Best way to use solution manual to learn

[playoff]

What's up PF, I hope everyone's enjoying the summer so far.

My studying habit last semester was disastrous, so I am trying to build a good habit over the summer. I feel that as I have the solution manual available, I might not learn to solve problems if I get to use it frequently, but I also don't want to spend too much time on a problem. What is your best use?

Thanks in advance!

 

[QuantumCurt]

The best way to use a solutions manual is as an ultimate last resort. Getting stumped on a problem and immediately resorting to the solutions manual can be quite tempting sometimes when one is in a hurry. We ultimately gain far more from solving a problem on our own. Solutions manuals are often useful because the author may have used a different approach. Sometimes I've found that my own approach is easier for me, and other times I see the solutions manual and think "wow, I WAY over-complicated this!"

I try not to resort to a solutions manual until I've been stumped on a problem for a couple of days. If I get stumped I usually put the problem aside and work through some other problems, or take a break and then revisit it. Sometimes after sleeping on it, the solution will come to me. There have been times that I've had a physics or math problem on my mind, and that aha! moment will hit while I'm laying down to go to bed, or while I'm taking a shower or something like that. The aha! moment is much more beneficial when it's our own aha!, rather than one from a solutions manual.

In short, solutions manuals can be very useful, but they can also be a crutch that prevents real learning. They are a valuable tool when used in moderation and only as a last resort. That's my take on it anyway.

 

[micromass]

I guess a solution is to get a good book without a solution manual, so that you won't be tempted to read the solution. Whenever you solved it (or hit a block in the road), you should post here on PF, so we get to help you. This is much more productive than just reading the solution.

Many good books have other ways not to give solutions, but helping the student nevertheless. For example, Kleppner and Kolenkow give partial answers that you can check. While Morin's books have solved problems and unsolved ones.

 

[Vanadium 50]

The best time to use a solutions manual is after you have solved the problem yourself. Then you can look at their solution - did you miss a fact that would make your life easier? Is your solution as economical as it could be? Did you exploit all the symmetries? Etc.

 

[ELB27]

I would only add to the above that before checking with solutions, make sure to try and check your answer first by yourself. Does it make sense? Is it possible that your answer approaches this value when that quantity changes? etc. The problem with a solution manual is that it offers a quick and easy check of your answer but in real life there is no such easy way. You have to be able to effectively check your answer and confidently stand by it (or if it is an approximaton, say exactly what the error is, in which cases it is most accurate/inaccurate etc.)

 

[clope023]

What's up PF, I hope everyone's enjoying the summer so far.

My studying habit last semester was disastrous, so I am trying to build a good habit over the summer. I feel that as I have the solution manual available, I might not learn to solve problems if I get to use it frequently, but I also don't want to spend too much time on a problem. What is your best use?

Thanks in advance!

I disagree with QuantumCurt and others when they say a solution manual should be a last resort in any and all cases, though I do agree it ought to be used after an attempt at the solution yourself. Micromass' suggestion to post on PF is a nice one, but in practical reality using a pre-written guide is going to be more economical in terms of time than waiting for replies on a forum. The way that I found worked for me was understanding how the solution author arrived at the conclusions that they did, this often involved performing mathematical clean up duty with respect to filling in steps that the author merely hand waived as assumptions and being slightly more rigorous than the author with the derivation towards the final solution. This helped fill in gaps in my knowledge and helped me apply concepts to certain problems in ways I had not thought until I had attempted the problem in question and helped me apply that to other problems in homework and in tests.

 

[ZapperZ]

I disagree with QuantumCurt and others when they say a solution manual should be a last resort in any and all cases, though I do agree it ought to be used after an attempt at the solution yourself. Micromass' suggestion to post on PF is a nice one, but in practical reality using a pre-written guide is going to be more economical in terms of time than waiting for replies on a forum. The way that I found worked for me was understanding how the solution author arrived at the conclusions that they did, this often involved performing mathematical clean up duty with respect to filling in steps that the author merely hand waived as assumptions and being slightly more rigorous than the author with the derivation towards the final solution. This helped fill in gaps in my knowledge and helped me apply concepts to certain problems in ways I had not thought until I had attempted the problem in question and helped me apply that to other problems in homework and in tests.

