Making the right decision Pure Math

[Qstart]

Hi guys I'm here to ask the age-old question, namely, I am thinking of transferring from my highly ranked university where I finished my first year in an Engineering Physics type program to the university in my hometown where I want to study Pure Math (it is too late to transfer faculties at my current university). Am I being crazy? I want to go to grad school and I know how grim the situation can be for pure math, so I guess I'm looking for people to tell me otherwise or reassure me...

The other thing is that I may not even take any physics which in high school is what I always saw as being my calling. I had only had classical mechanics in my first year, but I like to read from textbooks from time to time and physics just doesn't grab me the way math does. Should I try continue to try it anyway (labs are what I really didn't like, is it advisable to just take non-lab courses or will grad schools think I'm just wasting their time?), is it possible to pick up physics in grad school if you wanted to do something math related?

tl;dr
-Switching from high prospects Engineering to Pure Math, am I crazy?
-Is it a waste of time to take physics without the lab component?
-If I wanted to research something like mathematical physics in grad school is it actually necessary to have a physics background, or can you pick it up on the spot?

 

[Student100]

Hi guys I'm here to ask the age-old question, namely, I am thinking of transferring from my highly ranked university where I finished my first year in an Engineering Physics type program to the university in my hometown where I want to study Pure Math (it is too late to transfer faculties at my current university). Am I being crazy? I want to go to grad school and I know how grim the situation can be for pure math, so I guess I'm looking for people to tell me otherwise or reassure me...

The other thing is that I may not even take any physics which in high school is what I always saw as being my calling. I had only had classical mechanics in my first year, but I like to read from textbooks from time to time and physics just doesn't grab me the way math does. Should I try continue to try it anyway (labs are what I really didn't like, is it advisable to just take non-lab courses or will grad schools think I'm just wasting their time?), is it possible to pick up physics in grad school if you wanted to do something math related?

tl;dr
-Switching from high prospects Engineering to Pure Math, am I crazy?
-Is it a waste of time to take physics without the lab component?
-If I wanted to research something like mathematical physics in grad school is it actually necessary to have a physics background, or can you pick it up on the spot?

Have you thought about switching from engineering physics to something more computationally based in physics? If you aren't enjoying the labs, well, that's what physics is all about. (To me anyway.)

What about physics did you find appealing?

If you can’t see yourself doing it anymore, then switching majors may be the best option for you. I’m surprised your university won’t allow a major change; here in the US I had just assumed that majors weren’t basically locked in until your junior year. Seeing as how most students end up in a major they didn’t declare as a freshman.

-No you aren’t crazy; you just discovered something about yourself.

-No, it’s not a waste depending on what you want to do in physics. I went lab heavy, mainly because I want to be an experimentalist someplace in CM. Engineering Physics is applied physics, not doing the lab sections would hurt you if you remained with that major.

-I’m not sure; I would assume some pure math majors that have taken most of their electives in physics would be competitive. I don’t really know, so maybe someone else can enlighten you here.

 

[Arsenic&Lace]

For your last point, somewhat major changes in graduate school from undergrad are not anywhere near unheard of. A friend of mine with an engineering physics undergrad is currently doing theoretical condensed matter physics at my local institution.

Pure mathematics (e.g. a PhD doing research in algebraic topology) might be more of a difficult switch if you don't take lots of pure math courses, but I've had multiple professors with an undergraduate degree in physics who obtained PhD's with the math department; in general, however, they focus on more physical topics such as differential equations. I am not sure what would happen if you attempted to get into a grad program studying number theory without a background in number theory/standard undergraduate algebra etc.

EDIT: Do you actually want to do mathematical or theoretical physics? Mathematical physics is very much a branch of the math department, while theoretical physics sits on the fence between the math and physics departments arguably (I believe theoretical physics is part of Cambridge's applied math department, for instance). The easiest way to becoming a mathematician might be mathematical physics.

 

[Qstart]

To clarify I'm only going into my second year! And mathematical physics is what I'm interested in, do you actually need a physics background for that or are you essentially provided with a set of axioms to work around?

I assumed lab work wouldn't be needed for mathematical physics and I could focus more on taking just EM, Quantum, General Relativity, and similar courses.

 

[Arsenic&Lace]

This is a difficult question to answer. However, in short, if you can find a math professor who specializes in mathematical physics or does both mathematical physics and other mathematics at the MATH department, you can avoid the lab courses

 

[Student100]

To clarify I'm only going into my second year! And mathematical physics is what I'm interested in, do you actually need a physics background for that or are you essentially provided with a set of axioms to work around?

