《離散數(shù)學(xué)結(jié)構(gòu)(第6版)(影印版)》先后改進(jìn)五版，歷經(jīng)25年，受到廣泛認(rèn)可，這使我們感到非常欣慰。同樣欣喜的是《離散數(shù)學(xué)結(jié)構(gòu)(第6版)(影印版)》前五版所選的內(nèi)容及解題方法也被廣泛肯定。例如，最近協(xié)會(huì)和其他機(jī)構(gòu)都大力推薦該書(shū)作為離散結(jié)構(gòu)的一學(xué)期的課程。在該版籌劃前，我們充分考慮了來(lái)自教師和學(xué)生的眾多建議和意見(jiàn)以改進(jìn)《離散數(shù)學(xué)結(jié)構(gòu)(第6版)(影印版)》的內(nèi)容和材料。盡管該版做了改進(jìn)并完善了很多，但是我們的目標(biāo)依然同前五版一樣：以一種簡(jiǎn)明的、學(xué)生能夠理解的方式來(lái)介紹離散數(shù)學(xué)的基本概念及其某些應(yīng)用。
目錄
PrefaceA Word to Students1 Fundamentals l.1 Sets and Subsets 1.2 Operations on Sets 1.3 Sequences 1.4 Properties of Integers 1.5 Matrices 1.6 Mathematical Structures2 Logic 2.1 Propositions and Logical Operations 2.2 Conditional Statements 2.3 Methods of Proof 2.4 Mathematical Induction 2.5 Mathematical Statements 2.6 Logic and Problem Solving3 Counting 3.1 Permutations 3.2 Combinations 3.3 Pigeonhole Principle 3.4 Elements of Probability 3.5 Recurrence Relations4 Relations and Digraphs 4.1 Product Sets and Partitions 4.2 Relations and Digraphs 4.3 Paths in Relations and Digraphs 4.4 Properties of Relations 4.5 Equivalence Relations 4.6 Data Structures for Relations and Digraphs 4.7 Operations on Relations 4.8 Transitive Closure and Warshall's Algorithm5 Functions 5.1 Functions 5.2 Functions for Computer Science 5.3 Growth of Functions 5.4 Permutation Functions6 Order Relations and Structures 6.1 Partially Ordered Sets 6.2 Ex.tremal Elements of Partially Ordered Sets 6.3 Lattices 6.4 Finite Boolean, Algebras 6.5 Functions on Boolean Algebras 6.6 Circuit Design7 Trees 7.1 Trees 7.2 Labeled Trees 7.3 Tree Searching 7.4 Undirected Trees 7.5 Minimal Spanning Trees8 Topics in Graph Theory 8.1 Graphs 8.2 Euler Paths and Circuits 8.3 Hamiltonian Paths and Circuits 8.4 Transport Networks 8.5 Matching Problems 8.6 Coloring Graphs9 Semigroups and Groups 9.1 Binary Operations Revisited 9.2 Semigroups 9.3 Products and Quotients of Semigroups 9.4 Groups 9.5 Products and Quotients of Groups 9.6 Other Mathematical Structures10 Languages and Finite-State Machines 10.1 Languages 10.2 Representations of Special Grammars and Languages 10.3 Finite-State Machines 10.4 Monoids, Machines, and Languages 10.5 Machines and Regular Languages 10.6 Simplification of Machines11 Groups and Coding 11.1 Coding of Binary Information and Error Detection 11.2 Decoding and Error Correction 11.3 Public Key CryptologyAppendix A: Algorithms and PseudocodeAppendix B: Additional Experiments in Discrete MathematicsAppendix C: Coding ExercisesAnswers to Odd-Numbered ExercisesAnswers to Chapter Self-TestsGlossary G-1Index 1-1Photo Credits P-1
PrefaceA Word to Students1 Fundamentals l.1 Sets and Subsets 1.2 Operations on Sets 1.3 Sequences 1.4 Properties of Integers 1.5 Matrices 1.6 Mathematical Structures2 Logic 2.1 Propositions and Logical Operations 2.2 Conditional Statements 2.3 Methods of Proof 2.4 Mathematical Induction 2.5 Mathematical Statements 2.6 Logic and Problem Solving3 Counting 3.1 Permutations 3.2 Combinations 3.3 Pigeonhole Principle 3.4 Elements of Probability 3.5 Recurrence Relations4 Relations and Digraphs 4.1 Product Sets and Partitions 4.2 Relations and Digraphs 4.3 Paths in Relations and Digraphs 4.4 Properties of Relations 4.5 Equivalence Relations 4.6 Data Structures for Relations and Digraphs 4.7 Operations on Relations 4.8 Transitive Closure and Warshall's Algorithm5 Functions 5.1 Functions 5.2 Functions for Computer Science 5.3 Growth of Functions 5.4 Permutation Functions6 Order Relations and Structures 6.1 Partially Ordered Sets 6.2 Ex.tremal Elements of Partially Ordered Sets 6.3 Lattices 6.4 Finite Boolean, Algebras 6.5 Functions on Boolean Algebras 6.6 Circuit Design7 Trees 7.1 Trees 7.2 Labeled Trees 7.3 Tree Searching 7.4 Undirected Trees 7.5 Minimal Spanning Trees8 Topics in Graph Theory 8.1 Graphs 8.2 Euler Paths and Circuits 8.3 Hamiltonian Paths and Circuits 8.4 Transport Networks 8.5 Matching Problems 8.6 Coloring Graphs9 Semigroups and Groups 9.1 Binary Operations Revisited 9.2 Semigroups 9.3 Products and Quotients of Semigroups 9.4 Groups 9.5 Products and Quotients of Groups 9.6 Other Mathematical Structures10 Languages and Finite-State Machines 10.1 Languages 10.2 Representations of Special Grammars and Languages 10.3 Finite-State Machines 10.4 Monoids, Machines, and Languages 10.5 Machines and Regular Languages 10.6 Simplification of Machines11 Groups and Coding 11.1 Coding of Binary Information and Error Detection 11.2 Decoding and Error Correction 11.3 Public Key CryptologyAppendix A: Algorithms and PseudocodeAppendix B: Additional Experiments in Discrete MathematicsAppendix C: Coding ExercisesAnswers to Odd-Numbered ExercisesAnswers to Chapter Self-TestsGlossary G-1Index 1-1Photo Credits P-1
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