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时间:2018-07-28
《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.eduMathematicalSubjectClassications(1991):12-01,13-01,15-01,16-01,20-01c1999E.H.ConnellMarch30,2001[http://www.math.miami.edu/ec/book/]iiiIn
2、troductionIn1965Irsttaughtanundergraduatecourseinabstractalgebra.Itwasfuntoteachbecausethematerialwasinterestingandtheclasswasoutstanding.FiveofthosestudentslaterearnedaPh.D.inmathematics.SincethenIhavetaughtthecourseaboutadozentimesfromvarioustexts.OvertheyearsIdevelopedasetoflecturenotesand
3、in1985Ihadthemtypedsotheycouldbeusedasatext.Theynowappear(inmodiedform)astherstvechaptersofthisbook.Hereweresomeofmymotivesatthetime.1)Tohavesomethingasshortandinexpensiveaspossible.Inmyexperience,studentslikeshortbooks.2)Toavoidallinnovation.Toorganizethematerialinthemostsimple-mindedstrai
4、ghtforwardmanner.3)Toorderthemateriallinearly.Totheextentpossible,eachsectionshouldusetheprevioussectionsandbeusedinthefollowingsections.4)Toomitasmanytopicsaspossible.Thisisafoundationalcourse,notatopicscourse.Ifatopicisnotusedlater,itshouldnotbeincluded.Therearethreegoodreasonsforthis.First,
5、linearalgebrahastoppriority.Itisbettertogoforwardanddomorelinearalgebrathantostopanddomoregroupandringtheory.Second,itismoreimportantthatstudentslearntoorganizeandwriteproofsthemselvesthantocovermoresubjectmatter.Algebraisaperfectplacetogetstartedbecausetherearemanyeasy"theoremstoprove.Therea
6、remanyroutinetheoremsstatedherewithoutproofs,andtheymaybeconsideredasexercisesforthestudents.Third,thematerialshouldbesofundamentalthatitbeappropriateforstudentsinthephysicalsciencesandincomputerscience.Zillionsofstudentstakecalculusandcookbooklinearalgebra,butfewtakeabstractalgebracourses.Som
7、ethingiswronghere,andonethingwrongisthatthecoursestrytodotoomuchgroupandringtheoryandnotenoughmatrixtheoryandlinearalgebra.5)Tooeranalternativeforcomputersciencemajorstothestandarddiscretemathematicscourses.Mostofthematerialintherstfo
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