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Studying Correlation between contest math training and grasping abilities?

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I have a notion that students involved in contest math/physics since high school 'develop' a better ability to pick up concepts (not in the context of contest math/physics) quicker and solve relatively more 'complex' problems.

In high school I heard about contest math but never really immersed myself into it. I have since then developed a fascination of sorts for those that do immerse themselves in problem solving of this sort. I wonder if those that do, end up with a better ability to analyse and apply concepts (be it in college or elsewhere) compared to those that don't.

On the other hand, it may be that I am simply overawed by those who have 'done contest math' while having no idea about what it really takes and what such an 'ability' really means.

I am asking this as I am wondering if I should try and 'pick up' contest math as a way to improve my 'logical thinking' and problem solving abilities. While mulling this over I had the following questions:

1. Is attempting to acquire the skill set related to contest math a worthwhile pursuit?

I understand that this could depend on the context and personal goals. One of my goals is to be able to pick up things quicker and be able to solve problems which are less 'algorithmic' as well. I have begun college and I feel such an ability would help me learn a lot more than otherwise while also 'developing' a more generally useful skill set.

2. If so, would working towards developing such a skill set stand me in good stead only within the context of the STEM courses in college which tend to have a heavy dose of theory and problem solving?

I understand that answering the above is also slightly subjective as I have not stated my long term goals or the directions I intend to take (be it in terms of wanting to do research/ be in a specific industry). Which brings me to my last question :

3. Does the answer to the above hinge solely on my long term goals? (Which I am fairly unclear about, but believe that an ability to learn new things and develop a relatively much stronger grasp over 'new concepts' would be an asset regardless)

Thank you for your time and perspective! Apologies if I am have not been clear with my reasoning.
 

fresh_42

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As with everything, practice will do a lot to improve certain skills. You won't be able to become a genius by practise alone, but you will improve. The ability to solve such math/physics contest questions is quite different from the ability to understand the stuff in a study. Yes, it will help you to solve more problems, as it trains you to think unconventionally and thus consider more options than by a training focused on algorithmic schemes. But that's it - in my opinion. To find nice tricks and shortcuts doesn't help you e.g. understand weak convergence in a Hilbert space. So it is a double-edged sword, because such a training is very time consumptive; time which will be lost for the practise of the ordinary stuff. And ordinary stuff is far more than tricky questions. I would learn to become a better chess player instead. It's an alternative to science focused learning and will improve your abilities to solve complex problems, too. Of course as a scientist in some theoretical branch you will have to develop such skills more than usual, since research is solving problems by means others haven't considered. However, you will have to master the ordinary stuff first - the more the bigger is your tool box for problem solutions.
 
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Thank you for you response!

The ability to solve such math/physics contest questions is quite different from the ability to understand the stuff in a study.
I believe I am splitting hairs at this point, but is there a 'sweet spot' between the two different abilities? Or does this depend very much on the concept being studied, the 'level' (undergrad, research) at which it is being studied and the reasons behind studying it (developing applications, research or merely acing courses and tests)....

time which will be lost for the practise of the ordinary stuff.
Apologies for being dense but by "ordinary stuff", do you mean concepts that may be of interest to one, or relevant to ones course of study (say basic Circuit Analysis as an introduction to electrical engineering for an undergrad) as opposed to solving contest math problems in Euclidean Geometry (where the topic of study itself does not add much value)?

Lastly, would it be fair to conclude that 'problem solving' abilities could develop in a natural way as one pursues a subject over the years (as compared to the steeper learning curve in contest math in this regard) while also adding to ones knowledge of a new and more 'relevant' field?

It could be that introductory STEM courses involve a fair bit of 'testing' and hence my line of thought, whereas in the bigger picture such 'training' may not be of much use (?).
 

fresh_42

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Those contest problems can be quite tricky. This might lead to even more effort or frustration, depending on your personal attitude. Acing courses and tests comes with the practice of the usual exercises. What you can learn from those contest questions is, that you often have a good or at least new idea after you paused from dealing with a certain question. I don't think this will help you with tests. I would really recommend to do the exercises in the textbooks. These are normally more than the available time allows you to solve. Textbook exercises will serve you better than any contest questions. And as said: it will likely require more time than you have at hand.

If you like contest questions, then you could take part in (or read) our monthly math challenge (see the General Math forum). This way you can practice, have usually easier questions than those olympiad problems, and usually get a solution offered by someone, if not you. In any case, treat contests as a kind of amusement. Your major goal should be the textbooks.
 

Dr. Courtney

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Don't know about contest math, but those I've mentored in competitive science projects have done very well in downstream research opportunities.
 

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