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Axiomatic Geometry

ISBN-10: 0821884786
ISBN-13: 9780821884782
Edition: 2013
Authors: John M. Lee
List price: $75.00 Buy it from $47.13
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Description: Jack Lee's book will be extremely valuable for future high school math teachers. It is perfectly designed for students just learning to write proofs; complete beginners can use the appendices to get started, while more experienced students can jump  More...

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Book details

List price: $75.00
Copyright year: 2013
Publisher: American Mathematical Society
Publication date: 4/10/2013
Binding: Hardcover
Pages: 469
Size: 7.00" wide x 9.75" long x 1.00" tall
Weight: 2.398
Language: English

Jack Lee's book will be extremely valuable for future high school math teachers. It is perfectly designed for students just learning to write proofs; complete beginners can use the appendices to get started, while more experienced students can jump right in. The axioms, definitions, and theorems are developed meticulously, and the book culminates in several chapters on hyperbolic geometry--a lot of fun, and a nice capstone to a two-quarter course on axiomatic geometry. --John H. Palmieri, University of Washington Lee's Axiomatic Geometry is suitable for an undergraduate college geometry course, and since it covers most of the topics normally taught in American high school geometry, it would be excellent preparation for future high school teachers. --Robin Hartshorne, University of California, Berkeley The story of geometry is the story of mathematics itself: Euclidean geometry was the first branch of mathematics to be systematically studied and placed on a firm logical foundation, and it is the prototype for the axiomatic method that lies at the foundation of modern mathematics. It has been taught to students for more than two millennia as a model of logical thought. This book tells the story of how the axiomatic method has progressed from Euclid's time to ours, as a way of understanding what mathematics is, how we read and evaluate mathematical arguments, and why mathematics has achieved the level of certainty it has. It is designed primarily for advanced undergraduates who plan to teach secondary school geometry, but it should also provide something of interest to anyone who wishes to understand geometry and the axiomatic method better. It introduces a modern, rigorous, axiomatic treatment of Euclidean and (to a lesser extent) non-Euclidean geometries, offering students ample opportunities to practice reading and writing proofs while at the same time developing most of the concrete geometric relationships that secondary teachers will need to know in the classroom.

John M. Lee is Professor of Mathematics at the University of Washington in Seattle, where he regularly teaches graduate courses on the topology and geometry of manifolds. He was the recipient of the American Mathematical Society's Centennial Research Fellowship and he is the author of three previous Springer books: the first edition (2000) and second edition (2010) of Introduction to Topological Manifolds and Riemannian Manifolds: An Introduction to Curvature (1997).

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