The art of problem solving vs. openstax textbooks

[nbafitis28]

hello, I was wondering which book is better for actually genuinely getting better at math (not just learning actual tricks but training your brain as if it were an actual muscle), the art of problem solving textbooks or the openstax math textbooks?

 

[WWGD]

Polya's " How to Solve it" and other books of his are classics in that area, but I don't have direct experience. I'd say solving former Putnam and IMO problems should be helpful.

 

[Albertus Magnus]

Interestingly, physicist Richard Feynmann said that problem solving was something that could be learned but not taught.

 

[pines-demon]

Interestingly, physicist Richard Feynmann said that problem solving was something that could be learned but not taught.

Source?

 

[Muu9]

Interestingly, physicist Richard Feynmann said that problem solving was something that could be learned but not taught.

That might be why the AoPS books have a lot of challenging problems relative to he amount of instruction.

OP, I would recommend the AoPS books

 

[Albertus Magnus]

Source?

The discussion is found in Feynmann's Tips on Physics chapter 2, sec. 2.6 He writes:

I don’t know how to tell you something that will transform you from a person who can’t analyze new situations or solve problems, to a person who can. In the case of the mathematics, I can transform you from somebody who can’t differentiate to somebody who can, by giving you all the rules. But in the case of the physics, I can’t transform you from somebody who can’t to somebody who can, so I don’t know what to do.

 

[gleem]

Many years ago, Cambridge University published a book of what was considered difficult problems. I see that they are currently publishing "200 Puzzling Problems in Physics: with hints and solutions"

 

[martinbn]

hello, I was wondering which book is better for actually genuinely getting better at math (not just learning actual tricks but training your brain as if it were an actual muscle), the art of problem solving textbooks or the openstax math textbooks?

Why do you want to limit yourself to only these two series? There are many other math books!

 

[nbafitis28]

Why do you want to limit yourself to only these two series? There are many other math books!

mostly because I managed to get these books for free

 

[nbafitis28]

mostly because I managed to get these books for free

but if there are better relatively cheap books I am willing to spend a little on those

 

[gleem]

Research done at Stanford University on solving math problems came up with four guidelines: know the subject of the problem so you have the resources to use., learn relevant heuristics, strategies or maneuvers that can simplify the work, develop a disciplined approach to working on problems ( e.g. know how to manage resources or when to change strategy), and finally believe that you can solve it. This belief helps choose the best approaches and how hard you work on a problem.

In other words, practice a lot.