# 离散数学及其应用（英文版）（第7版）

2012-09

ISBN: 9787111385509

• 　　《离散数学及其应用（英文版）（第7版）》是介绍离散数学理论和方法的经典教材，已经成为采用率最高的离散数学教材，被美国众多名校用作教材，获得了极大的成功。《离散数学及其应用（英文版）（第7版）》中文版也已被国内大学广泛采用为教材。作者参考用书教师和学生的反馈，并结合自身对教育的洞察，在第7版中做了大量的改进，使其成为更有效的教学工具。《离散数学及其应用（英文版）（第7版）》可作为1～2个学期的离散数学课程教材，适用于数学、计算机科学、计算机工程、信息技术等专业的学生。 prefaceiv
thecompanionwebsitexiv
tothestudentxvi
listofsymbolsxix

1thefoundations：logicandproofs
1.1propositionallogic
1.2applicationsofpropositionallogic
1.3propositionalequivalences
1.4predicatesandquantifiers
1.5nestedquantifiers
1.6rulesofinference
1.7introductiontoproofs
1.8proofmethodsandstrategy
end-of-chaptermaterial-

2basicstructures：sets，functions，sequences，sums，andmatrices
2.1sets
2.2setoperations
2.3functions
.2.4sequencesandsummations
2.5cardinalityofsets
2.6matrices
end-of-chaptermaterial

3algorithms
3.1algorithms
3.2thegrowthoffunctions
3.3complexityofalgofithms
end-of-chaptermaterial

4numbertheoryandcryptography
4.1divisibilitvandmodulararithmetic
4.2integerrepresentationsandalgorithms
4.3primesandgreatestcommondivisors
4.4solvingcongruences
4.5applicationsofcongruences
4.6cryptography
end-of-chaptermaterial

5inductionandrecursion
5.1mathematicalinduction
5.2stronginductionandwell-ordering
5.3recursivedefinitionsandstructuralinduction
5.4recursivealgorithms
5.5programcorrectness
end-of-chaptermaterial

6counting
6.1tllebasicsofcounting
6.2thepigeonholeprinciple
6.3permutationsandcombinations
6.4binomialcoefficientsandidentities
6.5generalizedpermutationsandcombinations
6.6generatingpermutationsandcombinations
end-of-chaptermaterial

7discreteprobability
7.1anintroductiontodiscreteprobability
7.2probabilitytheory
7.3bayes'theorem
7.4expectedvalueandvariance
end-of-chaptermaterial

8.1applicationsofrecurrencerelations
8.2solvinglinearrecurrencerelations
8.3divide-and-conqueralgorithmsandrecurrencerelations
8.4generatingfunctions
8.5inclusion-exclusion
8.6applicationsofinclusion-exclusion
end-of-chaptermaterial

9relations
9.1relationsandtheirproperties
9.2n-aryrelationsandtheirapplications
9.3representingrelations
9.4closuresofrelations
9.5equivalencerelations
9.6partialorderings
end-of-chaptermaterial

10graphs
10.1graphsandgraphmodels
10.2graphterminologyandspecialtypesofgraphs
10.3representinggraphsandgraphisomorphism
10.4connectivity
10.5eulerandhamiltonpaths
10.6shortest.pathproblems
10.7planargraphs
10.8graphcoloring
end-of-chaptermaterial

11trees
11.1introductiontotrees
11.2applicationsoftrees
11.3treetravcrsal
11.4spanningtrees
11.5minimumspanningtrees
end-of-chaptermaterial

12booleanalgebra
12.1booleanfunctions
12.2representingbooleanfunctions
12.3logicgates
12.4minimizationofcircuits
end-of-chaptermaterial