I assumed lab work wouldn't be needed for mathematical physics and I could focus more on taking just EM, Quantum, General Relativity, and similar courses.

So I trolled around the interweb and found some admission requirements to mathematical physics PhD programs. Take for example the Indiana University Bloomington:

Students in the Mathematical Physics Program must be enrolled in either the Department of Mathematics or the Department of Physics. Basic preparation should include courses in advanced calculus, linear algebra, modern algebra, complex variables, classical mechanics, electromagnetism, quantum mechanics, modern physics, thermodynamics, and statistical mechanics. Knowledge of the following fields is desirable: real analysis, differential equations, probability, topology, differential geometry, and functional analysis.

That would be more than doable for a pure math major.

Your issue is that you're enrolled in a engineering degree, are you in the engineering or physics department? EP degrees usually don't leave many electives to be chosen, so how well could you prepare yourself mathematically with what electives you have?

You may want to talk to the counselors at your school, as well.

 

[homeomorphic]

Am I being crazy?

Yes, and I'm allowed to say that because I switched from EE to math, myself.

I want to go to grad school and I know how grim the situation can be for pure math, so I guess I'm looking for people to tell me otherwise or reassure me...

Not much reassurance for me. It's pretty grim. I can say that grades tend not to be a big deal in grad school, so the coursework isn't that scary, even though it is pretty hard. The way I see it, qualifying exams aren't that scary because if you fail them, what are you missing? If you pass, you get to write a big nasty dissertation--that's the really scary part. I kind of envy the people who didn't pass. I suppose I should have just quit, but I got too far before I realized I should, so I just had to grit my teeth and finish the stupid thing. Actually, I'm thinking I might be better off in terms of finding a job if I had learned more practical skills, rather than finishing. Should have just transferred to EE grad school is what I should have done.

I can't really say too many positive things about research because it's hard for me to imagine that anyone would like it that much, after my experience. I suppose it would have been cool if I didn't have to write it all down, which was extremely tedious. And if you took out the part where I messed up several times and had to throw out 5 pages of stuff and got set back a few months each time. And it would have helped if what I was doing had some relation to reality, other than waving my hands and saying, "hey, it could be relevant to string theory (but I don't even really know why exactly)".

I don't like teaching either, but I can say that if you do like teaching, that is a big advantage.

The other thing is that I may not even take any physics which in high school is what I always saw as being my calling. I had only had classical mechanics in my first year, but I like to read from textbooks from time to time and physics just doesn't grab me the way math does.

That sounds like a pretty premature conclusion. Having textbooks grab you is, in my experience, little indication that current research in pure math is going to grab you. It's a fundamentally different activity than studying from textbooks. If reading hundreds and hundreds of pages of very technical stuff that is very removed from reality is your thing, go for it. At some point, I just realized I needed to come back down to Earth. What I am really curious about is the way the world works, rather than playing abstract games, just for the sake of it, and that's why I realized I made a mistake to put so much time into studying pure math. Life is too short and there's too much to find out about the things that really matter. Math matters, too, but to me, it doesn't matter until it finds some application to science or if it leads you to deep philosophical conclusions.

Should I try continue to try it anyway (labs are what I really didn't like, is it advisable to just take non-lab courses or will grad schools think I'm just wasting their time?), is it possible to pick up physics in grad school if you wanted to do something math related?

I never liked the way labs are taught. Too cook-book. I want to do my own experiments, not follow someone else's procedure. That may be why you don't like it, and I wouldn't blame you.

Unless you pick just the right department/people to work with, they'll probably tend to sway you very far in the math direction. I tried to learn about physics on the side, but it was pretty hard to get very far with it, even though I studied topological quantum field theory, which is nominally related to physics.

-Switching from high prospects Engineering to Pure Math, am I crazy?

Yes, unless you really know what you are getting into and have thought it all through very carefully, which I would tend to doubt at this stage. Even I thought I had thought everything through, but it didn't work out as planned.

-Is it a waste of time to take physics without the lab component?

No. I understand a fair amount of physics with very little lab experience in physics. Granted, I would understand it better, probably, with lab experience, but I still understand it enough to make some use of it, mathematically.

-If I wanted to research something like mathematical physics in grad school is it actually necessary to have a physics background, or can you pick it up on the spot?

In my particular area, topological quantum field theory, you basically don't even need to know any physics at all (although it's a plus if you do know a lot). Literally, if you had never taken a single physics class, you could probably work in the field, although, there's a side of the literature that would be completely inaccessible to you. It's not really physics, though.

 

[Gauss M.D.]

Which math courses are you basing your love for pure math on? Because let me tell you, getting sick of the subject despite initially feeling like you've found your calling is certainly possible.