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Thinking Geometrically

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Thinking Geometrically

Thinking Geometrically

A Survey of Geometries
Thomas Q. Sibley, Saint John's University, Minnesota
December 2015
Hardback
9781939512086
AUD$135.00
inc GST
Hardback
    Description

    This is a self-contained, comprehensive survey of college geometry that can serve a wide variety of courses for students of both mathematics and mathematics education. The text develops visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Chapter topics include Euclidean geometry, axiomatic systems and models, analytic geometry, transformational geometry, symmetry, non-Euclidean geometry, projective geometry, finite geometry, differential geometry, and discrete geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. Appendices include material from Euclid's first book, as well as Hilbert's axioms, and provide brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters.

    • Emphasises the best aspects of geometrical thinking: its beauty, visual insights, convincing proofs, broad connections, and more
    • The book's focus on developing reason and intuition will appeal to both students of mathematics and mathematics education
    • Historical material and biographies of famous geometers share some of the rich insights that history can provide

    Product details

    December 2015
    Hardback
    9781939512086
    509 pages
    262 × 182 × 35 mm
    1.13kg
    This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.

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    Contents

    Table of Contents

    • Preface
    • 1. Euclidean geometry
    • 2. Axiomatic systems
    • 3. Analytic geometry
    • 4. Non-Euclidean geometries
    • 5. Transformational geometry
    • 6. Symmetry
    • 7. Projective geometry
    • 8. Finite geometries
    • 9. Differential geometry
    • 10. Discrete geometry
    • 11. Epilogue
    • Appendix A. Definitions, postulates, common notions, and propositions from Book I of Euclid's Elements
    • Appendix B. SMSG axioms for Euclidean geometry
    • Appendix C. Hilbert's axioms for Euclidean plane geometry
    • Appendix D. Linear algebra summary
    • Appendix E. Multivariable calculus summary
    • Appendix F. Elements of proofs
    • Answers to selected exercises
    • Acknowledgements
    • Index.
      • Show more
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    About the authors
      Author
    • Thomas Q. Sibley , Saint John's University, Minnesota

      Thomas Q. Sibley is a Professor of Mathematics at Saint John's University, Minnesota. He has taught mathematics in the Democratic Republic of the Congo and Liberia as well as in the USA, and has received several teaching awards, including the Distinguished Teaching Award from the MAA, North Central Section (2003). He is a member of the American Mathematical Society, the Association for Women in Mathematics, the Society for Mathematical Biology, and the Council for Undergraduate Research.

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