Surreal Numbers

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.

出版者:Addison Wesley

作者:[美] Donald Knuth

页数:119

出版时间:1974-1-1

价格:GBP 18.99

装帧:Paperback

isbn号码:9780201038125

图书标签:数学计算机科学MathKnuth小说计算机SurrealNumber

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.

读后感

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...  

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。。。  

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...  

比较有趣的科学小品文，生动地演绎了一个数学公理体系构造数系的小故事，适合作为集合论的科普入门读物，故事挺有趣，数学方面的内容比较浅显。我其实更喜欢那个故事本身，写成小说发到起点上，他不香吗？手动狗头 “一对暧昧的异性友人，逃离尘世到海边生活，想要寻找人生的意...  

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。。。  

用户评价

虽然是大神写的。。。可是读了一半就读不下去了。不是很喜欢这种风格。。。

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

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！

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

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