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(cid:2) PRINCIPLES OF MATHEMATICS (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) PRINCIPLES OF MATHEMATICS A Primer VLADIMIRLEPETIC DePaulUniversity (cid:2) (cid:2) (cid:2) (cid:2) Copyright©2016byJohnWiley&Sons,Inc.Allrightsreserved PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey PublishedsimultaneouslyinCanada Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformor byanymeans,electronic,mechanical,photocopying,recording,scanning,orotherwise,exceptas permittedunderSection107or108ofthe1976UnitedStatesCopyrightAct,withouteithertheprior writtenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropriateper-copyfeeto theCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,(978)750-8400,fax (978)750-4470,oronthewebatwww.copyright.com.RequeststothePublisherforpermissionshould beaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ 07030,(201)748-6011,fax(201)748-6008,oronlineathttp://www.wiley.com/go/permissions. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsin preparingthisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyor completenessofthecontentsofthisbookandspecificallydisclaimanyimpliedwarrantiesof merchantabilityorfitnessforaparticularpurpose.Nowarrantymaybecreatedorextendedbysales representativesorwrittensalesmaterials.Theadviceandstrategiescontainedhereinmaynotbesuitable foryoursituation.Youshouldconsultwithaprofessionalwhereappropriate.Neitherthepublishernor authorshallbeliableforanylossofprofitoranyothercommercialdamages,includingbutnotlimitedto special,incidental,consequential,orotherdamages. (cid:2) (cid:2) Forgeneralinformationonourotherproductsandservicesorfortechnicalsupport,pleasecontactour CustomerCareDepartmentwithintheUnitedStatesat(800)762-2974,outsidetheUnitedStatesat (317)572-3993orfax(317)572-4002. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmay notbeavailableinelectronicformats.FormoreinformationaboutWileyproducts,visitourwebsiteat www.wiley.com. LibraryofCongressCataloging-in-PublicationData: Lepetic,Vladimir,1950-author. Principlesofmathematics:aprimer/VladimirLepetic. pagescm Includesindex. ISBN978-1-119-13164-9(cloth) 1.Mathematics–Philosophy.I.Title. QA8.4.L4472016 510.1–dc23 2015025151 Typesetin10.5/12.5pt,TimesbySPiGlobal,Chennai,India. PrintedintheUnitedStatesofAmerica 10987654321 1 2016 (cid:2) (cid:2) ToIvanandMarija (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) (cid:2) CONTENTS Preface xi (cid:2) (cid:2) 1 SetTheory 1 1.1 Introduction, 1 1.2 SetTheory – Definitions,Notation,andTerminology – WhatisaSet?, 3 1.3 SetsGivenbyaDefiningProperty, 15 1.4 TheAlgebraofSets, 25 1.5 ThePowerSet, 41 1.6 TheCartesianProduct, 44 1.7 TheSetsN,Z,andQ, 46 1.8 TheSetR – RealNumbersI, 71 1.9 AShortMusingonTransfiniteArithmetic, 80 1.10 TheSetR – RealNumbersII, 102 1.11 SupplementaryProblems, 109 2 Logic 115 2.1 Introduction, 116 2.2 PropositionalCalculus, 121 2.3 ArgumentsI, 146 2.4 ArgumentsII, 167 (cid:2) (cid:2) viii CONTENTS 2.5 AShortRevisittoSetTheory, 171 2.6 BooleanAlgebra, 173 2.7 SupplementaryProblems, 177 3 Proofs 183 3.1 Introduction, 183 3.2 DirectProof, 193 3.3 IndirectProof, 212 3.4 MathematicalInduction, 218 3.5 SupplementaryProblems, 241 4 Functions 247 4.1 Introduction, 247 4.2 Relations, 248 4.3 Functions, 274 4.4 SupplementaryProblems, 321 5 GroupTheory 327 5.1 Introduction, 327 (cid:2) 5.2 FundamentalConceptsofGroupTheory, 328 (cid:2) 5.3 Subgroups, 356 5.4 CyclicGroups, 382 5.5 HomomorphismsandIsomorphisms, 385 5.6 NormalSubgroups, 404 5.7 Centralizer,Normalizer,Stabilizer, 412 5.8 QuotientGroup, 419 5.9 TheIsomorphismTheorems, 427 5.10 DirectProductofGroups, 437 5.11 SupplementaryProblems, 441 6 LinearAlgebra 447 6.1 Introduction, 447 6.2 VectorSpace, 449 6.3 LinearDependenceandIndependence, 456 6.4 BasisandDimensionofaVectorSpace, 461 6.5 Subspaces, 469 6.6 LinearTransformations – LinearOperators, 477 6.7 IsomorphismofLinearSpaces, 489 6.8 LinearTransformationsandMatrices, 501 6.9 LinearSpaceM , 507 mn (cid:2)

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Presents a uniquely balanced approach that bridges introductory and advanced topics in modern mathematics An accessible treatment of the fundamentals of modern mathematics, Principles of Mathematics: A Primer provides a unique approach to introductory andadvanced mathematical topics. The book featur

Principles of Mathematics: A Primer PDF

671 Pages·2016·2.66 MB·English

by Vladimir Lepetic

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Author:	Vladimir Lepetic
Publication Year:	2016
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Language:	English
File Size:	2.66
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