How many problems/exercises should be done for understanding?

[serllus reuel]

I was debating between here and "General Physics", but since this is more about learning physics than the actual physics, here it is.

I am currently a high school student and am studying physics and math on my free time. Since I've never taken an actual physics course, my general method of study is to read a book in order, and do most or all of the problems that have answers in the back, which generally amounts to about half of all the problems. However, I've noticed that the homework commonly assigned in college courses is much less, about ten per lecture. For example, when looking for solutions to Kleppner/Kolenkow I found that there were a few professors who posted them online for their students, but the total homework only amounted to about 100 problems per semester!

This got me thinking, is my learning philosophy of "do endless problems" incorrect, or do university students actually do many more problems on their own, in class, etc. Or is there much more to physics than theoretical problems? I probably could understand the physics by doing less problems, but doing more doesn't seem to hurt.

 

[Mmm_Pasta]

Doing more problems can be a waste of time. You should also do problems whose answers are not in the back as these problems can be interesting. A few simple problems will suffice. I would concentrate on the challenging ones as these can have interesting results and can give you insight.

One-hundred problems in a semester seems average to me assuming they have a good balance between simple and challenging problems. I've never bothered to count the amount of problems I got in a semester, though. There are quite a bit of problems students can do outside of the classroom, but due to time constraints and course work from other classes, a reasonable load has to be given.

 

[micromass]

If you read a problem and you immediately know how to solve it, or you know it's very like an already solved problem, then don't bother with it. Only do problems that are genuinely challenging for you.

If you work through [STRIKE]crap[/STRIKE] books like Halliday & Resnick or Stewart, then most problems will be a waste of time, so don't bother making all of them. In quality books like Kleppner or most upper-level books, all the problems usually are challenging and different. So you should do (or at least attempt) them all.

 

[Saitama]

If you work through [STRIKE]crap[/STRIKE] books like Halliday & Resnick

I disagree with this. That book isn't crap. For someone who is completely new to physics, that is a good start depending on the level of Math the person knows. I myself have worked through it but yes, later on I had to leave it because the problems were not challenging enough.

 

[zephyr5050]

I think your philosophy that doing more problems can't hurt is good. Of course you shouldn't be sitting there working through problems that present you no challenge. You wouldn't still practice your multiplication tables would you? I think the reason college courses don't often have a great number of problems assigned is purely because of time constraints. Personally, I would take 3 difficult physics/math/other science courses a semester (plus another non-science course) and from each class I generally received 10-12 homework sets a semester with 5-8 problems per set. That's a range of 50-100 problems a semester per class. In total, a difficult semester could be upwards of 300 problems. Some of those problems were very difficult as well. Generally they never repeated material from class, merely added to it or used ideas from class, so it always took me a long time to solve the problems. If you can solve a problem in less than 30 minutes, it's probably too easy for you and you should move on to the next level. I remember sitting at a table for hours working on only 5 problems and leaving with pages and pages of math.

But that's just my two pence from my experiences. Take what you will.

 

[serllus reuel]

Thanks for the advice and info. I forgot to mention that, apart from pure interest in physics, I am preparing for Physics Olympiad, so perhaps problem solving would be useful.

My thinking has been that much of physics is about problem solving, so if you're going to spend a few hours reading or being lectured to, might as well spend another few hours or more solving problems. But I see that that may not be the case; my original question was intended to be general, however, I've only just gotten beyond the Halliday Resnick level, and yeah, quite a few of the exercises are no-physics plug-ins. There's probably a whole world of difficult problems out there that I haven't seen yet.

 

[Minhtran1092]

This got me thinking, is my learning philosophy of "do endless problems" incorrect, or do university students actually do many more problems on their own, in class, etc. Or is there much more to physics than theoretical problems? I probably could understand the physics by doing less problems, but doing more doesn't seem to hurt.

