Should I Work Out Every Problem in the Book?

[aLearner]

Ok, this is a serious question. It seems like some experience will be lost if I don't do this, but like most self-study efforts, it's time consuming. Any suggestions?

 

[Dembadon]

Ok, this is a serious question. It seems like some experience will be lost if I don't do this, but like most self-study efforts, it's time consuming. Any suggestions?

Do as many as you have time for. If it works out to be every single problem, great! However, many students don't have the time to work every single problem, so do as many as you can without compromising your performance in other courses.

 

[aLearner]

Do as many as you have time for. If it works out to be every single problem, great! However, many students don't have the time to work every single problem, so do as many as you can without compromising your performance in other courses.

Yes sir. Also, why do you think it is necessary to do every problem? Just so I have a logical reason.

And is there anything else with doing a lot of problems that I need to be doing in order to improve my understanding. It seems like doing problems is the only way to really physics.

 

[Dembadon]

Yes sir. Also, why do you think it is necessary to do every problem? Just so I have a logical reason.

And is there anything else with doing a lot of problems that I need to be doing in order to improve my understanding. It seems like doing problems is the only way to really [learn] physics.

You answered it yourself (in bold)!

Doing physics (or math for that matter) is really the only way to learn it. It's one thing to understand what the professor does during lectures; it all makes sense and looks easy when they work examples on the board. However, it's another thing to be able to put pencil to paper and work problems yourself. The more problems you work, the more you will begin to understand the concepts and how they relate to each other.

 

[aLearner]

You answered it yourself (in bold)!

Doing physics (or math for that matter) is really the only way to learn it. It's one thing to understand what the professor does during lectures; it all makes sense and looks easy when they work examples on the board. However, it's another thing to be able to put pencil to paper and work problems yourself. The more problems you work, the more you will begin to understand the concepts and how they relate to each other.

Ok! Thanks!

 

[bp_psy]

It depends on the book. If the book has ~200 problems at the end of each chapter it is probably to much or most of the problems are trivial and repetitive. If you have 10-30 problems at the end of the chapter it may be a good idea to try most of them.

 

[Bipolarity]

Here is what I do in mathematics:
1) Read the text of the chapter. Try to solve the example solved problems within the text without seeing the solution. And then look at the full solution, and see if you were right (or wrong and see why).
2) Look at the problems at the end of the section. See which ones involve brute force and which ones involve thinking. Skip the ones which involve brute force, and then do the ones which involve thinking (these are often the true/false problems, as well as the "proof-type" problems.
3) By the end of this, the material should be thoroughly grasped, but there may still be problems you couldn't solve. Leave them for now, and take a break.
4) Attempt the critical thinking problems when you get back.
5) Repeat steps 3-4 until you are sure that every problem is within your reach.
6) Prove the theorems in the text. Sometimes this will be impossible because it requires advanced knowledge from advanced courses. Textbooks will usually mention this. Write the theorem down somewhere, so you can attempt the proof at some later point during your lifetime (by which time you might probably have gained the necessary knowledge).

So yes, you should *KNOW* how to solve every problem, but you shouldn't necessarily solve them. Just at least make sure you can map the problem's solution properly in your head. If you can't, then solve it with paper.

BiP

 

[vish22]

I think it'd be better to genuinely understand the chapter in a few readings and realize what message its trying to convey-then go through the problems to try and get a mental revision of what you just learned and see if they could be applied there-directly or indirectly.And if you feel you can work it out using a different method-then do that.Not necessary to do donkey work on each problem.Just jot down steps for challenging ones if you don't have time.
And I'm just a novice,but I think reading relevant journal articles after finishing off some chapters in physics and maths would be lovely.

PS:I remember getting paranoid if I used to get one answer wrong. Thats really demotivating.Avoid that and just enjoy what you had just learnt!

 

[Polymath89]

I have a related question to this one. Do you guys think it makes sense to solve problems to which no solutions are given?

 

[vish22]

There's always physicsforums.

 

[AlephZero]

I have a related question to this one. Do you guys think it makes sense to solve problems to which no solutions are given?

Once you get outside of a classroom, you will NEVER have to solve a problem where somebody has already given you the answer. So you might as get used to the idea!

 

[aLearner]

So here's a checklist from what I've collected from everyone's suggestions.

1) Read a section in the chapter.
2) Then, do the example problems for that section without looking at the solutions.
3) After that, look at the solution and see where you agree, but more importantly, where you differ from the solution.
4) Understand why you went wrong, and make a note (mental or physical) about it
5) Look at the problem set and answer the ones relevant to that section. If the problems get too redundant, simply write down the outline of the solution. Skip the ones that you are unable to solve.
6) Check your solutions.
7) Review.
8) If critical thinking questions are present, answer them next
9) Review.
10) Figure out how to solve the problems you couldn't solve from different sources like PF, teachers, mentors, books, etc.
11) If within mathematical ability, work out every theorem, every proof, and make sure you have it down to the bone. If not, skip for now, but make a note of it and get back to it when mathematical ability is improved.
12) Repeat the steps for all the other sections until the entire chapter is done.
13) Review
14) Read up articles related to the chapter
15) Smile, because you now have a very firm understanding of the chapter you just covered.

 

[Bipolarity]

So here's a checklist from what I've collected from everyone's suggestions.

1) Read a section in the chapter.
2) Then, do the example problems for that section without looking at the solutions.
3) After that, look at the solution and see where you agree, but more importantly, where you differ from the solution.
4) Understand why you went wrong, and make a note (mental or physical) about it
5) Look at the problem set and answer the ones relevant to that section. If the problems get too redundant, simply write down the outline of the solution. Skip the ones that you are unable to solve.
6) Check your solutions.
7) Review.
8) If critical thinking questions are present, answer them next
9) Review.
10) Figure out how to solve the problems you couldn't solve from different sources like PF, teachers, mentors, books, etc.
11) If within mathematical ability, work out every theorem, every proof, and make sure you have it down to the bone. If not, skip for now, but make a note of it and get back to it when mathematical ability is improved.
12) Repeat the steps for all the other sections until the entire chapter is done.
13) Review
14) Read up articles related to the chapter
15) Smile, because you now have a very firm understanding of the chapter you just covered.

Yes that is exactly what I do. You will find that this a very time consuming process, but it will consolidate your understanding better than any other method in my opinion... for step 5, you don't necessarily have to "write the outline of the solution". As long as you can map the steps of the solution in your mind,you should be fine. Writing is only necessary when you actually want to find the solution (i.e. on a test), or when the problem is so intricate that you cannot do the "solution mapping" in your head. But for easier problems it is completely unnecessary.

BiP

 

[aLearner]

haha awesome! thanks !