The Four Pillars of Geometry 2024 pdf epub mobi 电子书

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The Four Pillars of Geometry 2024 pdf epub mobi 电子书著者简介

John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

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发表于2024-11-22

The Four Pillars of Geometry 2024 pdf epub mobi 电子书

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一般而言，要想找到一本体现某些真正的几何思想精髓的书并不是很容易，但我还是有幸读到了John Stillwell的这本《Four Pillars of Geometry》，读完后至今仍令人荡气回肠！这本书不算太艰深，但真的不同于传统的介绍几何的读物，特别是展现了很多本科生并不熟悉的视角，使人...

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出版者:Springer

作者:John Stillwell

出品人:

页数:229

译者:

出版时间:2010-12-1

价格:USD 54.95

装帧:Paperback

isbn号码:9781441920638

丛书系列:Undergraduate Texts in Mathematics

图书标签: 数学几何 Geometry Stillwell Springer Mathematics 數學几何与拓扑

The Four Pillars of Geometry 2024 pdf epub mobi 电子书图书描述

For two millennia the right way to teach geometry was the Euclidean approach, and in many respects, this is still the case. But in the 1950s the cry "Down with triangles!" was heard in France and new geometry books appeared, packed with linear algebra but with no diagrams. Was this the new right approach? Or was the right approach still something else, perhaps transformation groups?

The Four Pillars of Geometry approaches geometry in four different ways, spending two chapters on each. This makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic. Not only does each approach offer a different view; the combination of viewpoints yields insights not available in most books at this level. For example, it is shown how algebra emerges from projective geometry, and how the hyperbolic plane emerges from the real projective line.

The author begins with Euclid-style construction and axiomatics, then proceeds to linear algebra when it becomes convenient to replace tortuous arguments with simple calculations. Next, he uses projective geometry to explain why objects look the way they do, as well as to explain why geometry is entangled with algebra. And lastly, the author introduces transformation groups---not only to clarify the differences between geometries, but also to exhibit geometries that are unexpectedly the same.

All readers are sure to find something new in this attractive text, which is abundantly supplemented with figures and exercises. This book will be useful for an undergraduate geometry course, a capstone course, or a course aimed at future high school teachers.

The Four Pillars of Geometry 2024 pdf epub mobi 电子书

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我读过的讲的最清晰的数学书

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这本书相对于他的曲面的几何一书是一个简单版本。喜欢他的风格，喜欢他的思考

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我读过的讲的最清晰的数学书

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选这本书读的原因很简单——看完Naive Lie Theory之后就觉得John Stillwell有种看问题本质，思路开阔，循循善诱的特质。因而想看看他的其他作品，恰巧geometry又是我感兴趣的题目。在包头往返北京的火车上读了大半，剩下的回家后4h读完，200页左右的书还是好读，清晰的框架对于我这种转数学的同学很友好。projective geometry, non-Euclidean geometry部分是我收获最大的，比如ordinary perspective preserves straightness，non-Euclidean perspective preserves angle。比如作者成功说服了我非欧空间的引入帮助了对projective line 的理解。

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继Rudin的Principles of Mathematical Analysis之后最喜欢的教材，简直可以当故事书看，越基础越抽象的东西就越有意思~

The Four Pillars of Geometry 2024 pdf epub mobi 电子书