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A Course in Modern Geometries
Tag Description
099$aOnline resource: Springer
100$aCederberg, Judith N.
245$aA Course in Modern Geometries$h[EBook] /$cby Judith N. Cederberg.
250$aSecond Edition.
260$aNew York, NY :$bSpringer New York :$bImprint: Springer,$c2001.
300$aXIX, 441 p.$bonline resource.
338$aonline resource$bcr$2rdacarrier
440$aUndergraduate Texts in Mathematics,$x0172-6056
505$a1 Axiomatic Systems and Finite Geometries -- 2 Non-Euclidean Geometry -- 3 Geometric Transformations of the Euclidean Plane -- 4 Projective Geometry -- 5 Chaos to Symmetry: An Introduction to Fractal Geometry -- Appendices -- B Hilbert’s Axioms for Plane Geometry -- C Birkhoff’s Postulates for Euclidean Plane Geometry -- D The SMSG Postulates for Euclidean Geometry -- E Some SMSG Definitions for Euclidean Geometry -- F The ASA Theorem -- References.
520$aA Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 continues the synthetic approach as it introduces Euclid's geometry and ideas of non-Euclidean geometry. In Chapter 3, a new introduction to symmetry and hands-on explorations of isometries precedes the extensive analytic treatment of isometries, similarities and affinities. A new concluding section explores isometries of space. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3-4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. The new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Each chapter includes a list of suggested resources for applications or related topics in areas such as art and history. The second edition also includes pointers to the web location of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions of these explorations are available for "Cabri Geometry" and "Geometer's Sketchpad". Judith N. Cederberg is an associate professor of mathematics at St. Olaf College in Minnesota.
538$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710$aSpringerLink (Online service)
830$aUndergraduate Texts in Mathematics,$x0172-6056
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