Using Geometry in Teaching Group Theory

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Abstract
  • Discrete groups of isometries provide a rich class of groups for detailed study in an undergraduate course in abstract algebra. After developing some geometric tools, we illustrate several important ideas from group theory via symmetry groups. In particular, we consider conjugation, homomorphisms, normal and nonnormal subgroups, generators and relations, quotient groups and direct and semidirect products. Understanding of these topics can be enhanced using symmetries of frieze and wallpaper patterns. We describe
    several examples in detail and indicate how other geometric investigations could be undertaken. We also indicate how four commercial software packages (The Geometer’s Sketchpad, KaleidoTile, TesselMania and Kali) can be used to enhance students’ understanding.
TitleUsing Geometry in Teaching Group Theory
CreatorGordon, Gary
SourceInnovations in Teaching Abstract Algebra
Academic DepartmentMathematics
DivisionNatural Sciences
OrganizationLafayette College
Date Issued2002
Date Available2023-06-01
TypePart of Book
LanguageEnglish
Bibliographic CitationGordon, G. (2002) "Using Geometry in Teaching Group Theory." In A. C. Hibbard and E. J. Maycock (eds.), Innovations in Teaching Abstract Algebra (pp. 25-33). Washington, DC: Mathematical Association of America
Standard IdentifierHandle 10385/rj4306148
Permalinkhttp://hdl.handle.net/10385/rj4306148
Rights Statement In Copyright In Copyright
Rights HoldersMathematical Association of America
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