陶哲轩教你学数学
Solving Mathematical Problems
Terence Tao · 初版 2006 年
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4位读者提及
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“本书引领读者掌握解决 Mathematical Olympiad 级别数学问题所涉及的各种策略。Solving Mathematical Problems 全书包含大量的练习题与范例解答。本书仅要求读者具备基础高中数学知识，非常适合对纯粹数学感兴趣的普通读者和14岁以上的学生。”——封底第[4]页。
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这里提到的 Tao 的《Solving Mathematical Problems: A Personal Perspective》（https://www.amazon.com/Solving-Mathematical-Problems-Persona...）是一本极好的书，提供了解决数学问题的关键方法，现在已经是一部经典了……
Tao's Solving Mathematical Problems: A Personal Perspective (https://www.amazon.com/Solving-Mathematical-Problems-Persona...) mentioned here is an excellent book that provides keys to mathematical approach to problems and is now a classic…
……那种类型，如果你看不出事情是怎么做出来的，对你学习下一步该怎么做就毫无帮助。Tao 在这方面是个巨大的特例。他的《How to Solve Mathematical Problems》（http://www.amazon.com/Solving-Mathematical-Problems-Personal...）比 Polya 的名作更有针对性，但在帮助理解数学家如何思考方面要有效得多。你可以免费获取第一章（http://www.math.ucla.edu/~tao/preprints/problem.ps）……
…type, where if you didn't see how things done would't or couldn't help you in learning how to proceed. Tao is a big outlier in this regard. His How to Solve Mathematical Problems (http://www.amazon.com/Solving-Mathematical-Problems-Personal...) is more focused than Polya's famous book but is a much better help in learning how mathematicians think. You can get the first chapter for free (http://www.math.ucla.edu/~tao/preprints/problem.ps),…
书的话我推荐《Men of Mathematics》，它激励了无数人走上数学职业道路，还有 Terence Tao 的《Solving Mathematical Problems》，非常精彩。要是你不差钱，也就是说愿意花大概 200 美元，gomboc（http://en.wikipedia.org/wiki/Gömböc）是个很棒的物件，你可以在 gomboc-shop.com 买到
For books i'd suggest Men of Mathematics that has inspired countless people to math careers or Terence Tao's Solving Mathematical Problems, which is excellent. Now, if money's no object, i.e. you're willing to spend around $200, the gomboc (http://en.wikipedia.org/wiki/Gömböc) is a wonderful object to buy, you can buy it at the gomboc-shop.com
虽然涉及面不是很广，但 Terence Tao 的《Solving Mathematical Problems》（https://books.google.com/books/about/Solving_Mathematical_Pr...）比我在该水平见过的任何其他书都更能让你理解数学思维。
It's not wide-ranging but Terence Tao's Solving Mathematical Problems (https://books.google.com/books/about/Solving_Mathematical_Pr...) makes you understand mathematical thinking better than any other book I have seen at that level.
……https://github.com/photonlines/Intuitive-Guide-to-Maxwells-Equations - 《Introduction to Elementary Particles》（David J. Griffiths） - 《An Invitation to Applied Category Theory: Seven Sketches in Compositionality》（Brendan Fong, David I Spivak） - 《Solving Mathematical Problems: A Personal Perspective》（Terence Tao）
…https://github.com/photonlines/Intuitive-Guide-to-Maxwells-Equations - Introduction to Elementary Particles (David J. Griffiths) - An Invitation to Applied Category Theory: Seven Sketches in Compositionality (Brendan Fong, David I Spivak) - Solving Mathematical Problems: A Personal Perspective (Terence Tao)
……这符合楼主提问的本意。当然，刷完任何一本线性代数教材都能提高你的线性代数水平。顺着楼主的问题来说：G. Polya 的《How to Solve it》、Terrence Tao 的《Solving Mathematical Problems》、Keith Devlin 的《Introduction to Mathematical Thinking》都很神，尤其是《How to Solve it》，绝对是旷世经典。
…that answers the spirit of OP's question. Sure working through ANY Linear Algebra textbook is going to improve your Linear Algebra skills. In the spirit of OP's question: How to Solve it by G. Polya Solving Mathematical Problems by Terrence Tao Introduction to Mathematical Thinking by Keith Devlin Are all amazing, How to Solve it in particular is an all time classic.