Enhance Your Problem Solving Skills in Maths and Physics with These Resources

[Arcthor]

I am leaving high school (or Sweden's equivalent) and I will be entering a hard physics / math program at university this fall.

I feel like I understand all the concepts in maths and physics, but I would like some practice on pure problem solving since that is really what I am interested in, instead of just brainless solving of differential equations without getting an explanation of why the method works.

Are there any books or websites that offer hard problems that requires creativity to solve with the knowledge of a high-school education aimed at natural science and maths?

In essence, I want to improve my problem solving abilities related to maths and physics.

 

[DEvens]

At this level there are loads.

Schaum's outline series is exactly that. Plus it's relatively cheap. Also, if you go to your Amazon website and type in "physics problem solver" you will likely get a large selection of possible books. Then go to your favorite place to buy books and load up.

 

[Arcthor]

At this level there are loads.

Schaum's outline series is exactly that. Plus it's relatively cheap. Also, if you go to your Amazon website and type in "physics problem solver" you will likely get a large selection of possible books. Then go to your favorite place to buy books and load up.

Thank you! I think I'll order:

https://www.amazon.com/dp/0071763465/?tag=pfamazon01-20

https://www.amazon.com/dp/0071754873/?tag=pfamazon01-20

Although, do you think it is necessary to practice problem solving based on pure math, or will problem solving based on physics involve all the necessary math?

 

[jack476]

I am leaving high school (or Sweden's equivalent) and I will be entering a hard physics / math program at university this fall.

I feel like I understand all the concepts in maths and physics, but I would like some practice on pure problem solving since that is really what I am interested in, instead of just brainless solving of differential equations without getting an explanation of why the method works.

Are there any books or websites that offer hard problems that requires creativity to solve with the knowledge of a high-school education aimed at natural science and maths?

In essence, I want to improve my problem solving abilities related to maths and physics.

What do you mean "problem solving"?

Do you mean solving problems related to content, ie, the techniques you'll need in a physics or calculus class? In that case, I would recommend Schaum's Outlines (as has already been said), and maybe something from the "Demystified" series if you want a very gentle introduction.

If you mean solving math problems as a skill in itself rather than techniques (or problems where the emphasis is on solving puzzle-like problems rather than mastering certain skills, such as in math competitions) then my recommendations are G Polya's "How to Solve It" (a classic, should be easily found in any university library), Schoenfeld's "Mathematical Problem Solving", "A Primer for Mathematics Competitions" by Zawaira and Hitchcock, Street Fighting Mathematics by Mahajan (Also recommend the open MIT course by the same title), and The Mathematical Olympiad Handbook by Gardner. Their purpose isn't to teach you specific mathematical techniques but rather how to dissect and approach mathematical problems, "metamathematics" as Schoenfeld put it in one of his books (with obvious extension to physical science and engineering). Those books have greatly broadened my own outlook and I have done much better in my classes for having read them. Most of those assume a mastery of only basic (High school or college freshman) math.

 

[MidgetDwarf]

Learning discrete math could help problem solving.. All the problems look like puzzles to my eyes. There are also olympiad and the cc american contest problems online, if you want to get nice and dirtu.

 

[MidgetDwarf]

Do you know how to prove what you know so far? Or have you just mastered the computational aspect?