Course in Modern Geometries (eBook)

Judith N. Cederberg (Autor)

eBook Download: PDF

2013
Springer New York (Verlag)
978-1-4757-3490-4 (ISBN)

Infos

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 Poincare model, isometries, projectivities, conics and fractals. Parallel versions of these explorations are available for "e;Cabri Geometry"e; and "e;Geometer's Sketchpad"e;. Judith N. Cederberg is an associate professor of mathematics at St. Olaf College in Minnesota.

Produkt-Details

• Erscheint lt. Verlag: 9.3.2013
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 1-4757-3490-5 / 1475734905
• ISBN-13: 978-1-4757-3490-4 / 9781475734904