Are problem sets like theoretical physics?

[DukeofDuke]

Hi PF,

This semester I'm finally starting to enjoy problem sets. I was wondering, how similar are the skills used to solve problem sets to the skills theoretical physicists use to solve actual problems?

Thanks,
DoD

 

[twofish-quant]

It's one skill.

The problem sets give you a mental toolbox of things that you can use when you do come up with a real world problem. The big difference is that in real world problems, the problem is sometimes that you aren't sure what the problem is, so if you can do calculations quickly and efficiently, you can try different things to see what works.

One analogy is that if you are a novelist or a speechwriter, you want to get your basic grammar and vocabulary right. If you are even thinking about the meaning of each word as you write, you won't get very far. Problem sets are set up so that if you solve the same types of problem over and over again, they become second nature, so that when you see something similar out there, you aren't thinking about things too much when you are solving them.

 

[Klockan3]

If you are even thinking about the meaning of each word as you write, you won't get very far. Problem sets are set up so that if you solve the same types of problem over and over again, they become second nature, so that when you see something similar out there, you aren't thinking about things too much when you are solving them.

I disagree completely with this, thinking is what makes us different from computers.

A novelist have to think through how the words fit together and what images they create for the reader. Of course he needs to know what the words means without thinking, but that is similar to how a physicist needs to know his own terminology. But when you are solving problems you really need to think, what are you actually doing? What do you want to know? What exactly do you know?

When solving problems just become a mechanical thing then people start to do really dumb mistakes and they lose the big picture. By thinking through properly what you are doing you will get a much better understanding of why it did or didn't work when you try new approaches on a problem which is fundamental for just about everything.
Or maybe I misunderstood what you meant and you are talking about simple things like doing the calculus bits or so? Since for those I agree in a way, but I still don't want for people to ever stop thinking about the things they do.

 

[MathematicalPhysicist]

Klockan, we need to separate technique issues and theoretical issues.

Obviously without understanding the theory you won't procceed with your studies, and they would seem as meaningless.
But knowing the theory without even doing one technical exercise is a sure route to not assimilating the theory in your head.

 

[Klockan3]

Klockan, we need to separate technique issues and theoretical issues.

Obviously without understanding the theory you won't procceed with your studies, and they would seem as meaningless.
But knowing the theory without even doing one technical exercise is a sure route to not assimilating the theory in your head.

I do not disagree with that though, I disagree with the notion that you should learn to do everything mechanically.

But now that I think of it I realize that people maybe need it, I got almost 100% accuracy with my calculations with barely any training and I always try to get the students to understand the importance of having such a high accuracy. Uff, sorry, I really shouldn't go into these discussions. I never saw the point in doing the countless exercises people do but people don't react well when I ask them about it.

 

[sponsoredwalk]

assimilating the theory in your head.

Kind of sums it up. When you have to learn about 10 different areas of mathematics & physics at once it can tend to creep up on you, especially when it's something new and not so cemented in memory, and without the familiarity of focusing on one single aspect and practising how to use it mechanically you just don't understand the principle involved. There's a high chance that you could lose the ability to find the answer.

But knowing the theory without even doing one technical exercise is a sure route to not assimilating the theory in your head.

If it weren't this way then we would all be happy to just read popular science books :tongue2:
There's no better way to prove to yourself that you have nailed a concept than by getting the answers right based on intuitive knowledge or a gut feeling of what to do.

 

[Klockan3]

If it weren't this way then we would all be happy to just read popular science books :tongue2:

Not really, popular science books do not explain anything, they just tell you that things are cool. So I never read them since it is more frustrating than anything else.

Also I never do exercises, I have figured that I probably should but I hate it. To me the best way to test if you understand something or not is to wing things like exams and every other form of examination, if you still get a good grade then you understood otherwise you better work on your understanding.

The problem with doing too many exercises is that it is easy to fall into the trap where you do things by memorising solutions rather than understanding the concepts. If you understand the concepts you should get an A without any other preparation.

