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Geometry by Its History (Undergraduate Texts in Mathematics / Readings in Mathematics) [Englisch] [Gebundene Ausgabe]

Alexander Ostermann , Gerhard Wanner

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Kurzbeschreibung

12. April 2012 3642291627 978-3642291623 2012

In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in  geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19thcentury.

Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.


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From the reviews:

Choice - Outstanding Academic Title in 2012

“This is an excellent, challenging textbook as well as a valuable resource for historical information, problems, and student projects. The historical content is broad based, comprehensive, and reliable. Each chapter has extensive exercises, many taken directly from or based on historical sources … . Hints and solutions for all problems are given in an appendix. Thorough bibliography. Summing Up: Highly recommended. Lower-division undergraduates and above.” (C. A. Gorini, Choice, Vol. 50 (3), November, 2012)

“There is a lot of interesting material in this book, supplemented by a lot of very nice artwork and many interesting exercises … . I would think that any other college instructor … with an interest in geometry would also want a copy on his or her shelf.” (Mark Hunacek, The Mathematical Association of America, June, 2012)

“This book belongs on the bookshelf of every geometer. … The authors have penned their book with students of geometry as well as science in mind. In fact, the book would serve well as a second year mathematics course in a classical liberal arts setting. … the book treats many interesting and beautiful problems, introducing powerful concepts along the way, and yet is written at a level suitable for an introductory course of geometry or even advanced mathematics.” (Alan S. McRae, Mathematical Reviews, February, 2013)

Buchrückseite

In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in  geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19th century.

Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.


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5.0 von 5 Sternen This is a marvelous book. 5. Januar 2014
Von D. Vader - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe|Verifizierter Kauf
Everyone interested in the history of mathematics should own this book. I'm not sure I agree with the author's idea of using history to teach geometry, but simply as a source book for the history of geometry, this book can't be beat. There are a great many illustrations in many languages, each serving a specific purpose which the author makes clear. This is more than an undergraduate textbook, it is a scholarly masterpiece.
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