Revolutions of Geometry (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

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9780470167557: Revolutions of Geometry (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

Guides readers through the development of geometry and basic proof writing using a historical approach to the topic

In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfully equipped with the necessary logic to develop a full understanding of geometric theorems.

Following a presentation of the geometry of ancient Egypt, Babylon, and China, the author addresses mathematical philosophy and logic within the context of works by Thales, Plato, and Aristotle. Next, the mathematics of the classical Greeks is discussed, incorporating the teachings of Pythagoras and his followers along with an overview of lower-level geometry using Euclid's Elements. Subsequent chapters explore the work of Archimedes, Viete's revolutionary contributions to algebra, Descartes' merging of algebra and geometry to solve the Pappus problem, and Desargues' development of projective geometry. The author also supplies an excursion into non-Euclidean geometry, including the three hypotheses of Saccheri and Lambert and the near simultaneous discoveries of Lobachevski and Bolyai. Finally, modern geometry is addressed within the study of manifolds and elliptic geometry inspired by Riemann's work, Poncelet's return to projective geometry, and Klein's use of group theory to characterize different geometries.

The book promotes the belief that in order to learn how to write proofs, one needs to read finished proofs, studying both their logic and grammar. Each chapter features a concise introduction to the presented topic, and chapter sections conclude with exercises that are designed to reinforce the material and provide readers with ample practice in writing proofs. In addition, the overall presentation of topics in the book is in chronological order, helping readers appreciate the relevance of geometry within the historical development of mathematics.

Well organized and clearly written, Revolutions of Geometry is a valuable book for courses on modern geometry and the history of mathematics at the upper-undergraduate level. It is also a valuable reference for educators in the field of mathematics.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

About the Author :

Michael O'Leary, PhD, is Professor of Mathematics at the College of DuPage. He received his PhD in mathematics from the University of California, Irvine in 1994.

Review :

"An excellent supplemental resource or main textbook for an overview of mathematics course for upper-level undergraduate and graduate students." (Choice, October 2010).

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

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Description du livre John Wiley and Sons Ltd. Hardback. État : new. BRAND NEW, Revolutions of Geometry, Michael O'Leary, Based on the premise that in order to write proofs, one needs to read finished proofs as well as study both their logic and grammar, Revolutions in Geometry depicts how to write basic proofs in various fields of geometry. This accessible text for junior and senior undergraduates explains the general development of geometry throughout time, discusses the involvement of its major contributors, and places the proofs into the context of geometry's history to illustrate how crucial proof writing is to the job of a mathematician. N° de réf. du libraire B9780470167557

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Description du livre John Wiley and Sons Ltd, United States, 2010. Hardback. État : New. 1. Auflage. Language: English . Brand New Book. Based on the premise that in order to write proofs, one needs to read finished proofs as well as study both their logic and grammar, Revolutions in Geometry depicts how to write basic proofs in various fields of geometry. This accessible text for junior and senior undergraduates explains the general development of geometry throughout time, discusses the involvement of its major contributors, and places the proofs into the context of geometry s history to illustrate how crucial proof writing is to the job of a mathematician. N° de réf. du libraire BZV9780470167557

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Description du livre John Wiley and Sons Ltd, United States, 2010. Hardback. État : New. 1. Auflage. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. Based on the premise that in order to write proofs, one needs to read finished proofs as well as study both their logic and grammar, Revolutions in Geometry depicts how to write basic proofs in various fields of geometry. This accessible text for junior and senior undergraduates explains the general development of geometry throughout time, discusses the involvement of its major contributors, and places the proofs into the context of geometry s history to illustrate how crucial proof writing is to the job of a mathematician. N° de réf. du libraire BZV9780470167557

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