4 Set Operations1.5 Functions1.6 Sequences1.7 Properties of FunctionsOffice HoursSupplementary Exercises2 Elementary Logic2.1 Informal Introduction2.2 Propositional Calculus2.3 Getting Started with Proofs2.4 Methods of ProofOffice Hours2.5 Logic in Proofs2.6 Analysis of ArgumentsSupplementary Exercises3 Relations3.1 Relations3.2 Digraphs and Graphs3.3 Matrices3.4 Eauivalence Relations and Partitions3.5 The Division Aigorimm ana integers mod pSupplementary Exercises4 Induction and Recursion4.1 Loop Invariants4.2 Mathematical InductionOffice Hours4.3 Big-Oh Notation4.4 Recursive Definitions4.5 Recurrence Relations4.6 More Induction4.7 The Euclidean AlgorithmSupplementary Exercises5 Counting5.1 Basic Counting Techniques5.2 Elementary Probability5.3 Inclusion-Exclusion and Binomial Methods5.4 Counting and PartitionsOffice Hours5.5 Pigeon-Hole PrincipleSupplementary Exercises6 Introduction to Graphs and Trees6.1 Graphs6.2 Edge Traversal Problems6.3 Trees6.4 Rooted Trees6.5 Vertex Traversal Problems6.6 Minimum Spanning TreesSupplementary Exercises7 Recursion, Trees, and Algorithms7.1 General Recursion7.2 Recursive Algorithms7.3 Depth-First Search Algorithms7.4 Polish Notation7.5 Weighted TreesSupplementary Exercises8 Digraphs8.1 Digraphs Revisited8.2 Weighted Digraphs and Scheduling NetworksOffice Hours8.3 Digraph AlgorithmsSupplementary ExercisesDiscrete Probability9.1 Independence in Probability9.2 Random Variables9.3 Expectation and Standard Deviation9.4 Probability DistributionsSupplementary Exercises10 Boolean Algebra10.1 Boolean Algebras10.2 Boolean Expressions10.3 Logic Networks10.4 Karnaugh Maps10.5 Isomorphisms of Boolean AlgebrasSupplementary Exercises11 More on Relations11.1 Partially Ordered Sets11.2 Special Orderings11.3 Multiplication of Matrices11.4 Properties of General Relations11.5 Closures of RelationsSupplementary Exercises12 Alqebraic Structures12.1 Groups Acting on Sets12.2 Fixed Points and Subgroups12.3 Counting Orbits12.4 Group Homomorphisms12.5 Semigroups12.6 Other Algebraic SystemsSupplementary Exercises13 Predicate Calculus and Infinite Sets13.1 Quantifiers and Predicates13.2 Elementary Predicate Calculus13.3 Infinite SetsSupplementary ExercisesDictionaryAnswers and HintsIndex
本书通过大量示例深入浅出地介绍了离散数学的主要内容，包括集合、序和函数，基础逻辑，关系，归纳与递归，计数，图与树，递归、树与算法，有向图，离散概率，布尔代数，代数结构，谓词演算与无限集等。各章节配有相当数量的练习题，书后给出了提示和答案，对教师授课和读者迅速掌握有关知识很有帮助。本书内容丰富，结构清晰、系统，讲解通俗易懂，而且注重实用性，既可作为计算机科学和计算机数学等专业的本科生和研究生的教科书，又可作为工程技术人员的参考书。
无
内容充分，论述详细，习题还附有答案，没治了。