離散數(shù)學(xué)

內(nèi)容概要

本書通過大量示例深入淺出地介紹了離散數(shù)學(xué)的主要內(nèi)容，包括集合、序和函數(shù)，基礎(chǔ)邏輯，關(guān)系，歸納與遞歸，計數(shù)，圖與樹，遞歸、樹與算法，有向圖，離散概率，布爾代數(shù)，代數(shù)結(jié)構(gòu)，謂詞演算與無限集等。各章節(jié)配有相當(dāng)數(shù)量的練習(xí)題，書后給出了提示和答案，對教師授課和讀者迅速掌握有關(guān)知識很有幫助。本書內(nèi)容豐富，結(jié)構(gòu)清晰、系統(tǒng)，講解通俗易懂，而且注重實用性，既可作為計算機科學(xué)和計算機數(shù)學(xué)等專業(yè)的本科生和研究生的教科書，又可作為工程技術(shù)人員的參考書。

作者簡介

作者：(美)羅斯(Kenneth A.Ross) (美)賴特 (Charles R.B.Wright)

書籍目錄

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

編輯推薦

本書通過大量示例深入淺出地介紹了離散數(shù)學(xué)的主要內(nèi)容，包括集合、序和函數(shù)，基礎(chǔ)邏輯，關(guān)系，歸納與遞歸，計數(shù)，圖與樹，遞歸、樹與算法，有向圖，離散概率，布爾代數(shù)，代數(shù)結(jié)構(gòu)，謂詞演算與無限集等。各章節(jié)配有相當(dāng)數(shù)量的練習(xí)題，書后給出了提示和答案，對教師授課和讀者迅速掌握有關(guān)知識很有幫助。本書內(nèi)容豐富，結(jié)構(gòu)清晰、系統(tǒng)，講解通俗易懂，而且注重實用性，既可作為計算機科學(xué)和計算機數(shù)學(xué)等專業(yè)的本科生和研究生的教科書，又可作為工程技術(shù)人員的參考書。

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