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.
發表於2024-06-19
Surreal Numbers 2024 pdf epub mobi 電子書 下載
確實是好東西,很值得一看,個人認為齣彩的部分是譯者對作者意思的精準把握,確實是傳神之作。 第 25 頁“如果成立的話,那我就會將 (Y, phi) (此處 phi 錶示空集)稱為“正”數”,之後又發現此中 Y 必須滿足其中至少一個元素大於或相似於 0,隻要滿足瞭這個條件,它就成被稱...
評分 評分我看這裏的留言,包括書評和筆記沒一個人說明白這本書到底講瞭個什麼,到底什麼思路,整體脈絡到底是什麼的問題,總在扯些沒用的,所以我決定留言在這裏。 這本書是這樣,英文名應該叫 超現實的數,其實就是說一種數論吧,原文是這樣寫的 他們兩個發現石碑後,覺得這應該是一...
評分前麵還好。 感覺最後兩張,沒說明白。 1.牽涉到無窮的歸納法,看瞭幾遍,還是沒看懂作者在說什麼。 2.超實數的乘法,隻是起瞭個頭,剩下的完全沒說好嗎?可能是要讓讀者自己證明吧? 所以感覺結尾倉促。難道是一周快結束瞭,急著要把書結尾? 還有,吐槽一下翻譯,physic...
評分哲學是人類文明初期最早而且是唯一的學科。在古希臘,哲學"Φιλοσοφία" (philo-sophia)一詞是由“Philo”和“Sophia”組成,前者意為感情和愛,後者意為理性和智慧。在古希臘智者的心中,哲學是研究感性和理性平衡的學問。數學是哲學中最重要的一部分,是最早從哲學...
圖書標籤: 數學 計算機科學 Math Knuth 小說 計算機 Surreal Number
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評分第一口氣讀完瞭1-3章,第二口氣讀完瞭剩餘部分;不推公式也很好看。
評分第一口氣讀完瞭1-3章,第二口氣讀完瞭剩餘部分;不推公式也很好看。
評分對話體形式來討論自然數這個基礎,在此基礎上定義瞭加法和乘法,非常的嚴謹,不過也很抽象比較難以理解,對人的挑戰很大!
評分不得不佩服Knuth的yy能力。。。這書還不錯,感覺蠻嚴謹的。後續部分理解有點睏難
Surreal Numbers 2024 pdf epub mobi 電子書 下載