13modelingcornputation
13.1languagesandgrammars
13.2finite-statemachineswithoutput
13.3finite-statemachineswithnooutput
13.4languagerecognition
13.5turingmachines
end-of-chaptermaterial

appendixes
1axiomsfortherealnumbersandthepositiveintegers
2exponentialandlogarithmicfunctions
3pseudocode

photocreditsc-1
indexofbiographiesi-1
indexi-2
• ##### 内容简介:
《离散数学及其应用（英文版）（第7版）》是介绍离散数学理论和方法的经典教材，已经成为采用率最高的离散数学教材，被美国众多名校用作教材，获得了极大的成功。《离散数学及其应用（英文版）（第7版）》中文版也已被国内大学广泛采用为教材。作者参考用书教师和学生的反馈，并结合自身对教育的洞察，在第7版中做了大量的改进，使其成为更有效的教学工具。《离散数学及其应用（英文版）（第7版）》可作为1～2个学期的离散数学课程教材，适用于数学、计算机科学、计算机工程、信息技术等专业的学生。
• ##### 目录:
prefaceiv
thecompanionwebsitexiv
tothestudentxvi
listofsymbolsxix

1thefoundations：logicandproofs
1.1propositionallogic
1.2applicationsofpropositionallogic
1.3propositionalequivalences
1.4predicatesandquantifiers
1.5nestedquantifiers
1.6rulesofinference
1.7introductiontoproofs
1.8proofmethodsandstrategy
end-of-chaptermaterial-

2basicstructures：sets，functions，sequences，sums，andmatrices
2.1sets
2.2setoperations
2.3functions
.2.4sequencesandsummations
2.5cardinalityofsets
2.6matrices
end-of-chaptermaterial

3algorithms
3.1algorithms
3.2thegrowthoffunctions
3.3complexityofalgofithms
end-of-chaptermaterial

4numbertheoryandcryptography
4.1divisibilitvandmodulararithmetic
4.2integerrepresentationsandalgorithms
4.3primesandgreatestcommondivisors
4.4solvingcongruences
4.5applicationsofcongruences
4.6cryptography
end-of-chaptermaterial

5inductionandrecursion
5.1mathematicalinduction
5.2stronginductionandwell-ordering
5.3recursivedefinitionsandstructuralinduction
5.4recursivealgorithms
5.5programcorrectness
end-of-chaptermaterial

6counting
6.1tllebasicsofcounting
6.2thepigeonholeprinciple
6.3permutationsandcombinations
6.4binomialcoefficientsandidentities
6.5generalizedpermutationsandcombinations
6.6generatingpermutationsandcombinations
end-of-chaptermaterial

7discreteprobability
7.1anintroductiontodiscreteprobability
7.2probabilitytheory
7.3bayes'theorem
7.4expectedvalueandvariance
end-of-chaptermaterial

8.1applicationsofrecurrencerelations
8.2solvinglinearrecurrencerelations
8.3divide-and-conqueralgorithmsandrecurrencerelations
8.4generatingfunctions
8.5inclusion-exclusion
8.6applicationsofinclusion-exclusion
end-of-chaptermaterial

9relations
9.1relationsandtheirproperties
9.2n-aryrelationsandtheirapplications
9.3representingrelations
9.4closuresofrelations
9.5equivalencerelations
9.6partialorderings
end-of-chaptermaterial

10graphs
10.1graphsandgraphmodels
10.2graphterminologyandspecialtypesofgraphs
10.3representinggraphsandgraphisomorphism
10.4connectivity
10.5eulerandhamiltonpaths
10.6shortest.pathproblems
10.7planargraphs
10.8graphcoloring
end-of-chaptermaterial

11trees
11.1introductiontotrees
11.2applicationsoftrees
11.3treetravcrsal
11.4spanningtrees
11.5minimumspanningtrees
end-of-chaptermaterial

12booleanalgebra
12.1booleanfunctions
12.2representingbooleanfunctions
12.3logicgates
12.4minimizationofcircuits
end-of-chaptermaterial

13modelingcornputation
13.1languagesandgrammars
13.2finite-statemachineswithoutput
13.3finite-statemachineswithnooutput
13.4languagerecognition
13.5turingmachines
end-of-chaptermaterial

appendixes
1axiomsfortherealnumbersandthepositiveintegers
2exponentialandlogarithmicfunctions
3pseudocode

photocreditsc-1
indexofbiographiesi-1
indexi-2

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