Elements_of_Abstract_and_Linear_Algebra

《Elements_of_Abstract_and_Linear_Algebra》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、ElementsofAbstractandLinearAlgebraE.H.ConnelliiE.H.ConnellDepartmentofMathematicsUniversityofMiamiP.O.Box249085CoralGables,Florida33124USAec@math.miami.eduMathematicalSubjectClassications(1991):12-01,13-01,15-01,16-01,20-01c1999{2002E.H.ConnellApril30,2002[http://www.math.miami.edu/ec/book

2、/]iiiIntroductionIn1965Irsttaughtanundergraduatecourseinabstractalgebra.Itwasfuntoteachbecausethematerialwasinterestingandtheclasswasoutstanding.FiveofthosestudentslaterearnedaPh.D.inmathematics.SincethenIhavetaughtthecourseaboutadozentimesfromvarioustexts.OvertheyearsIdevelopedasetoflectur

3、enotesandin1985Ihadthemtypedsotheycouldbeusedasatext.Theynowappear(inmodiedform)astherstvechaptersofthisbook.Hereweresomeofmymotivesatthetime.1)Tohavesomethingasshortandinexpensiveaspossible.Inmyexperience,studentslikeshortbooks.2)Toavoidallinnovation.Toorganizethematerialinthemostsimple-

4、mindedstraightforwardmanner.3)Toorderthemateriallinearly.Totheextentpossible,eachsectionshouldusetheprevioussectionsandbeusedinthefollowingsections.4)Toomitasmanytopicsaspossible.Thisisafoundationalcourse,notatopicscourse.Ifatopicisnotusedlater,itshouldnotbeincluded.Therearethreegoodreasonsf

5、orthis.First,linearalgebrahastoppriority.Itisbettertogoforwardanddomorelinearalgebrathantostopanddomoregroupandringtheory.Second,itismoreimportantthatstudentslearntoorganizeandwriteproofsthemselvesthantocovermoresubjectmatter.Algebraisaperfectplacetogetstartedbecausetherearemanyeasy"theorem

6、stoprove.Therearemanyroutinetheoremsstatedherewithoutproofs,andtheymaybeconsideredasexercisesforthestudents.Third,thematerialshouldbesofundamentalthatitbeappropriateforstudentsinthephysicalsciencesandincomputerscience.Zillionsofstudentstakecalculusandcookbooklinearalgebra,butfewtakeabstracta

7、lgebracourses.Somethingiswronghere,andonethingwrongisthatthecoursestrytodotoomuchgroupandringtheoryandnotenoughmatrixtheoryandlinearalgebra.5)Tooeranalternativeforcomputersciencemajorstothestandarddiscretemathematicscourses.Mostofthematerialinthe