问题解决策略
Problem-solving strategies
Arthur Engel · 初版 1998 年
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Problem-Solving Strategies是一本独特的竞赛试题集，汇集了来自二十多项面向高中生的重大国家及国际数学竞赛的题目。书中对解题策略展开了深入探讨。本书面向各级别竞赛的教练与参赛选手，直至最高水平赛事：IMO、Tournament of the Towns以及Putnam competition的非微积分部分。对于需要从易到难各类题目的数学社团高中教师，以及希望布置“每周一题”的辅导教师
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Arthur Engel 写的《解题策略》（Problem-Solving Strategies）[1] 那本书里有一大堆这样的题，我甚至觉得就包括现在这一道。很有趣的一本书。[1]https://www.google.com/books/edition/Problem_Solving_Strateg...
Bunch of problems like this are in the book "Problem-Solving Strategies" by Arthur Engel [1], I believe even including this particular one. Fun book. [1]https://www.google.com/books/edition/Problem_Solving_Strateg...
如果你想找纸质书，可以试试《Problem Solving Strategies》（http://www.amazon.com/Problem-Solving-Strategies-Problem-Boo...）或者《Problem Solving Through Problems》（http://www.amazon.com/Problem-Solving-Through-Problems-Larso...）。
If you are looking for a physical book, try Problem Solving Strategies (http://www.amazon.com/Problem-Solving-Strategies-Problem-Boo...) or Problem Solving Through Problems (http://www.amazon.com/Problem-Solving-Through-Problems-Larso...).
……依我看最好的准备方法就是从现在到开课这段时间多做证明题。试着在网上找点证明题练习看自己能不能做出来，或者找一本离散数学入门书。Engel 的 Problem-Solving Strategies 是一本好书，不过对初学者来说稍微有点进阶了。
…best way to prepare imo is to just do proofs between now and the start of the course. Try to find practice proof problems online and see if you can do them or find an entry-level book on discrete math. Problem-Solving Strategies by Engel is a good but slightly more advanced book for a beginner.
Arthur Engel 的 Problem-Solving Strategies。它不仅仅是一本教材，而且不太容易消化。这本书配合互联网是一个强大的组合，不仅能学到炫酷的数学技巧，还能建立心智模型 / 问题框架构建……
Problem-Solving Strategies by Arthur Engel. It's more than a textbook and not easily absorbed. The book + the internet is a powerful combination for not just learning cool math skills but building mental models/ problem framing…
看完了所有评论，我也来分享一下我的选择：1. Stewart 和 Tall 写的《The foundations of mathematics》 2. Arthur Engel 写的《Problem Solving Strategies》 3. Rotman 写的《Journey into Mathematics》 4. Knuth 等人写的《Concrete Mathematics》
After reading all the comments I am sharing my choices 1. The foundations of mathematics by Stewart and Tall 2. Problem Solving Strategies by Arthur Engels 3. Journey into Mathematics by Rotman 4. Concrete Mathematics by Knuth et al.
……敏锐察觉自己的论证何时不够严密、何时做出了错误假设；把你的思维模块化；更加熟练地运用逻辑“语汇”。至于书籍，我个人最喜欢的是 Problem Solving Strategies（Engel 著）和 Art and Craft of Problem Solving（Zeitz 著）。这两本书都非常平易近人，有大量的例子，能让你从不同的视角看待数学的魅力所在。
…awareness of when your arguments are not airtight or when you make false assumptions - modularize your thinking - become more fluent with logical "vocabulary" As for books, my personal favorites were Problem Solving Strategies (Engel) and Art and Craft of Problem Solving (Zeitz). They're both really approachable, have plenty of examples, and will give you a different perspective on what math can be about.