It depends on the university culture, professor, and the course rigor. I've taken non-rigorous courses where exam questions are similar to HW questions and exam questions boil down to the application of concepts. To prepare for these exams, it's best to do more practice problems. The idea is that by doing more practice problems you will do similar problems on exams faster and earn yourself more time to spend on the difficult problems.

In general, it never hurts to spend more time with the concepts. Spending time engaging with concepts allows you to be flexible when applying them to solve problems. It is more likely that you'll solve any problem you'll encounter if you're comfortable with the theory. The trade off is that while you're able to solve the problem, you might be more hesitant along the problem solving process.

If you aren't being tested, you'll learn better by focusing on theory and doing only challenging problems.

 

[ZombieFeynman]

If you work through [STRIKE]crap[/STRIKE] books like Halliday & Resnick

This is cork-sniffing, in my humble opinion. Halliday and Resnick (and other similar books) is very valuable to beginning students. Personally, I think Kleppner/Kolenkow is a bit of a pointless book. If you're too advanced for Halliday/Resnick, you might as well not waste time on Kleppner when you can dive into Taylor or Marion and Thornton.

Perhaps you think those books are crap too? Maybe you'd have students dive straight into Arnol'd...

:tongue:

I know in my time, I used Halliday and Resnick much more than Kleppner.

[/Two cents]

 

[micromass]

This is cork-sniffing, in my humble opinion. Halliday and Resnick (and other similar books) is very valuable to beginning students. Personally, I think Kleppner/Kolenkow is a bit of a pointless book. If you're too advanced for Halliday/Resnick, you might as well not waste time on Kleppner when you can dive into Taylor or Marion and Thornton.

Perhaps you think those books are crap too? Maybe you'd have students dive straight into Arnol'd...

:tongue:

I know in my time, I used Halliday and Resnick much more than Kleppner.

[/Two cents]

You seem to think I dislike Halliday and Resnick because the books are too easy. I never said anything like that.

 

[ZombieFeynman]

You seem to think I dislike Halliday and Resnick because the books are too easy. I never said anything like that.

Why do you dislike them then?

 

[WannabeNewton]

If you're too advanced for Halliday/Resnick, you might as well not waste time on Kleppner when you can dive into Taylor or Marion and Thornton.
[/Two cents]

While I don't find it joyful to condone books (I mean what am I going to get out of it really), there is a reason why many top universities use Kleppner and Kolenkow for honors mechanics classes. It actually teaches physics and throws at you problems that, as G.H. Hardy said, have a bit of spin. It won't give you trivial problems that just test your ability to recall and apply physics equations like a mindless robot; this is also exactly what Marion and Thornton make you do; the book is the king of mindless derivations with no physical insight.

To the OP, I agree with micromass and the others. If you are going to devote time to problems make sure they are of high quality. Do problems that actually test your understanding and make you struggle for some time on end for it is these problems that will actually help you learn physics. There is no point in doing all the problems in the text if they are too trivial for you or are unbearably boring and needlessly tedious. Take a look at this list of books to find good physics texts for whatever it is you are interested in: http://www.ocf.berkeley.edu/~abhishek/chicphys.htm

 

[ZombieFeynman]

While I don't find it joyful to condone books (I mean what am I going to get out of it really), there is a reason why many top universities use Kleppner and Kolenkow for honors mechanics classes. It actually teaches physics and throws at you problems that, as G.H. Hardy said, have a bit of spin. It won't give you trivial problems that just test your ability to recall and apply physics equations like a mindless robot; this is also exactly what Marion and Thornton make you do.

Are you implying that Halliday and Resnick (or the newer book by Knight that many places are adopting) do not teach physics? Do they not contain challenging problems?

I remember being stumped by many of the "challenge" problems in Knight.

I TAed for Honors Physics and it seemed like many of the students in it had their abilities tested quite nicely by Knight as well.

I'm not trashing Kleppner, but I think when someone calls a widely used physics text [SRIKE]crap[/STRIKE], they could be specific as to why they think so. I also think that alternate opinions are always valuable.

