The Princeton Companion to Mathematics

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Timothy Gowers is the Rouse Ball Professor of Mathematics at the University of Cambridge. He received the Fields Medal in 1998, and is the author of Mathematics: A Very Short Introduction. June Barrow-Green is lecturer in the history of mathematics at the Open University. Imre Leader is professor of pure mathematics at the University of Cambridge.

出版者:Princeton University Press
作者:Gowers, Timothy (EDT)/ Barrow-Green, June (EDT)/ Leader, Imre (EDT)
出品人:
页数:1056
译者:
出版时间:2008-9-28
价格:GBP 77.00
装帧:Hardcover
isbn号码:9780691118802
丛书系列:
图书标签:
  • 数学 
  • Mathematics 
  • 科普 
  • 数学史 
  • Princeton 
  • ModernMath 
  • Math 
  • 数学文化 
  •  
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This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more.

Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.

* Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors

* Presents major ideas and branches of pure mathematics in a clear, accessible style

* Defines and explains important mathematical concepts, methods, theorems, and open problems

* Introduces the language of mathematics and the goals of mathematical research

* Covers number theory, algebra, analysis, geometry, logic, probability, and more

* Traces the history and development of modern mathematics

* Profiles more than ninety-five mathematicians who influenced those working today

* Explores the influence of mathematics on other disciplines

* Includes bibliographies, cross-references, and a comprehensive index

具体描述

读后感

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This is real modern mathematics. Most of the stuff is in Part III, IV, V and VII. Part III includes 99 'mathematical concepts', i.e. compactness, differential forms, Hamiltonians, homotopy groups and so on. These are mostly short articles of about two pages...  

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这本书网络上能下pdf版本。不过好像缺目录。 觉得这书写的不错。适合学过一些基础数学(分析,线性代数,交换代数,几何)的人看看  

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最近数学学的有点乱想厘清一下数学的各种分支的关系,于是翻出了之前借的这本曾三年前翻过的这本《指南》。结果,学过的部分像爱因斯坦的广义相对论,PDE,计算复杂性,数值分析等,看的比较容易点,其他部分又是走马观花了。 如果有缘,下次可能会把它当作工具书。 我感觉这本...  

评分

这本书网络上能下pdf版本。不过好像缺目录。 觉得这书写的不错。适合学过一些基础数学(分析,线性代数,交换代数,几何)的人看看  

评分

关于作者T.Gowers爵士我是在世界大数学家画传里面看到的,做泛函和组合数学,fields奖得主。gowers邀请了很多数学家一起完成各个部分的编辑,可以算是最新的数学百科全书了。 这本书的译者是原来武大的校长齐民友教授,翻译的时候已经80岁了。从翻译的质量来说,足可以看出用心...  

用户评价

评分

花了四个月啃完,算是对现代数学的各个分支宽搜了一遍吧,和很多概念混了个眼熟。有些章节还是相当好看的,但感觉整书看到一半多一点之后趣味性急转直下

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:O1-4/P957

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第一章中有一节Some Fundamental Mathematical Definitions,由现代数学最主要的四种数讲起,他们是代数的主角。然后站高些看看数到底是一种什么结构,又有那些相似或同理的非数字结构,如何人为的造出一些结构来做实验,验证我们脑袋里的一些假设性的问题,以及有了这些代数研究对象后其互相影响互动的机制。接着是与代数采用了完全不同的办法解决问题的数学分析。代数要的是逻辑推理出的质的抽象结论,分析则更关注如何更准确的量的描述一个具体的对象。最后一部分是关于几何的,关注人对图像进行思考的角度以及由此引出的各种解惑之道。

评分

第一章中有一节Some Fundamental Mathematical Definitions,由现代数学最主要的四种数讲起,他们是代数的主角。然后站高些看看数到底是一种什么结构,又有那些相似或同理的非数字结构,如何人为的造出一些结构来做实验,验证我们脑袋里的一些假设性的问题,以及有了这些代数研究对象后其互相影响互动的机制。接着是与代数采用了完全不同的办法解决问题的数学分析。代数要的是逻辑推理出的质的抽象结论,分析则更关注如何更准确的量的描述一个具体的对象。最后一部分是关于几何的,关注人对图像进行思考的角度以及由此引出的各种解惑之道。

评分

由名家执笔,非常好,避免国内理工科学生对数学的支离破碎地理解,也能让你充分领略到数学的美. 窥到现代数学的基本概貌.

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