 

[MathematicalPhysicist]

The problem with doing too many exercises is that it is easy to fall into the trap where you do things by memorising solutions rather than understanding the concepts. If you understand the concepts you should get an A without any other preparation.

In theory you are right, in practice...
Btw, doing too many exercises changes from one person to another.

P.s
In preparation for exams, usually there isn't enough time to do a lot of exercises anyway.

 

[twofish-quant]

Also I never do exercises, I have figured that I probably should but I hate it. To me the best way to test if you understand something or not is to wing things like exams and every other form of examination, if you still get a good grade then you understood otherwise you better work on your understanding.

That strategy wouldn't have worked for me as an undergrad, because where I went to school, no one got a good grade on the examinations. The examinations were always set up so that everyone would get a bad grade on them, and the question is how bad.

The problem with doing too many exercises is that it is easy to fall into the trap where you do things by memorising solutions rather than understanding the concepts.

Depends on the types of exercises. If they throw a lot of problems that are very different, then you can't solve things by memorization, because there are too many things to memorize.

If you understand the concepts you should get an A without any other preparation.

Again this depends on the educational philosophy of the school. Where I went do school, "understanding the concepts" meant being able to solve problems. Also the tests were set up to be really, really hard and so the teachers would intentionally put a lot of material that wasn't covered in class to see if you could figure things out on the fly.

Part of the reason for this testing philosophy was to drive home the point that *no one* really fully understands the concepts.

 

[Phyisab****]

Also I never do exercises, I have figured that I probably should but I hate it. To me the best way to test if you understand something or not is to wing things like exams and every other form of examination, if you still get a good grade then you understood otherwise you better work on your understanding.

The problem with doing too many exercises is that it is easy to fall into the trap where you do things by memorising solutions rather than understanding the concepts. If you understand the concepts you should get an A without any other preparation.

Well that sounds great but seriously? How far did you make it with this technique? And how can you ever prepare to solve problems on an exam if you never solve any problems? That's how you test yourself to see if you missed anything before the exam.

 

[Klockan3]

Well that sounds great but seriously? How far did you make it with this technique? And how can you ever prepare to solve problems on an exam if you never solve any problems? That's how you test yourself to see if you missed anything before the exam.

I am ~1 year off graduating with a masters in maths and theoretical physics. Before exams I glance over some problems and their solutions to see if there are any steps I don't understand, if there are I look them up in the book otherwise I check the next problem.

That strategy wouldn't have worked for me as an undergrad, because where I went to school, no one got a good grade on the examinations. The examinations were always set up so that everyone would get a bad grade on them, and the question is how bad.

So, what do this have to do with anything? Ok, so you had hard courses, if you did less bad you understood better? It isn't that hard to understand what I meant...

Depends on the types of exercises. If they throw a lot of problems that are very different, then you can't solve things by memorization, because there are too many things to memorize.

Sir, you are seriously underestimating memorisation. While yes, you can't memorise everything, you can memorise a ton while only understanding a few things and get by well with that. Talking with people it usually scares me how little they actually understand of what they have learned.

Again this depends on the educational philosophy of the school. Where I went do school, "understanding the concepts" meant being able to solve problems. Also the tests were set up to be really, really hard and so the teachers would intentionally put a lot of material that wasn't covered in class to see if you could figure things out on the fly.

Part of the reason for this testing philosophy was to drive home the point that *no one* really fully understands the concepts.

How do any of this explain why it is good to do a lot of exercises? The only thing you learn on that is solution strategies and it is a terrible way to do that, not to mention that according to you they do not even test on the standard solution strategies either!

Also, for someone who never do exercises every test is a test of what you mentioned, basically it makes the tests a much better check of understanding than what they usually are.

 

[twofish-quant]

So, what do this have to do with anything? But doing like I do seems to be the best way to tackle those courses, since then you haven't trained on solving specific problems but instead on understanding the material in general.

