離散數(shù)學(xué)及其應(yīng)用

內(nèi)容概要

本書從Thomson Learning出版公司引進(jìn)。本書內(nèi)容包括：復(fù)合陳述中的邏輯，定量陳述中的邏輯，基礎(chǔ)數(shù)論及證明方法，數(shù)理推斷及序列，集合論，計(jì)算和概率，函數(shù)，遞歸，運(yùn)算法則及效率，關(guān)系，圖和樹，常規(guī)表達(dá)式和自動(dòng)控制。    本書可作為高等院校理工科專業(yè)學(xué)生作為離散數(shù)學(xué)雙語教材使用，與其同類教材相比；本書有以下幾個(gè)突出的特點(diǎn)：1．著重邏輯推理；2．以螺旋前進(jìn)的方式介紹并運(yùn)用概念，便于學(xué)生了解及進(jìn)一步掌握；3．大量的圖表便于學(xué)生直觀理解；4．習(xí)題配置合理，書后給出了習(xí)題答案．5．有與本書配套的網(wǎng)絡(luò)資源。    本書敘述詳盡、語言表達(dá)流暢，適合于理工科各專業(yè)學(xué)生作為雙語教材使用，也可供教師教學(xué)參考。

作者簡(jiǎn)介

作者：(美國(guó))蘇杉娜

書籍目錄

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

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