But I disagree with that because in the context of this question and the OP, this person already should have seen examples on how problems of the same type being solved, either in class, or in textbooks. Solution manuals, at least the good ones, offer a step-by-step approach in solving a problem, not just spew out an answer. In most cases, these are done only for a very limited number of problems. So one doesn't have a lot to go by as far as actually attempting a problem and then checking the solution manual.

The good solution manuals, such as the Students Solution Manual to Mary Boas's "Mathematical Methods in the Physical Sciences", not only show how to solve a problem from the very beginning, but also discuss the rational for a particular approach and pitfalls that students often make. The best thing to do is to try and solve the problem first, and then figure out where one either got stuck, or got it wrong. You learn more from what you did wrong than what you did right. Looking at the solution first doesn't quite allow you to get it "wrong". And often times, it looks obvious when one is just looking at it (how many times have students often said "It looks so easy when you do it!"), but it isn't obvious when one is tackling it.

Zz.

 

[QuantumCurt]

I disagree with QuantumCurt and others when they say a solution manual should be a last resort in any and all cases, though I do agree it ought to be used after an attempt at the solution yourself. Micromass' suggestion to post on PF is a nice one, but in practical reality using a pre-written guide is going to be more economical in terms of time than waiting for replies on a forum. The way that I found worked for me was understanding how the solution author arrived at the conclusions that they did, this often involved performing mathematical clean up duty with respect to filling in steps that the author merely hand waived as assumptions and being slightly more rigorous than the author with the derivation towards the final solution. This helped fill in gaps in my knowledge and helped me apply concepts to certain problems in ways I had not thought until I had attempted the problem in question and helped me apply that to other problems in homework and in tests.

If we're looking at this purely in terms of time efficiency, then perhaps you're right. One will get through the homework assignment much more quickly if they're regularly resorting to solutions manuals. However, maximum time efficiency isn't the concern for everyone. For me, learning the material is far more important than doing as much as possible in a given amount of time. I learn far more from really understanding 5 problems than I learn from halfway understanding 50 problems.

 

[clope023]

If we're looking at this purely in terms of time efficiency, then perhaps you're right. One will get through the homework assignment much more quickly if they're regularly resorting to solutions manuals. However, maximum time efficiency isn't the concern for everyone. For me, learning the material is far more important than doing as much as possible in a given amount of time. I learn far more from really understanding 5 problems than I learn from halfway understanding 50 problems.

I believe you're mis-characterizing what I mean. The goal should always be to gain the ability to solve problems by yourself as that's how you'll be tested; thinking about problems really really hard never really translated to developing that ability for me until I was able to see a wider breadth of examples (from solution manual or Schaum's outlines), rather than the overly simplistic examples presented in the lecture class room.

 

[neosoul]

I agree with quantumcurt. It is best for you to use it if and only if you just absolutely cannot solve a problem that you have tried to solve numerous times. It's very helpful, too. In fact my best Calculus teacher encourages me to not resort to solutions manuals, and stay away from Schaum's when really trying to retain information. He solves all the problems in each textbook he gets without a solution manual.

 

[mathwonk]

last time i taught calculus i used the solutions manual as a doorstop for my office. that worked pretty well. once i actually picked it up and read something from it. that also got a good laugh.

 

[symbolipoint]

At one time, I reviewed a course in which I had studied for credit decades ago. This was at at time during which I was no longer a student. My working of the problem exercises for the course textbook BECAME my solution manual. There was an officially published solution manual/answer key book to be used by teachers. A few times, I checked it and I must say, I generally like the solutions I made myself better than the official publication from the textbook company.