How Many Problems to Do When Self-Studying Physics?

[crastinus]

I looked around for where this question might already be answered (or at least addressed; I'm not sure there is any "one" answer), but, finding none, I decided to ask it myself.

For someone self-studying physics, is it necessary to do all the problems in the textbook being used? (I'm using University Physics.) In general, it seems that it is not, but how does one know which problems to do? I've been doing them all myself, which has been great, but if I knew how to better focus my time and effort that would be helpful. (I even googled around for a syllabus using this book, to see what problems would be assigned, but no real luck on that end.)

I will add too that I know one must really work through the material, not just read the book and do a few quick problems. My question is more about how to manage the process better than just doing everything in the book. (Or, perhaps, doing everything IS the best way for the self-studier! That would be good to know.)

(This is somewhat subjective, of course, and will differ for each person. But my question is meant to be general.)

Thanks.

 

[Voq]

I guess until you think you understand certain subject. Professor once said if you don't know how to do certain problem you still lack knowledge in theory. (Or something like that.) Only you can know your holes in knowledge on subject while studying it.

 

[crastinus]

That is certainly a good point.

Any more practical guidance would be helpful too!

 

[jtbell]

Exercises/problems in introductory textbooks usually have a lot of duplication, in two ways. This is so teachers and professors can assign different problems for homework in different years, or use some problems for homework and others on exams. And so students can do more problems for practice if they feel they need it.

First, some problems are almost identical, just with different numbers or maybe slightly different scenarios that use the same equations (e.g. an accelerating racecar versus an accelerating bicycle, but both ask for the acceleration needed to cover a given distance in a given time). If you did the first one with no trouble, there's no need to do the others if you can recognize them.

Second, groups of problems often use the same physical principles, but they give values of different combinations of variables to start with, and ask you to solve for different variables. After a while you can see you're using the same equations and concepts, but with different starting points and algebra. If you do a bunch of them without trouble, there's no reason to do more.

 

[crastinus]

Oh, I see what you mean. That makes sense. I've encountered some of that already, as you can imagine. But I didn't quite know the reasons behind why it was done.

Here's an interesting article on this point; it's called "Why students still can't solve physics problems after solving over 2000 problems", American Journal of Physics 82, 906 (2014): https://doi.org/10.1119/1.4881606

Which I guess underscores the points made by both already: one must master the subject, not just do problems, although being able to do problems is central.

How does one best form the mind to understand physics? The research (as above) suggests that just doing problems is not enough.

 

[aabottom]

When I took integral 5 hour calculus, I had 3 days between exams until the one for integral calculus. I re-did every assigned problem in the 3 days before the exam. I aced the exam, but my brain was frying when I came out.

Your choices:
1) Do all the problems.
2) Solve the problems in general way, using only symbols in algebra/ calculus/ math. Write the answer in terms of symbols used for the input parameters. Then you understand the problem and can solve any problem by plugging in the numbers.

 

[Voq]

According to the study it is about ability to problem solve and learning strategies. Interesting study indeed. Maybe it is genetics that peaks? After all they had strategic mindset. How did they got it? According to the psychology environment shapes us a lot but how can that be correlated to the initial mindset needed for that kind of problem solving (and if correlation is exact). And indeed it is correlated because it is the same mind, at least to some degree (you need some background). It is just one of many defining solutions of the mind according to my understanding and knowledge. Also maybe there is no so much correlation between that all. Maybe someone else can pin point that solution.. In the end it is hard because you are trying to define ability of something so complex like human being. I am sure there is exact answer. Or at least more defined.

 

[crastinus]

Here's an interesting bit to add: http://groups.physics.umn.edu/physed/

This group of physicists is concerned to give "better than textbook" problems to students. Their contention is that only by doing "real" physics can a student learn it, and no amount of canned textbook problems will help.

Of course, I guess my takeaway from all this is this:

One has to engage with the study of physics actively, making the material one's own; part of doing this is problem solving, even textbook problems, but the lion's share seems to be actively thinking over things and coming up with questions, searching for answers, etc. (Which is pretty much the case in any discipline.)

Thanks for the contributions.

 

[gibberingmouther]

i feel like i don't need to do more than a couple problems if i understand the concepts and math derivations well. i don't need to do example problems to learn how to problem solve because i read the textbook carefully and do some extra work to understand where the equations come from.

i will admit i take a lot of caffeine ... or else i probably wouldn't be as good of a mathematical thinker, imo.

 

[Thinkaholic]

Do the easier problems first, then when you get the hang of the easy ones, search for harder ones and attempt those. Keep doing more difficult and difficult problems until you have a great grasp on the subject. This works like a charm for me.

 

[momof4]

I guess it depends on why you are self-studying. Is it for enjoyment or are you planning on testing out of the class? I am the ultimate nerd. Even back in high school, I would do all the questions, even unassigned ones, for math and physics because I thought they were fun. I like solving problems. Is there a reason that you don't want to do them all , like boredom, time constraints, etc?