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I am currently studying mathematics and I am getting conflicting opinions on whether referencing a solution manual when working on problems is a good thing or a bad thing. For examples in many problem solving books for Olympiad or Putnam, the authors recommend you to study the solution even if can solve the problem on your own to perhaps emphasize a specific technique and on the other hand, some other people have told me that it is better not to have a solution manual. The concrete example was a post here for Spivak's Calculus on Manifolds

http://www.physicsforums.com/showthread.php?t=133706

" @mruncleramos: I've come to realize over time that it is better not to have a solutions manual.

@Daverz: How did you come to that realization?

When you get totally stuck, it's better IMO to have a solution you can learn from than to just forget about it. Also, the solution might better than or just different from your own, and you can learn from that also.

@mathwonk: anyone at the level of spivaks book is harmed more than helped by a solutions manual. i.e. if you need a solutions manual, you aren't getting spivak.

so the most useful answer is to advise the asker to go back to work trying to grasp the subject and work the problems himself.

this was essentially mruncleamos's answer.

a beginning grad student should be able to read this book and do most of these problems."

So all this goes back to my question from your experiences whether a solution helps or harms/hinders in advanced mathematics.

The mathematics that I am currently studying are literally 'elementary' compared to many of the topics discussed on this site so I would like your insights to be able to develop good study habits early on.

Cheers.

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Way I see it, as long as you make an honest effort at solving the problem(s) on your own before looking at the solution manual, it's all good. If you get the right answer and a.) the book's solution matches yours, then you're learning; b.) the book uses a different route, you can make a comparison and see which of your solution or the book's would be more comfortable for you to do. And in the (hopefully!) rare case that you have it right and the book solution is all wrong, then you have something to write to the author with... – J. M. Aug 13 '12 at 4:26
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I think it boils down to having sat with a problem for 30 minutes, is it better to look at the solution or attempt for another thirty minutes? – okmijn22 Aug 13 '12 at 4:46
@okmijn22 If you have more ideas to try, then try them. If you've tried every path you can think of, then slowly read the solution until you see something new. Put the solution away and see if you can continue using your new idea. – Austin Mohr Aug 13 '12 at 5:11
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That "honest effort" is the crux of the matter. It can be awfully tempting to peek at the manual rather than working it out on your own. You need a lot of self-discipline to avoid this. – Robert Israel Aug 13 '12 at 6:47
i) I try to solve the problem by myself. ii) I ask for a hint from someone else who solved that problem before. iii) I ask the problem here. – Erno Nemecsek Aug 24 '12 at 7:53

closed as not constructive by Austin Mohr, BenjaLim, rschwieb, Cameron Buie, Hagen von Eitzen Sep 28 '12 at 19:50

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