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dc.contributor.authorTian, Chen
dc.date.accessioned2014-03-04T18:30:02Z
dc.date.available2014-03-04T18:30:02Z
dc.date.issued2010-05
dc.identifier.othertian_chen_201005_ma
dc.identifier.urihttp://purl.galileo.usg.edu/uga_etd/tian_chen_201005_ma
dc.identifier.urihttp://hdl.handle.net/10724/26516
dc.description.abstractThis thesis illuminates some connections between high school algebra and abstract algebra. The concepts of function (e.g., homomorphism and 1-1 correspondence) and algebraic structure (e.g., ring, field, and group) are compatible with each other. This thesis mainly deals with (1) functions from an overall structural perspective, (2) the solvability of some polynomial equations in certain algebraic systems, and (3) the real numbers from both constructive and axiomatic approaches. Throughout this thesis I provide possible questions or tasks that teachers can use to challenge students to think of mathematics in a bigger picture as well as help students develop an admiration for some aesthetic dimensions of mathematics. I identify some questions that high school students might ask and provide answers are given from a relatively advanced mathematical standpoint to illuminate the connections between high school algebra and abstract algebra. The notion of limit in calculus and the interaction between algebra and geometry are also rendered in several contexts.
dc.languageeng
dc.publisheruga
dc.rightspublic
dc.subjecthigh school algebra
dc.subjectabstract algebra
dc.subjectconnections
dc.subjectalgebraic structure
dc.subjectisomorphism
dc.subjectthe real numbers
dc.subjectpolynomials
dc.titleAn exploration of connections between high school algebra and abstract algebra
dc.typeThesis
dc.description.degreeMA
dc.description.departmentMathematics and Science Education
dc.description.majorMathematics Education
dc.description.advisorDenise S. Mewborn
dc.description.committeeDenise S. Mewborn
dc.description.committeeRoy Smith
dc.description.committeeJeremy Kilpatrick


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