What happens in the "real world" is that often no one cares if you have a general understanding of the material. What people do care about is if you can solve a specific problem.

Sir, you are seriously underestimating memorisation.

You are seriously underestimating the cleverness of instructors to develop problem sets for which memorization is not that useful. It was pretty standard in my physics years for instructors to allow students to take to the test a single sheet of paper, where you could write anything you want. The logic was that if you could solve the problems with memorization, then do it.

While yes, you can't memorise everything, you can memorise a ton while only understanding a few things and get by well with that. Talking with people it usually scares me how little they actually understand of what they have learned.

It really depends on how the course is set up. It's possible to set up a course and tests so that memorization will get you nowhere. Conversely, there are courses in which there is no fundamental understanding.

How do any of this explain why it is good to do a lot of exercises? The only thing you learn on that is solution strategies and it is a terrible way to do that, not to mention that according to you they do not even test on the standard solution strategies either!

I think it's a wonderful of doing that, since you end up teaching yourself things that the teacher didn't intend to teach you. If you have a group of people stare at a hard problem long enough, they will often develop insights and solution techniques that the instructor was unaware of.

The fun thing is that in some problems, there are no standard solution strategies.

 

[Klockan3]

What happens in the "real world" is that often no one cares if you have a general understanding of the material. What people do care about is if you can solve a specific problem.

Of course, unless you want to do theoretical science. Then in the end the most important thing is to understand. Also understanding things is my only motivator, I do not care much about money or so.

You are seriously underestimating the cleverness of instructors to develop problem sets for which memorization is not that useful. It was pretty standard in my physics years for instructors to allow students to take to the test a single sheet of paper, where you could write anything you want. The logic was that if you could solve the problems with memorization, then do it.

This was standard where I went too. We even have a course where you can bring anything you want to the exam, even any amount of old exam solutions and such. Many had problems with that course but still a lot managed to get through it with good grades through memorising solutions and ways to identify which formula to use.

It really depends on how the course is set up. It's possible to set up a course and tests so that memorization will get you nowhere. Conversely, there are courses in which there is no fundamental understanding.

Yup, I really hate the courses were they don't expect you to understand anything. But I have yet to see a course where people can't get by with mostly a lot of memorising.

I think it's a wonderful of doing that, since you end up teaching yourself things that the teacher didn't intend to teach you. If you have a group of people stare at a hard problem long enough, they will often develop insights and solution techniques that the instructor was unaware of.

The fun thing is that in some problems, there are no standard solution strategies.

Yeah, I love when they give out really hard problems, I do not oppose to that. I just don't understand why it means that you should focus so much on learning how to do standard problems. You should solve each type of problem at the most once imo.

Edit: Also, the biggest problem with memorising is that the memories you get doing that do not last that long. When you understand something it usually stick around for a really long time. This is what you carry with you after you graduate, not the formulas or the solution methods you memorised. Of course it is impossible to get by without understanding anything, but you can get quite close.

 

[twofish-quant]

Yup, I really hate the courses were they don't expect you to understand anything. But I have yet to see a course where people can't get by with mostly a lot of memorising.

Maybe I've just been luckier. After high school, I've never had a single science or engineering course in which it was possible to survive with just memorization.

 

[Klockan3]

Maybe I've just been luckier. After high school, I've never had a single science or engineering course in which it was possible to survive with just memorization.

I think that we maybe just have different definitions of memorization and understanding. They are virtually the same and every person have to make their own cut on what kind of knowledge is to put in which definition, so it wouldn't be strange at all.

My own definition is that I understand something when I can't imagine how it could be in any other way and the way I see it agrees with everything else I know that is in any way relevant to the subject. I love that feeling of everything being crystal clear, but it don't happen too often. That definition do not fit well when it comes to evaluating others so then I just try to evaluate based on what they are struggling with, which is impossible to do without any form of bias.