When to check the solutions during self-study?

[Weightlifting]

Hi all!

As I've mentioned in a previous post a while ago, I've started studying Calculus from "Calculus, a complete course" by R.A. Adams & C. Essex. I've managed to get through a good part of it already, and I plan to continue to more physics related textbooks afterwards. The end-goal I have in mind is to apply to a graduate physics program somewhere in the future, when my personal finances stabilize. So I want to use the time I have now to prepare. Note that I have a BSc in Physics already.

However, I noticed one thing I cannot seem to find a good strategy in one aspect of self-study. When do I look at the solutions? I have a solutions manual for the above mentioned book, with thorough explanation of the solutions. I like to check the solutions after I've finished a set of problems on a particular chapter, to see whether I made any mistakes. However, when I get stuck on a problem, I get the urge to look at the solutions. Of course I won't look immediately the second I get stuck, and will check the chapter text before giving up, but what is the cut-off point to this? Is there a rule-of-thumb that you use to see when to stop trying at a problem? I can imagine begin stuck at a problem for 20h over multiple days won't be the most productive use of time. Yet on the other hand I think it will help you develop the ability to approach tough questions from various angles. I've tried various things, from looking at the solutions rather quickly, to not looking until I feel like I've solved the problem. However, I don't feel like I found what works for me yet.

What are your opinions on this? When do you start looking at the solutions? While I was studying at Uni, I would usually work on problems with other students, and we could figure out various ways to tackle problems together, which was often very effective. However, now that I'm self-studying, I don't really have that luxury. Thank you!

 

[Orodruin]

I would suggest not looking at the solutions until you have solved it yourself or you are really really stuck. If you get stuck for some time, do something else for a while. Solve other problems, take a walk, etc. The brain works pretty well subconsciously when you have thought about a problem for some time.

I also suggest making use of our homework forums (problems do not need to be actual homework) where people will give you useful hints instead of blurting out the full solution.

 

[symbolipoint]

What are your opinions on this? When do you start looking at the solutions? While I was studying at Uni, I would usually work on problems with other students, and we could figure out various ways to tackle problems together, which was often very effective. However, now that I'm self-studying, I don't really have that luxury. Thank you!

You already have the right instinct for what to do. You described the right or suitable guidelines about using solution manual or answer key. Work a problem, and if stuck, continue restudying, reviewing quickly/not so quickly, retry problem. If still stuck, then try to check the solution in, if possible, a limited way to attempt taking a first clue and continue any attempt to solve the problem before checking the rest of the official manual's solution.

Something more you should be aware of. Example problems, during the process of the books' instructional presentations are also problems for YOU to try to answer or solve. The solutions are included right with these example problems. Treat these the same way as you would if you have a separate solution manual or answer key!

 

[symbolipoint]

If you get stuck for some time, do something else for a while. Solve other problems, take a walk, etc. The brain works pretty well subconsciously when you have thought about a problem for some time.

Yes that is also a great GREAT suggestion.

 

[Weightlifting]

I would suggest not looking at the solutions until you have solved it yourself or you are really really stuck. If you get stuck for some time, do something else for a while. Solve other problems, take a walk, etc. The brain works pretty well subconsciously when you have thought about a problem for some time.

I also suggest making use of our homework forums (problems do not need to be actual homework) where people will give you useful hints instead of blurting out the full solution.

You already have the right instinct for what to do. You described the right or suitable guidelines about using solution manual or answer key. Work a problem, and if stuck, continue restudying, reviewing quickly/not so quickly, retry problem. If still stuck, then try to check the solution in, if possible, a limited way to attempt taking a first clue and continue any attempt to solve the problem before checking the rest of the official manual's solution.

Something more you should be aware of. Example problems, during the process of the books' instructional presentations are also problems for YOU to try to answer or solve. The solutions are included right with these example problems. Treat these the same way as you would if you have a separate solution manual or answer key!

Thank you both! This was really helpful! I will stop looking at the solutions manual until I feel like I've solved the problem, taking both of your suggestions into account when I get stuck.

 

[Frabjous]

There is also the question of how what percentage of the problems you are having issues with. If it is large, you probably need to improve how you are studying from the book.

 

[Weightlifting]

There is also the question of how what percentage of the problems you are having issues with. If it is large, you probably need to improve how you are studying from the book.

I very much agree! At this time, it's mainly the 'challenge problems' I get stuck on, as I've got a basic understanding of the material I'm going through right now, due to my Physics BSc. However, I will have to see how I fare when I get to newer frontiers. Other than that, the following insights have been extremely helpful in my self-study journey as of yet:
https://www.physicsforums.com/insights/how-to-study-mathematics/
https://www.physicsforums.com/insights/overcame-learning-challenges-faced-studying-stem/

 

[Frabjous]

That’s a good sign. Given that it is a small number of problems, when you look at the solution you should also think about “why“ you could not figure it out.