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.
草读了一遍, 如果在读的时候, 能在纸上演绎, 推理,效果就更好了。 最好根据已知条件自己推敲一切。 这是一本关于, 逻辑演绎,归类,类比,推理,猜想,反证的书。
评分用2个地铁时间看了将近一半。 就像高德纳大神所言,本书的目标并非真的要教给读者Conway教授的理论,而是想让读者学到,一个人要如何着实来研究这么一套理论来。采用两个人的对话体,用简短精辟的语言用集合论来描述数学,思路清晰巧妙,富有哲理,不愧为上帝的作品。 译者翻译...
评分当我们想当然地总是assume too much还自以为经验丰富、懂得多的时候,真正的数学家们总会本能地问上一句为什么会有这样的现象,这样的现象是否就是“事实”,是否能找到证明...然后就有了公理、然后就有了简约优美或繁琐复杂的重重证明、然后就有了引理、然后就有了定理... Kn...
评分很有意思的一本书~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《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
评分第一口气读完了1-3章,第二口气读完了剩余部分;不推公式也很好看。
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!
评分http://en.wikipedia.org/wiki/Surreal_number
评分the ultimate geek tool
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