A Course in Modern Geometries (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
441
Utgivningsdatum
2004-09-01
Upplaga
2nd ed. 2001. Corr. 2nd printing 2004
Förlag
Springer-Verlag New York Inc.
Illustratör/Fotograf
Tab 151 Abb
Illustrationer
7 Tables, black and white; XIX, 441 p.
Dimensioner
240 x 162 x 30 mm
Vikt
800 g
Antal komponenter
1
Komponenter
1 Hardback
ISBN
9780387989723
A Course in Modern Geometries (inbunden)

A Course in Modern Geometries

Inbunden Engelska, 2004-09-01
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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 Poincare model, isometries, projectivities, conics and fractals. Parallel versions are available for "Cabri Geometry" and "Geometers Sketchpad".
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Fler böcker av Judith N Cederberg

  • Course in Modern Geometries

    Judith N Cederberg

    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 t...

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Second Edition J. N. Cederberg A Course in Modern Geometries "Cederberg's book has the virtue of exceptionally clear exposition and at the same time, it is brief enough not to exhaust one's patience . . . I have seen hundreds of college-level texts on geometry and this is one of the handful I like the most." -THE UMAP JOURNAL

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Innehållsförteckning

1 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.