Solving Mathematical Problems
by Terence Tao · first published 2006
75% recommend25% neutral
"This text leads the reader through the various tactics involved in solving mathematical problems at the Mathematical Olympiad level. Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only basic high-school mathematics, the text is ideal for general readers and students 14 years and above with an interest in pure mathematics."--P. [4] of cover.
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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…
on “The Mind of a Mathematician” ↗…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),…
on “The Singular Mind of Terry Tao” ↗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
on “Ask HN: Graduation Present for Aspiring Math Major?” ↗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.
on “Ask HN: Are there books for mathematics like Feynman's lectures on physics?” ↗…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)
on “Ask HN: Serious mathematics books that can replace a good teacher?” ↗…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.
on “Ask HN: Math books that made you significantly better at math?” ↗Solving Mathematical Problems: A Personal Perspective would be more appealing. You can write a comment to highlight the part of the book that you like
on “Examples in Number Theory by Terence Tao [2005][PostScript]” ↗