经典的高等代数(英文版)

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1、ElementsofAbstractandLinearAlgebraE.H.ConnelliiE.H.ConnellDepartmentofMathematicsUniversityofMiamiP.O.Box249085CoralGables,Florida33124USAec@math.miami.eduMathematicalSubjectClassications(1991):12-01,13-01,15-01,16-01,20-01c1999E.H.ConnellMarch20,2004iiiIntroductionIn1965Irsttaughtanundergra

2、duatecourseinabstractalgebra.Itwasfuntoteachbecausethematerialwasinterestingandtheclasswasoutstanding.FiveofthosestudentslaterearnedaPh.D.inmathematics.SincethenIhavetaughtthecourseaboutadozentimesfromvarioustexts.OvertheyearsIdevelopedasetoflecturenotesandin1985Ihadthemtypedsotheycouldbeuseda

3、satext.Theynowappear(inmodiedform)astherstvechaptersofthisbook.Hereweresomeofmymotivesatthetime.1)Tohavesomethingasshortandinexpensiveaspossible.Inmyexperience,studentslikeshortbooks.2)Toavoidallinnovation.Toorganizethematerialinthemostsimple-mindedstraightforwardmanner.3)Toorderthematerial

4、linearly.Totheextentpossible,eachsectionshouldusetheprevioussectionsandbeusedinthefollowingsections.4)Toomitasmanytopicsaspossible.Thisisafoundationalcourse,notatopicscourse.Ifatopicisnotusedlater,itshouldnotbeincluded.Therearethreegoodreasonsforthis.First,linearalgebrahastoppriority.Itisbette

5、rtogoforwardanddomorelinearalgebrathantostopanddomoregroupandringtheory.Second,itismoreimportantthatstudentslearntoorganizeandwriteproofsthemselvesthantocovermoresubjectmatter.Algebraisaperfectplacetogetstartedbecausetherearemanyeasy"theoremstoprove.Therearemanyroutinetheoremsstatedherewithou

6、tproofs,andtheymaybeconsideredasexercisesforthestudents.Third,thematerialshouldbesofundamentalthatitbeappropriateforstudentsinthephysicalsciencesandincomputerscience.Zillionsofstudentstakecalculusandcookbooklinearalgebra,butfewtakeabstractalgebracourses.Somethingiswronghere,andonethingwrongist

7、hatthecoursestrytodotoomuchgroupandringtheoryandnotenoughmatrixtheoryandlinearalgebra.5)Tooeranalternativeforcomputersciencemajorstothestandarddiscretemathematicscourses.Mostofthematerialintherstfourchaptersofthistextiscoveredinvariou