Learning Styles: Passion for Science & Passing Exams

[deRham]

"But I have gone through a physics/maths double major without doing any computational exercises since 6th grade in elementary school and I am currently in grad school"

Therein may be our misunderstanding. I think some of the 'theoretical' things you may have done, I may classify as computations [but not trivial ones, rather very respectable things]. I am a mathematician [into the more abstract fields], and not a physicist.

I don't define a computation as something with lots of numbers and multiplying a million messy matrices. I define it as when you actually determine a specific detail about an example [which is how mathematicians tend to define it]. Sorry for the confusion if it was there.

Certainly I think practicing gross computations for too long is silly. For instance, taking a million integrals is not the way to learn. A few computations in the sense of taking integrals or such can be healthy, but not more than that.

"the ones I have talked to really do not want to stop doing exercises"

Depending on how repetitive their work is, they may be wasting their time. If they are illustrating a new realization of the theory for themselves, they are spending it wisely.

 

[deRham]

"I understand how to graph rational equations, but I would be stupid to move on before going through a bunch of test problems to make sure I'm comfortable doing them."

"Why?"

If it's a useful skill [to your goals], you should practice it simply because it will be useful to you. If one's understanding of the theory is sufficient to be able to do all the test questions in one's head, then there's no need to worry.

"To me, you needing to do a lot of computations to "understand" is a sign that you don't really understand."

A LOT is not necessary. But some computations can expose misunderstanding of the theory! Computations are a sanity check, not the end-all that some make them to be.

 

[Klockan3]

Therein may be our misunderstanding. I think some of the 'theoretical' things you may have done, I may classify as computations [but not trivial ones, rather very respectable things]. I am a mathematician [into the more abstract fields], and not a physicist.

I haven't done those kinds of exercises either, I haven't done any exercises at all except for the mandatory hand ins of proofs you have to do in just about every upper level maths course. (There is really no good alternative to hand ins in those classes)

And I am not just a physicist, I have taken several grad level maths courses... I am currently deciding if I want to do my thesis with the maths department or the physics one. When I was younger I was more into physics but when I noticed that they in general have poor understanding of what they are doing compared to mathematicians I decided to at least read as much maths as the pure maths people who go into fields relating to physics.

A LOT is not necessary. But some computations can expose misunderstanding of the theory! Computations are a sanity check, not the end-all that some make them to be.

This I agree completely with and is what I am trying to tell people. I think that the reason that I can go on like I describe above has a lot to do with my near perfect memory and I have noticed that most have an atrocious habit of forgetting a lot of things so I can't really say that something that works for me would also work for them.

When I was younger I thought that everyone else was just stubborn for doing it the hard way, but then I started to notice how bad their memories were.

 

[deRham]

OK, so you are in favor of exercises which bring something new out of the theory, but not those which are repetitive and serve only as a memory crutch. That I am in accord with.

As to my comment about computations and your background - I am well aware you're both a physics and math student and have probably taken lots of math. Remember, though, that something like "what is a universal covering space of so and so" would count as a computation to me. Anything involving using the theory to actually describe something in more detail within the context of an example. Not only math courses, but entire math research articles can be modeled on these sorts of pursuits. I'm not limiting "computation" to multiplying 2 matrices 20 times ... and it sounded like our different definitions of computation came from our different backgrounds. The sort of computation I'm talking about has nothing to do with memory or repetition, but with raw reasoning itself.

Anyway, I think we're probably on the same page.