A Course In Modern Geometries Is Designed For A Junior-senior 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 Introduces Euclid's Geometry And The Basic Ideas Of Non-euclidean Geometry. The Synthetic Approach Of Chapters 1 - 2 Is Followed By The Analytic Treatment Of Transformations Of The Euclidean Plane In Chapter 3. Chapter 4 Presents Plane Projective Geometry Both Synthetically And Analytically. The Extensive Use Of Matrix Representations Of Groups Of Transformations In Chapters 3 - 4 Reinforces Ideas From Linear Algebra And Serves As Excellent Preparation For A Course In Abstract Algebra. Each Chapter Includes A List Of Suggested Sources For Applications And/or Related Topics. By Judith N. Cederberg.

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Cederberg, Judith N. (author.)

J. H Ewing

Springer Nature (Textbooks & Major Reference Works), New York, NY, 2013

Undergraduate texts in mathematics, New York, NY, 1989

United States, United States of America

lg974655

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A Course in Modern Geometries is designed for a junior-senior 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 non-Euclidean geometry. In Chapter 3, a new introduction to symmetry and hands-on 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 3-4 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 self-similarity 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 author-developed guides for dynamic software explorations of the Poincaré 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.

Front Matter....Pages i-xii
Axiomatic Systems and Finite Geometries....Pages 1-24
Non-Euclidean Geometry....Pages 25-73
Geometric Transformations of the Euclidean Plane....Pages 74-126
Projective Geometry....Pages 127-200
Back Matter....Pages 201-233

2013-08-01