 

[WannabeNewton]

I personally have yet to find a problem in Halliday and Resnick that would match the truly difficult problems in Kleppner or Morin. I distinctly recall my AP Physics C teacher telling our class that if we wanted to just get a 5 on the AP exam then Halliday and Resnick will do but if we wanted a truly deep understanding of introductory mechanics then we would need something else. The quality of the problems really make a difference in my experience.

 

[micromass]

I personally have yet to find a problem in Halliday and Resnick that would match the truly difficult problems in Kleppner or Morin. I distinctly recall my AP Physics C teacher telling our class that if we wanted to just get a 5 on the AP exam then Halliday and Resnick will do but if we wanted a truly deep understanding of introductory mechanics then we would need something else. The quality of the problems really make a difference in my experience.

That's true. But it's not even about having truly difficult problems. The problems should be insightful at least. Halliday is just plug n chug. There are 50 problems at the end of the chapter, and most are just tedious computations. I don't think that's good to learn physics with. I don't think it's very hard to give problems that are easy, but also very insightful.

I'm not saying Kleppner is a good first intro to physics, it's too difficult for that. But that doesn't mean Halliday is a good book.

 

[WannabeNewton]

This got me thinking, is my learning philosophy of "do endless problems" incorrect, or do university students actually do many more problems on their own, in class, etc. Or is there much more to physics than theoretical problems? I probably could understand the physics by doing less problems, but doing more doesn't seem to hurt.

In my experience this really depends on the textbook. I was in your exact same situation with regards to Kleppner and Kolenkow. I did as many problems as I possibly could and got help from the forum whenever I got stuck (don't get into the habit of looking up the solutions from those university pages-I did that for some of the problems and it really took away the understanding). One of the bigger problems with self-studying is knowing which problems to do and how many to do.

Thankfully most of the problems in Kleppner are quite fun and instructive so if you have free time then certainly try to do as many as you can because it won't hurt. I admit it does have a rather large number of problems but it isn't as bad as the book I mention below.

Also there are some books where there are only like 6-10 problems a chapter (e.g. my favorite general relativity text "General Relativity"-M. Wald) in which case you can certainly attempt all the problems and ideally solve them all (with some help here and there ).

On the other hand there are physics textbooks in which there are just sooooooooooooo many end of chapter problems that doing them all, even if you have free time, is quite a pain and I personally wouldn't even attempt to do every single one. An example of this is the 3rd edition of Purcell and Morin "Electricity and Magnetism" (which I'm trying to get my younger brother to do as a matter of fact!). It has like on average 30-40 problems per chapter that have worked solutions and another 30-50 which don't and that's right per chapter (Halliday and Resnick is no stranger to this either). Attempting to do them all would be insane.

Thankfully Morin labels the difficulty of this problems from 1-4 (akin to Halliday and Resnick) so you can seek out the hard/interesting ones. And let me tell you, this book has some damn hard problems. In the UChicago undergraduate physics texts reviews/recommendations page I linked above, the Purcell part says "Also, many of its problems fall into the class of 'You should work this out for yourself at least once in your life.'"

 

[micromass]

which I'm trying to get my younger brother to do as a matter of fact!

I feel your pain. I'm trying to get my sister to work through Carothers. But she doesn't want to.

 

[serllus reuel]

An example of this is the 3rd edition of Purcell and Morin "Electricity and Magnetism" (which I'm trying to get my younger brother to do as a matter of fact!). It has like on average 30-40 problems per chapter that have worked solutions and another 30-50 which don't and that's right per chapter (Halliday and Resnick is no stranger to this either). Attempting to do them all would be insane.

And I was thinking of using both that and Griffiths for extra problems, when I get into E&M. Thanks for the info.

 

[serllus reuel]

Regarding the Halliday Resnick-type books: I first learned physics by going straight through the mechanics section of Serway; I would measure my progress by how much notebook paper I used, on a good day I would get almost ten pages filled. At the time, the problems seemed challenging and interesting but looking back it was probably because I had never seen any physics before. However, I somewhat agree with ZombieFeynman that those books can be a useful introduction.

