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 b...
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. 0201038129B04062001
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 ...
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.
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...
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Donald Knuth 作者
范德蛙
电子工业出版社2012版
Matthew
电子工业出版社2012版
蓬山远
电子工业出版社2012版
Kissinger
电子工业出版社2012版
0 有用 孟先生 2015-11-02 16:47:00
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。
0 有用 lred 2023-04-01 05:31:29 江苏
一男一女 在荒岛上 研究数学 well im sorry im not complicated enough for u
0 有用 低调的小哥儿 2020-03-07 12:12:27
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！
0 有用 水如歌 2026-03-15 14:20:06 云南
对话体的问题是，我们看不到 Alice 和 Bob 的演草纸。
0 有用 O(1) 的小乐 2012-01-18 09:34:31
不得不佩服Knuth的yy能力。。。这书还不错，感觉蛮严谨的。后续部分理解有点困难