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Visual Group Theory

Visual Group Theory
作者:Nathan Carter
出版社:The Mathematical Association of America
出版年:2009-05
ISBN:9780883857571
行业:其它
浏览数:240

内容简介

Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts. But its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective.

The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.

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作者简介

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目录

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读书文摘

群论研究发现了一个关于饰带模式的非常有趣的事实:任何饰带模式的对称都可以由七个不同的无限群中的一个来描述。也就是说,虽然你可以用一生的时间来创造各种不同的饰带模式,但是任何模式的对称只能是七个不同类型中的一个。

在数学界,人们通过事先约定法则,可以确保在讨论数学对象时,所有人头脑中想的是同样的事物。换句话说,把思想整理为法则,可以确保大家使用的是相同的语言,从而使交流问题最小化。

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