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I’ve been grappling with a question that I’ve yet to find an answer to. I love solving math problems and I'm going to college this fall for a degree in computer science. Looking long-term, I would like to attend grad school and find a job in research. As a result, I want to adopt a learning style that best balances nurturing my potential as a future researcher and safeguarding a high GPA. My problem is that I often refuse to admit defeat on challenging problems and end up spending a considerable amount of time attempting to solve them. Being able to solve a difficult problem is rewarding, but more often than not, I would have to give up at some point, resorting to the solution, and realizing that half the day is gone.

I understand that failed attempts are not a waste, but I’m concerned that if I continue with this study approach, I may struggle to keep pace with the fast-paced learning expected in college . I would greatly appreciate any advice on the optimal amount of time one should dedicate to something equivalent to a textbook problem before deciding to seek the solution. I understand that the optimal time can vary from person to person, but I suppose having a ballpark idea or being aware of relevant considerations would help me manage my study time more effectively.

Thank you!

ten_to_tenth
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  • If you check how many MSE questions I posted you can easily deduce my answer. – Kurt G. Jun 04 '24 at 14:05
  • @KurtG. I'm sorry but your comment might have gone over my head. Are you suggesting that one should just work through problems independently rather than asking for help/avoiding asking for help? (I noticed that you posted zero questions). – ten_to_tenth Jun 04 '24 at 14:12
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    Titel: There is no optimal time. It really depends on the context. How much of the prerequisites are available to you (from a course)? How difficult is the exercise? For example, suppose your exercise in elementary number theory is, to show that there are infinitely many odd prime numbers. Then how long should you try it? If you already know that there are infinitely many prime numbers, then you should never ask for help. If not, it depends whether or not you have seen Euclid's method. Still, you should spend as long as you need to finish it. – Dietrich Burde Jun 04 '24 at 14:25
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    There are many factors affecting the decision. Some problems may require half a day to solve. Figure out how much time you have to finish a homework and divide by the number of problems is one approach. I do not think there is a universal answer to this question. – Vasili Jun 04 '24 at 14:26
  • DietrichBurde and Vasili: Thank you very much! I also just went through the post marked as similar and found excellent advice, some of which reflect yours. – ten_to_tenth Jun 04 '24 at 14:36
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    A rule of thumb : 0ne hour-one hour and a half, then switch to another activity, then come back some hours later, or, better, have a night in between ; on the next morning it may happen that everything is clearer... (many people have experienced it, not restricted to mathematics...) – Jean Marie Jun 04 '24 at 18:38
  • @JeanMarie Thank you very much! I guess I will buy a timer and set a limit between 30' to an hour and a half for most problems going forward and see how it works out. – ten_to_tenth Jun 05 '24 at 00:14

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