Donald E. Knuth is known throughout the world for his pioneering work on algorithms and programming techniques, for his invention of the Tex and Metafont systems for computer typesetting, and for his prolific and influential writing. Professor Emeritus of The Art of Computer Programming at Stanford University, he currently devotes full time to the completion of these fascicles and the seven volumes to which they belong.
From the Back Cover
Nearly 30 years ago, John Horton Conway introduced a new way to construct numbers. Donald E. Knuth, in appreciation of this revolutionary system, took a week off from work on The Art of Computer Programming to write an introduction to Conway's method. Never content with the ordinary, Knuth wrote this introduction as a work of fiction--a novelette. If not a steamy romance, the book nonetheless shows how a young couple turned on to pure mathematics and found total happiness.
The book's primary aim, Knuth explains in a postscript, is not so much to teach Conway's theory as "to teach how one might go about developing such a theory." He continues: "Therefore, as the two characters in this book gradually explore and build up Conway's number system, I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself."... It is an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other "real" value does. The system is truly "surreal." quoted from Martin Gardner, Mathematical Magic Show, pp. 16--19
Surreal Numbers, now in its 13th printing, will appeal to anyone who might enjoy an engaging dialogue on abstract mathematical ideas, and who might wish to experience how new mathematics is created.
很有意思的一本书~推荐学数学和对数学有兴趣的童鞋们读读~书中关于数系、极限的论述通俗易懂又充满学术性,充分体现了逻辑的美感。 而对于对数学不感兴趣的童鞋也可以从这本书领略到数系的神奇,会对数学改观也说不定呢~
评分看过英文版的,这本书从另一个新的便于常人理解的角度研究了数系的产生和发展,摆脱了以往数学的繁琐和逻辑化,而改用平常的语言,通俗的对话体作为阐述方式,让数系、极限等系统的知识贯穿于全书。并且告诉我们一些无法用语言描述的道理,很值得一看。。。
评分由于书中的集合论方面的东西在大学里面学过,所以我更注重本书中所描述的对知识的发现过程,或者说对问题的发现过程 工作中,难得不是去怎样解决问题,而是去定义问题,甚至是发现问题! 书中部分用词是很哲学化的,从某种程度上,这本书给我们的只是心法,只有切身体会那种...
评分推荐一份论文,对理解本书可能会有些帮助 An Introduction to Surreal Number http://www.whitman.edu/mathematics/SeniorProjectArchive/2012/Grimm.pdf 这份论文将 Surreal Number 书中 Alice 和 Bill 的结论用形式化的语言来描述和证明。形式化的证明虽然看起来不像小说一...
评分《研究之美》这本书,讲述了一对情侣一次偶然地遇到了一些记有各种不认识的符号的石头,并通过研究这些符号之间的关系,从而发现了一种新理论的故事。这种理论,从书的前言可以知道,称为 Conway 的超实数理论。 此书是斯坦福大学的非常有名的高德纳教授所写。在大二时候,我...
http://en.wikipedia.org/wiki/Surreal_number
评分the ultimate geek tool
评分the ultimate geek tool
评分the ultimate geek tool
评分对话体形式来讨论自然数这个基础,在此基础上定义了加法和乘法,非常的严谨,不过也很抽象比较难以理解,对人的挑战很大!
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