出版时间:2005-3 出版社:高等教育出版社 作者:苏杉娜 页数:904
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内容概要
本书从Thomson Learning出版公司引进。本书内容包括:复合陈述中的逻辑,定量陈述中的逻辑,基础数论及证明方法,数理推断及序列,集合论,计算和概率,函数,递归,运算法则及效率,关系,图和树,常规表达式和自动控制。 本书可作为高等院校理工科专业学生作为离散数学双语教材使用,与其同类教材相比;本书有以下几个突出的特点:1.着重逻辑推理;2.以螺旋前进的方式介绍并运用概念,便于学生了解及进一步掌握;3.大量的图表便于学生直观理解;4.习题配置合理,书后给出了习题答案.5.有与本书配套的网络资源。 本书叙述详尽、语言表达流畅,适合于理工科各专业学生作为双语教材使用,也可供教师教学参考。
作者简介
作者:(美国)苏杉娜
书籍目录
Chapter 1 The Logic of Compound Statements 1.1 LogicalForm and LogicalEquivalence 1.2 Conditional Statements 1.3 Valid andInvalid Arguments 1.4 Application:Digital Logic Circuits 1.5 Application:Number Systems and Circuits for Addition Chapter 2 The Logic of Quantified Statements 2.1 Introduction to Predicates and Quantified Statements / 2.2 Introduction to Predicates and Quantified Statements II 2.3 Statements Containing Multiple Quantifiers 2.4 Arguments with Quantified Statements 111Chapter 3 Elementary Number Theoryand Methods ofProof 3.1 Direct Proofand Counterexample h Introduction 3.2 Direct Proofand Counterexample II Rational Numbers 3.3 Direct Proof and Counterexample IIh Divisibility 3.4 Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder Theorem 3.5 Direct Proofand Counterexample V:Floorand Ceiling 3.6 Indirect Argument:Contradiction and Contraposition 3.7 Two Classica|Theorems 3.8 Application:Algorithms Chapter 4 Sequences and MathematicalInduction 4.1 Sequences 4.2 Mathematical Induction, 4.3 Mathematical Induction II 4.4 Strong Mathematical Inductiopand the Well-Ordering Principle 4.5 Application:Correctness ofAlgorithms Chapter 5 Set Theory 5.1 Basic Definitions of Set Theory 5.2 Properties of Sets 5.3 Disproofs,AlgebraicProofs.andBooleanAlgebras 5.4 Russell~Paradox and the Halting Problem Chapter 6 Countingand Probability 6.1 Introduction 6.2 Possibility Trees and the Multiplication Rule 6.3 Counting Elements of Disjoint Sets:The Addition Rule 6.4 Counting Subsets of a Set:Combinations 6.5 r-Combinations with Repetition AIIowed 6.6 The Algebra of Combinations 6.7 The Binomia|Theofem 6.8 Probability Axioms and Expected Value 6.9 Conditional Probability,Bayes"Formula,and Independent Evenrs Chapter 7 Functions 7.1 Functions Defined on General Sets 7.2 One-to-One and Onto,Inverse Functions 7.3 Application:The Pigeonhole Principle 7.4 Composition of Functions 7.5 Cardinality with Applications to Computability Chapter 8 Recursion 8.1 Recursively Defined Sequences 8.2 Solving Recurrence Relations by Iteration 8.3 Second-Order Linear Homogenous Recurrence Relations 8.4 General Recursive Definitions Chapter 9 The EfficiencyofAlgorithms 9. 1 Real-Valued Functions ofa Real Variable and Their Graphs 9.2 Ο.Ω.and ΘNotationS 9.3 Application:Efficiency ofAlgorithms/ 9.4 Exponential and Logarithmic Functions:Graphs andOrders 9.5 Application:Efficiency ofAlgorithms II Chapter 10 Relations 10.1 Relations on Sets 10.2 Reflexivity,Symmetry,and Transitivity 10.3 Equivalence Relations 10.4 Modular Arithmetic with Applications to Cryptography 10.5 Partia|Order Relations Chapter 11 Graphs and Trees 11.1 Graphs:An Introduction 11.2 Paths and Circuits 11.3 Matrix Representations of Graphs 11.4 Isomorphism of Graphs 11.5 Trees 11.6 Spanning TreesChapter 12 RegularExpressionsandFinite.StateAutomata 12.1 Forma|Languages and Regular Expressions 12.2 Finite-State Automata 12.3 Simplifying Finite-State Automata AppendixA Properties ofthe Real Numbers A-1Appendix B Solutions and Hints to Selected Exercises A-4
编辑推荐
《离散数学及其应用》(第3版影印版)适合高校使用.
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