DiscreteMathematics
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作者编者:陈明//董焕河//段华|责编:李鹏飞
出版社西安电子科大
ISBN9787560669090
出版时间2023-07
装帧其他
开本其他
定价29元
货号31816836
上书时间2024-07-06
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目录
Chapter 1 Propositional Logic
1.1 The Basics of Propositional Logic
1.1.1 Propositions and Operators
1.1.2 Propositional Formulas
1.2 Propositional Equivalence
1.2.1 Equivalence and Some Basic Properties
1.2.2 Normal Form
1.3 Rules of Inference and Proof for Propositional Logic
1.3.1 Valid Arguments
1.3.2 Building Arguments and Proofs
Exercise 1
Chapter 2 Predicate Logic
2.1 The Basics of Predicate Logic
2.1.1 Language of Predicate Logic
2.1.2 Predicate Formulas
2.2 Predicate Equivalences
2.2.1 Equivalences
2.2.2 Prenex Normal Form
2.3 Rules of Inference for Predicate Logic
Exercise 2
Chapter 3 Sets
3.1 The Basics of Sets
3.1.1 The Set Concept and Set Description
3.1.2 Set Equality and Relationship between Sets
3.1.3 Some Special Sets
3.2 Operations on Sets
3.2.1 The Basic Operation
3.2.2 Set Identities
3.3 Principle of Inclusion-Exclusion
Exercise 3
Chapter 4 Relations
4.1 The Basics of Relations
4.1.1 Order Pairs and Cartesian Product
4.1.2 Concept and Representations of Binary Relations
4.1.3 Operations on Relations
4.1.4 Properties of Relations
4.1.5 Closures of Relations
4.2 Equivalence Relations
4.2.1 Definition of Equivalence Relations
4.2.2 Partitions
4.3 Partial Order Relations
4.3.1 Definition of Partial Order
4.3.2 Hasse Diagrams
4.3.3 Special Elements in Posets
Exercise 4
Chapter 5 Functions
5.1 The Basics of Function
5.1.1 Concept and Properties of Functions
5.1.2 Inverse Function and Composition of Functions
5.2 Countability of Sets
内容摘要
Thebookismainlyaimedatthebilingualcurriculumdesignofdiscretemathematics.Itcanmeettheneedsofthetypesofanintroductiontothefundamentalideasofdiscretemathematics,andasafoundationforthedevelopmentofmoreadvancedmathematicalconcepts.Thebookincludesfourparts.ThefirstpartismathematicallogicwhichcoverspropositionallogicinChapter1andpredicatelogicinChapter2.Itgivesamethodhowtoexpressnaturallanguagestatementsusingsymbolsasthefoundationtodiscretemathematics,especiallyforsets.Thelogicpartsincludeequivalentcalculationandthediscussionofproof.ThesecondpartissettheorywithsetsinChapter3,relationsinChapter4,andfunctionsinChapter5,whichisthebasicsofthewholemathematics.Chapter3presentsbasictypesofsetsandtheiroperations.Chapter4presentsdefinition,propertiesandoperationsofrelations,alongwiththeirrepresentationasdirectedgraphsandconnectionswithmatrices.Chapter5restatesthefunctionfromtheperspectiveofrelations,includingcountablesetsanduncountablesets.ThethirdpartisgraphtheoryinChapter6whichisthesourcesfordatastructuresandalgorithms.Itcoversterminology,representationandspecialstructureofgraphs.Thelastpart,thatisahighlyabstractpart,isalgebraicsystemsinChapter7,whichcoverssemigroups,groupsringsandfields.Byalgebraicsystemswecanfindcommonalitiesofmanyfamiliarrules.Thisbookcanbeusedasadiscretemathematicscourse'sreferenceforcomputer,mathematics,bigdatatechnologyandsomerelateddisciplinesinInstitutionsofHigherLearning,andcanalsoprovideusefulhelpforotherreadersofdiscretemathematics,especiallyforbilinguallearning.
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