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A Course In Modern Geometries (Undergraduate Texts In Mathematics),New
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A Course In Modern Geometries Is Designed For A Juniorsenior Level Course For Mathematics Majors, Including Those Who Plan To Teach In Secondary School. Chapter 1 Presents Several Finite Geometries In An Axiomatic Framework. Chapter 2 Continues The Synthetic Approach As It Introduces Euclid'S Geometry And Ideas Of Noneuclidean Geometry. In Chapter 3, A New Introduction To Symmetry And Handson Explorations Of Isometries Precedes The Extensive Analytic Treatment Of Isometries, Similarities And Affinities. A New Concluding Section Explores Isometries Of Space. Chapter 4 Presents Plane Projective Geometry Both Synthetically And Analytically. The Extensive Use Of Matrix Representations Of Groups Of Transformations In Chapters 34 Reinforces Ideas From Linear Algebra And Serves As Excellent Preparation For A Course In Abstract Algebra. The New Chapter 5 Uses A Descriptive And Exploratory Approach To Introduce Chaos Theory And Fractal Geometry, Stressing The Selfsimilarity Of Fractals And Their Generation By Transformations From Chapter 3. Each Chapter Includes A List Of Suggested Resources For Applications Or Related Topics In Areas Such As Art And History. The Second Edition Also Includes Pointers To The Web Location Of Authordeveloped Guides For Dynamic Software Explorations Of The Poincar Model, Isometries, Projectivities, Conics And Fractals. Parallel Versions Of These Explorations Are Available For 'Cabri Geometry' And 'Geometer'S Sketchpad'.Judith N. Cederberg Is An Associate Professor Of Mathematics At St. Olaf College In Minnesota.
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