How Can I Improve My Problem Solving Skills?

[pivoxa15]

I find that when doing problems in pure maths, I need to look at the solution very often and is happy just to be able to understand what the solution is trying to say and reconstruct it out. Thats a bad sign. What should I be doing? If I don't look at the solution then it might take ages and with no reward.

 

[mjsd]

solving maths problem often requires some wit... yes, it is true that it is not for everyone. And for some, they have to learn by examples (or looking at the solns). however, to go beyond that you mustn't be "satisfied" what the soln is telling you.. the next step to compensate for the fact that you didn't work it out yourself is to go back and work out the logic behind the soln and why your method of approach didn't work. Often I found that undestand a soln (fully) takes LONGER than working it out from scratch (if you can actually work it out), this is because you end up following up a lot of concepts implied by the solutions.

remember there is no shame in looking at the soln if you can fully learn from it. but then only question you really should be asking yourself is
"Is maths too hard for me?"
since once you are in research, there is *no solutions* for you to look up and you must rely on experience and wit!

 

[Gib Z]

I Rip out the solution pages and try then try them myself. If after 15 minutes of no progress, I get a hint from a teacher, but I make sure they don't tell me the solution.

 

[phy-79]

well, I'm a subject to 100's and 100's of mathematical problems and i used to have tis prob.
i got really fed up with this and so consulted my teacher who sed that i needed some motivation and an aim to solve a prob.Intrest also plays an impt role.
well, after this i strted to do probs in the proper way.
it just worked out for me!

 

[pivoxa15]

well, I'm a subject to 100's and 100's of mathematical problems and i used to have tis prob.
i got really fed up with this and so consulted my teacher who sed that i needed some motivation and an aim to solve a prob.Intrest also plays an impt role.
well, after this i strted to do probs in the proper way.
it just worked out for me!

What is this proper way?

 

[pivoxa15]

I noticed that for physics subjects, understanding fully worked exampled or solutions can get you a long way as many questions such as on exams are close to the worked out examples done by lecturers. Maths is different however as problems can be different to worked examples and knowing the worked examples may not help at all.

 

[AlephZero]

I noticed that for physics subjects, understanding fully worked exampled or solutions can get you a long way as many questions such as on exams are close to the worked out examples done by lecturers.

It might get you through an exam, but unfortunately it won't get you very far after that. Most "real world" problems don't come nicely packaged so they match the examples in your textbook or lecture notes.

The bad news is, I don't know any better general problem solving method than a catch-phrase from the lecturer in a differential equations course, which he usually repeated several times per lecture: "The way you solve this is to look at it till you see what the solution is".

Reading somebody else's solutions is useful, but not the complete answer. As an analogy, just reading books and watching films is unlikely to make you into a first-rate novelist or film director.

 

[pivoxa15]

It might get you through an exam, but unfortunately it won't get you very far after that. Most "real world" problems don't come nicely packaged so they match the examples in your textbook or lecture notes.

The bad news is, I don't know any better general problem solving method than a catch-phrase from the lecturer in a differential equations course, which he usually repeated several times per lecture: "The way you solve this is to look at it till you see what the solution is".

Reading somebody else's solutions is useful, but not the complete answer. As an analogy, just reading books and watching films is unlikely to make you into a first-rate novelist or film director.

I think you're right. Feyman said: "What I cannot create I do not understand."

And his problem solving algorithm was 1. Look at the problem 2. Think deeply 3. Right down the solution

The brain works in weird ways and there is nothing like working out the solution of a problem yourself. However its very frustraing when you can't do that.