Resources like "How to solve it" by Polya

Question

In How to Solve It, G. Polya describes methods of problem solving. I'm looking for more resources discussing the meta-level of how math is done.

Answer 1

For online resources

1. https://artofproblemsolving.com/ - Check the resources link
2. https://terrytao.wordpress.com/career-advice/
3. https://brilliant.org/

For books

1. The Art and Craft of Problem Solving - Paul Zeitz
2. Anything by Titu Andreescu (2 examples being: 103 Trigonometry Problems or Putnam and Beyond)
3. Problem Solving Strategies - Arthur Engel

That should be a good start. You can also check out any book pertaining to preparation for the International Mathematical Olympiad, those also have good problem solving tips.

Hope this helps!

Answer 2

Terence Tao: Solving mathematical problems: A personal perspective

Answer 3

Tao's and Polya's are the ones that I'll recommend to my friends. I'd like to add some that are also on my shelf:

1. Problem-Solving Strategies by Engel, Arthur
2. Problem-Solving Through Problems by Loren C. Larson (this one is easier)

As Bruno's mentioned, books on MO's and any other mathematics competitions can really give you insights on problem solving. If you feel books on competitions are too much/"heavy", general problem books are the alternatives.

Answer 4

I have a short list:

• Mathematical Tapas https://www.springer.com/br/book/9783319421858 (this is the volume 1. There is volume 2, too, and it's good but not have solutions).

• Proofs from the BOOK, Aigner and Ziegler.

• How to prove it, Daniel Valleman

• How to read and do proofs, Daniel Solow.

• How to think like a mathematician, Kevin Houston

What I'm using: I'm using the last one, and it's very good.