Geometries pdf epub mobi txt 电子书 下载 2024


Geometries

简体网页||繁体网页
A. B. Sossinsky
American Mathematical Society
2012-7-3
301
USD 48.00
Paperback
Student Mathematical Library
9780821875711

图书标签: 几何  数学  数学-抽象代数  数学-几何   


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发表于2024-12-23

Geometries epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

Geometries epub 下载 mobi 下载 pdf 下载 txt 电子书 下载 2024

Geometries pdf epub mobi txt 电子书 下载 2024



图书描述

The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal—although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms “toy geometries”, the geometries of Platonic bodies, discrete geometries, and classical continuous geometries.

The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking this knowledge may refer to a compendium in Chapter 0. Per the author's predilection, the book contains very little regarding the axiomatic approach to geometry (save for a single chapter on the history of non-Euclidean geometry), but two Appendices provide a detailed treatment of Euclid's and Hilbert's axiomatics. Perhaps the most important aspect of this course is the problems, which appear at the end of each chapter and are supplemented with answers at the conclusion of the text. By analyzing and solving these problems, the reader will become capable of thinking and working geometrically, much more so than by simply learning the theory.

Ultimately, the author makes the distinction between concrete mathematical objects called “geometries” and the singular “geometry”, which he understands as a way of thinking about mathematics. Although the book does not address branches of mathematics and mathematical physics such as Riemannian and Kähler manifolds or, say, differentiable manifolds and conformal field theories, the ideology of category language and transformation groups on which the book is based prepares the reader for the study of, and eventually, research in these important and rapidly developing areas of contemporary mathematics.

Geometries 下载 mobi epub pdf txt 电子书

著者简介

A. B. Sossinsky: Independent University of Moscow, Moscow, Russia


图书目录


Geometries pdf epub mobi txt 电子书 下载
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用户评价

评分

用群论系统地描述几类几何(Erlangen纲领),它们之间的层级关系,以及如何构造几类非欧几何。本书或将是本名著

评分

用群论系统地描述几类几何(Erlangen纲领),它们之间的层级关系,以及如何构造几类非欧几何。本书或将是本名著

评分

用群论系统地描述几类几何(Erlangen纲领),它们之间的层级关系,以及如何构造几类非欧几何。本书或将是本名著

评分

用群论系统地描述几类几何(Erlangen纲领),它们之间的层级关系,以及如何构造几类非欧几何。本书或将是本名著

评分

用群论系统地描述几类几何(Erlangen纲领),它们之间的层级关系,以及如何构造几类非欧几何。本书或将是本名著

读后感

评分

1. A. B. Sossinsky的《Geometries》是作者在莫斯科独立大学为一年级本科生开设讨论班用的讲义,出版的版本隶属于美国数学会本科生系列丛书Student Mathematical Library,第64卷。全书分16章,另加两个附录,共约300页。整体的脉络大致追随了F. Klein的纲领。 2. 因为这学期的...

评分

1. A. B. Sossinsky的《Geometries》是作者在莫斯科独立大学为一年级本科生开设讨论班用的讲义,出版的版本隶属于美国数学会本科生系列丛书Student Mathematical Library,第64卷。全书分16章,另加两个附录,共约300页。整体的脉络大致追随了F. Klein的纲领。 2. 因为这学期的...

评分

1. A. B. Sossinsky的《Geometries》是作者在莫斯科独立大学为一年级本科生开设讨论班用的讲义,出版的版本隶属于美国数学会本科生系列丛书Student Mathematical Library,第64卷。全书分16章,另加两个附录,共约300页。整体的脉络大致追随了F. Klein的纲领。 2. 因为这学期的...

评分

1. A. B. Sossinsky的《Geometries》是作者在莫斯科独立大学为一年级本科生开设讨论班用的讲义,出版的版本隶属于美国数学会本科生系列丛书Student Mathematical Library,第64卷。全书分16章,另加两个附录,共约300页。整体的脉络大致追随了F. Klein的纲领。 2. 因为这学期的...

评分

1. A. B. Sossinsky的《Geometries》是作者在莫斯科独立大学为一年级本科生开设讨论班用的讲义,出版的版本隶属于美国数学会本科生系列丛书Student Mathematical Library,第64卷。全书分16章,另加两个附录,共约300页。整体的脉络大致追随了F. Klein的纲领。 2. 因为这学期的...

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