数学游戏必胜攻略
Winning Ways for Your Mathematical Plays
Elwyn R. Berlekamp、John Horton Conway、Richard K. Guy · 初版 1982 年
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为什么值得读
- 比学术专著更亲民，寓高深数学于游戏之中
- 是理解超实数与博弈论绝佳的轻松入门读物
- 对跳棋等游戏分析透彻，算法易记且易执行
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Winning Ways for Your Mathematical Plays
Elwyn R. Berlekamp、John Horton Conway、Richard K. Guy · 初版 1982 年
正在加载完整评论……
……Dasgupta、Papadimitriou 和 Vazirani 著）- 《Algorithm Design》（Kleinberg 和 Tardos 著）- 费曼物理学讲义 - 朗道与栗弗席兹系列 - Vladimir Arnold 关于 ODE 和经典力学的书 - 《Winning Ways for your Mathematical Plays》（Berlekamp 等人著）- 《Elements of Information Theory》（Cover & Thomas 著）- 《Information Theory, Inference, and Learning Algorithms》（MacKay 著）- 《Network Optimization》（Bertsekas 著）- 《Convex Optimization》……
…Dasgupta, Papadimitriou, and Vazirani) - Algorithm Design (by Kleinberg and Tardos) - Feynman Lectures on Physics - Landau & Lifschitz's series - Vladimir Arnold's books on ODEs and Classical Mechanics - Winning Ways for your Mathematical Plays (by Berlekamp et al.) - Elements of Information Theory (by Cover & Thomas) - Information Theory, Inference, and Learning Algorithms (by MacKay) - Network Optimization (by Bertsekas) - Convex Optimization…
……用 backtracking 会更难高效解开这个谜题，因为在走到最后一步之前，你根本看不出自己走错了路。如果你对跳棋谜题（peg-jumping puzzle）背后的数学感兴趣，可以看看 Berlekamp、Conway 和 Guy 写的《Winning Ways for your mathematical plays, Vol 2》，里面详细讨论了十字形跳棋谜题的数学原理。
…puzzle would be harder to solve efficiently with backtracking, because it's not obvious until the end that you're on the wrong path. If you're interested in the mathematics of peg-jumping puzzles, see "Winning Ways for your mathematical plays, Vol 2", by Berlekamp, Conway, and Guy, which discusses the mathematics of the plus-shaped peg-jumping puzzle in detail.
《Winning Ways for Your Mathematical Plays》[1] 这本书里有三种主要算法，都是沿着这种基本思路来的。它们实际上针对记忆和操作难度做过优化。里面还有针对移动特定方块的完整记录解法……
The book Winning Ways for Your Mathematical Plays[1] has three main algorithms that are in the vein of this basic idea. They were actually optimized for ease of remembering and executing on. With full documented solutions for moving specific cubes…
我相信这就是《Winning ways for your mathematical plays》的作者 Richard Guy。如果你对博弈论或趣味数学感兴趣，这本书绝对值得翻一翻。
I believe this is Richard Guy of "Winning ways for your mathematical plays". It's definitely worth browsing if you're interested in game theory or recreational math.
……1 False *Game> half + half == 1 True *Game> half * 1 == half True *Game> half * (one + one) > 1 False 学习的最佳资源都是 Conway 写的：《Winning Ways for your Mathematical Plays》（WW）和《On Numbers and Games》（ONAG）。WW 更加通俗易懂，通过游戏向你介绍数字，而 ONAG 更偏向硬核数学书，通过数字来解释游戏。WW 大概是……
…1 False *Game> half + half == 1 True *Game> half * 1 == half True *Game> half * (one + one) > 1 False The best resources for learning are both by Conway: "Winning Ways for your Mathematical Plays" (WW) and "On Numbers and Games" (ONAG). WW is more accessible and introduces you to numbers via games, whereas ONAG is more of a hard-core math book that explains games via numbers. WW is probably…
《On Numbers and Games》是一本好书，但可能有点难啃。Berlekamp、Conway 和 Guy 合著的《Winning Ways for your Mathematical Plays》是了解超现实数（surreal number）更平缓的入门途径，而且非常有趣。
"On Numbers and Games" is a great book but it can be tough. "Winning Ways for your Mathematical Plays" by Berlekamp, Conway & Guy is a gentler introduction to surreal number. It's also very fun.