Is Memorizing Theorems Necessary for Passing Exams in Mathematical Physics?

[GhostLoveScore]

I'm not sure if this question belongs to this forum, but here it goes.

When you were studying physics or mathematics, specifically mathematical theorems, what was required for passing the exam? We had a course called Mathematical Methods of physics and we had about 20 larger theorems that had proofs about half page or full page long. We also had bunch of smaller theorems and we were required to memorize all of them and we would have to write a proof for few randomly selected in the oral exam. I've always found that pretty unnecessary, memorizing stuff, and I was wondering if it was the same in other countries?

 

[jedishrfu]

What level of exam are you referring to? Graduate, Undergrad or High School.

In Highschool, we had to know how to do geometry proofs and trig derivations. In college, there were some proofs in Abstract Algebra and Topology that I remember but they were limited to the exam time of 45 minutes. In college Classical Mechanics, we were allowed to use a Math tables book for integrals and formulas similarly in QUantum Mechanics.

In graduate school, I remember we had to know Bessel, Legendre and Laguerre functions from memory as our QM prof required that. It was very tough for me as I had returned to school after having graduated 5 years earlier with a degree in Physics (ie I forgot much of what I learned in my higher level math courses if I ever learned it at all).

 

[GhostLoveScore]

Undergraduate

 

[member 587159]

If you understand what's going in, there is not a lot of memorising needed. Just knowing the key steps should often be enough to fill in the details.

 

[ZapperZ]

I'm not sure if this question belongs to this forum, but here it goes.

When you were studying physics or mathematics, specifically mathematical theorems, what was required for passing the exam? We had a course called Mathematical Methods of physics and we had about 20 larger theorems that had proofs about half page or full page long. We also had bunch of smaller theorems and we were required to memorize all of them and we would have to write a proof for few randomly selected in the oral exam. I've always found that pretty unnecessary, memorizing stuff, and I was wondering if it was the same in other countries?

First of all, the criteria for "passing" always depends on the instructor. He/she will have his/her own standards, based on the syllabus, on what level of knowledge is required to pass.

However, when I read your description of what you had to do, it felt rather odd for a course in "mathematical methods of physics". Usually, this is NOT a course on math, but rather on HOW to use the math. I've taken such a course before, and we never had to deal with proving theorems, etc. Rather, it involves problems in which we need to know how to use the math to solve those problems.

Was this course run by the math department? Or was it taught by a math faculty member?

Zz.

 

[GhostLoveScore]

However, when I read your description of what you had to do, it felt rather odd for a course in "mathematical methods of physics". Usually, this is NOT a course on math, but rather on HOW to use the math. I've taken such a course before, and we never had to deal with proving theorems, etc. Rather, it involves problems in which we need to know how to use the math to solve those problems.

Was this course run by the math department? Or was it taught by a math faculty member?

I'm not 100% sure about the assistant, but professor was from math department.
Using math to solve problems was one half of the course, knowing the theorems was the other half.

 

[ZapperZ]

I'm not 100% sure about the assistant, but professor was from math department.

That would explain why the heavy emphasis on proving theorems.

Using math to solve problems was one half of the course, knowing the theorems was the other half.

If you look at Mary Boas's "Mathematical Methods in the Physical Science", you'll see that she states theorems without proofs. She'll carefully describe the limits of validity of such theorems, etc., but she doesn't waste time in showing how they come about. In the preface, she encourages students who are interested in those things to pursue them, but she realizes that most physics and engineering students do not have the time or inclination to do that. So she goes straight into how to use these math. I believe Arfken's text does almost the same thing but with a bit more math.

That, in essence, is what I consider to be a course in mathematical physics.

Zz.