Axiomatic Geometry (Pure and Applied Undergraduate Texts) (Sally:…

Axiomatic Geometry (Pure and Applied Undergraduate Texts) (Sally: Pure and Applied Undergraduate Texts)
Publisher: American Mathematical Society
Date: 2013-05-11
ISBN-10: 0821884786
ISBN-13: 9780821884782
Language: English
Pages: 472
Added: 2018-09-19 13:46:11

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. Show more Show less aa6f488e6d5280e7291b9d9276761115

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