 

[serllus reuel]

(don't get into the habit of looking up the solutions from those university pages-I did that for some of the problems and it really took away the understanding).

I use those for answers mainly; for some reason, I feel that I must find out whether my answer is correct or not- is this normal?

 

[Von Neumann]

Are you implying that Halliday and Resnick (or the newer book by Knight that many places are adopting) do not teach physics? Do they not contain challenging problems?

I remember being stumped by many of the "challenge" problems in Knight.

I TAed for Honors Physics and it seemed like many of the students in it had their abilities tested quite nicely by Knight as well.

I'm not trashing Kleppner, but I think when someone calls a widely used physics text [SRIKE]crap[/STRIKE], they could be specific as to why they think so. I also think that alternate opinions are always valuable.

I agree with ZombieFeynman. H & R serves it's purpose as an intro text.

 

[deluks917]

I honestly prefer books with fewer problems for self study. Then you can actually do them all. It is basically impossible to reliably choose good problems to do when you are still learning the subject yourself.

 

[Group_Complex]

I use those for answers mainly; for some reason, I feel that I must find out whether my answer is correct or not- is this normal?

I agree with WannabeNewton, looking up the solutions (even to check your solution) is an indication that you probably do not understand the material well enough.

 

[WannabeNewton]

I use those for answers mainly; for some reason, I feel that I must find out whether my answer is correct or not- is this normal?

Well if you're just starting out the textbook/subject and want to see if your solutions are correct then I don't really see much of a problem with going that but you should really get more confident with your answers (I have personally found that this is certainly easier said than done) as the months go by because there are textbooks which just don't have any solutions available online at all. I was talking more about looking up solutions if you can't solve it yourself. That's when you should ask for help instead.

 

[serllus reuel]

WannabeNewton and Group_Complex: you have a good point, if one understands the material from reading the text and examples he should be able to solve the problems, and if a problem is solved, chances are it's correct if there is not numerical error. Still, I sometimes get the fear that even though I completely solved a problem I may have made a small error in the beginning that led to serious errors. Of course, I can do order of magnitude estimates and such, but there are those times when the answer turns out to be a complicated algebraic expression. I should probably get used to it, as I'll be doing more self-study in the future.

 

[verty]

My recipe is: attempt the question but not for more than 10 minutes, then do some research about the concepts involved and how to solve it, form a strategy for the question that ties into the concepts. Try another of the same type and work on honing your approach, iron out the wrinkles, make sure you know how the solution looks and plays out.

Then you can say you know the question, it'll never be foreign to you.

 

[WannabeNewton]

My recipe is: attempt the question but not for more than 10 minutes, then do some research about the concepts involved and how to solve it, form a strategy for the question that ties into the concepts.

This really depends on the type of problem though. If it's a non-trivial calculation then it is very possible that figuring out the calculation ends up taking a significant amount of time, even if you are well acquainted with the physical concepts and/or mathematics involved in the topic that the calculation is related to.

 

[verty]

This really depends on the type of problem though. If it's a non-trivial calculation then it is very possible that figuring out the calculation ends up taking a significant amount of time, even if you are well acquainted with the physical concepts and/or mathematics involved in the topic that the calculation is related to.

It sounds like you agree with me (edit - given that what we said was not incompatible). If it is a non-trivial calculation, it may be a waste of time to try to figure it out manually with little knowledge. Better to attempt it for a short period, see where one gets stuck or what steps one feels uncomfortable about, do research, come back with a strategy.

Problems are where one must use what is given in the current chapter/book, so if one is not finding it easy, one must return to the book (or website). I agree that not all calculations can be done in under 10 minutes, I meant only that one should after 10 minutes know if the difficulties have been ironed out or not.

At some point one must put effort in of course, but not without having made sure that one knows all that one should know.