**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.

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by Judith N. Cederberg

Cederberg, Judith N.

Springer New York : Imprint : Springer

Springer US

Undergraduate Texts in Mathematics, Undergraduate texts in mathematics, Second Edition., New York, NY, United States, 2001

Undergraduate texts in mathematics, 2nd ed., corrected 2nd printing, New York, 2005, ©2001

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

Undergraduate texts in mathematics, 2nd ed, New York, ©2010

Undergraduate texts in mathematics, 2nd ed, New York, 2011

United States, United States of America

sm21951990

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<p>Designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. The first chapter presents several finite geometries in an axiomatic framework, while Chapter 2 continues the synthetic approach in introducing both Euclids and ideas of non-Euclidean geometry. There follows a new introduction to symmetry and hands-on explorations of isometries that precedes an extensive analytic treatment of similarities and affinities. Chapter 4 presents plane projective geometry both synthetically and analytically, and 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. Throughout, each chapter includes a list of suggested resources for applications or related topics in areas such as art and history, plus this second edition points to Web locations of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions are available for "Cabri Geometry" and "Geometers Sketchpad".</p>


<p>"...this 2nd edition contains new material all throughout offering hands-on experience to develop intuitive understanding of a number of topics before their formal presentation."
</p>

Front Matter....Pages i-xix
Axiomatic Systems and Finite Geometries....Pages 1-32
Non-Euclidean Geometry....Pages 33-97
Geometric Transformations of the Euclidean Plane....Pages 99-211
Projective Geometry....Pages 213-313
Chaos to Symmetry: An Introduction to Fractal Geometry....Pages 315-387
Back Matter....Pages 389-444

"A Course in Modern Geometries, Second Edition, is designed for a junior- to senior-level course for mathematics majors, including those who plan to teach in secondary school."-- Book Jacket

Undergraduate Texts in Mathematics
Erscheinungsdatum: 01.12.2010

2013-08-01