Should I double major in math/ take extra semester?

[physucsc11]

I will be transferring to a different university this fall and I am trying to decide the following:
I am somewhat interested in math and am thinking of double majoring in it. However, I would only take math to complement my physics education. I am interested in learning group theory and differential geometry and topology as I know the most interesting physics is based on it. However, if I were to double major, it would require me to take an extra semester to finish. As I understand most graduate schools only accept Fall semester applications so I would basically be losing a year in the process. So do you guys think this would be worth it? Or is it better to just take more physics electives, graduate in 2 years, and take the math that I would have been taking as an undergrad in grad school? I know that most graduate level physics programs provide mathematical physics courses which cover group theory and diff geometry.

Also the other thing is that there are several physics electives that I wouldn't be able to take unless I took an extra semester since they have numerous prerequisites (such as solid state physics), so would this be a bad thing? Or could I just take those courses when I go to grad school and really figure out what it is I want to specialize in? Thanks.

 

[Asphodel]

If you're interested in it, go ahead and do it. Don't neglect the physics electives too much though. Some of them you can easily do without, but some stuff like stat mech should really be part of your core curriculum (if it's not already).

 

[mgiddy911]

can you take those math courses as electives and not double major? or do those 3 courses by themselves put you over?

 

[physucsc11]

If you're interested in it, go ahead and do it. Don't neglect the physics electives too much though. Some of them you can easily do without, but some stuff like stat mech should really be part of your core curriculum (if it's not already).

Everything I said was assuming I would take the core curriculum for sure, including 2 semesters of quantum mechanics and a semester of statistical mechanics.

can you take those math courses as electives and not double major? or do those 3 courses by themselves put you over?

I believe the program requires three electives which can be from any department, including mathematics.

Do you guys think its a disadvantage when applying to grad schools to go a semester over, or they don't really care?

 

[tmc]

I'd see two options:

1. Take the courses as electives without the double major, and see whether you can fit enough interesting courses into your schedule without the extra semester. Depending on the number of extra courses you want (and there are certainly many interesting math courses with large implications to theoretical physics), you might still be forced to have a Fall semester.

2. Take even more math courses. If you're going to take, say, five extra math courses and finish them after the Fall, you might as well take more during the winter (or more physics electives, or even grad courses in physics at your university). I'm sure there are more than enough math courses to allow you to do that, and this way you won't be wasting time sitting around until grad school. Moreover, no grad school would really care about you being one year older; most would actually prefer that, as you'd have a very strong math background (and if you take some grad courses in winter, you'll be able to prove them that you can handle grad-level coursework). Some universities also offer 1-year course-based Masters in Mathematics, which would accomplish what you're looking for as well.

It's fine not to have taken some physics electives. New grad students often take a number of undergrad courses; it's generally encouraged by the department.

 

[arunma]

Physucsc11, when I was in undergrad I was in basically the same situation as you. I was three math classes under the requirements necessary for a math degree, and I could spend an extra semester to complete it. I ended up doing a math degree in addition to my physics major, and I'm happy I did it, but I might not recommend this to others. There are a few positives. Physics majors typically do well in math, so a math major would be a good GPA booster. I don't know if physics grad programs care all that much that you have a math degree (I only gave it a mention on my essays), but as long as you did well in your courses they certainly aren't going to penalize you for taking the extra semester, so it won't hurt your chances or anything. And for me, I had a slight bonus my first semester of physics grad school. Since I had a math degree, I didn't have to take the "mathematical methods for physicists" class that most of the first years take.

There is a negative too. Unless you go into something like high energy theory (in which case you need to know group theory), advanced math courses aren't all that helpful in physics. In graduate level physics courses, you basically need to know single and multivariable calculus like the back of your hand (better, actually), and you need to have some familiarity with linear algebra (mostly for quantum mechanics). They say that you should also know complex analysis, but this is highly exaggerated. I took complex analysis as part of my math requirements in undergrad, and while it was interesting in its own right, it wasn't all that useful my first year of grad school. My E&M professor spent about twenty minutes one day doing a calculation that utilized a complex integration, and that's about it. Granted, that problem showed up on an exam, but I just copied the solution out of my notebook (it was open book/notes), so I really wouldn't have even needed to know the mathematical formalism behind this. All the other math you learn in advanced math courses isn't all that useful. My department even offers its own group theory class for the high energy theory students, so you don't need to take that in the math department either.

I'm essentially of the opinion that if you're going to do a second major in math, do it because you like math and not because it will be helpful to you in a physics graduate program. Remember that math isn't physics; mathematicians are interested in proofs and elegant solutions, physicists just want the results. If you really like doing proofs, then go ahead and do a math major, because you won't get a chance to take all of those interesting math classes once you're in grad school. But don't do it because it will better prepare you for life as a physicist. The kind of math physicists use isn't emphasized that much in math departments. But you'll learn it in your first year graduate courses, so this isn't something to worry about.

 

[2Tesla]

If you're planning on taking even just GR and field theory your first semester, you will be very glad to have some diff geom, complex analysis, group theory, etc. under your belt, before starting. If you decide not to take the extra semester, studying them over the summer would not be a bad idea.

 

[physucsc11]

Thank you for all the helpful advice so far.

Now Arunma, you said physics majors typically do well in math, so a math major would be a good GPA booster. However, I have never been very good at proofs. Also, the mathematics program at the university I will be transferring to is regarded as being very difficult. The only way I see myself getting good grades there in math is if I spend a lot of time studying for the math courses as opposed to learning physics.

Also, you said that grad programs offer mathematical physics courses which cover basically any math that I would ever need as a physicist. This sounds like something for me because like I said, I am interested in math as it applies to physics, but not for the sake of math itself. Sure, I can enjoy a beautiful proof, but I'm not sure this gives me reason enough to take an extra year.

2Tesla, you said that it would be helpful to know diff geom, complex analysis, group theory, etc before starting grad school. How difficult is it to self-study this math over the summer, say, as opposed to taking courses? Are there texts I can use which are aimed directly at physicists, that don't require going through an ocean of proofs?

At any rate, keep the replies going this has been helpful in getting me to think about whether or not pursuing a second degree in math would be a wise choice.

 

[arunma]

Now Arunma, you said physics majors typically do well in math, so a math major would be a good GPA booster. However, I have never been very good at proofs. Also, the mathematics program at the university I will be transferring to is regarded as being very difficult. The only way I see myself getting good grades there in math is if I spend a lot of time studying for the math courses as opposed to learning physics.

I see. If you honestly believe that you could only do a math major by compromising on physics, then I might recommend against it. Physics admissions committees aren't like their counterparts in undergrad or med school. As I heard from one of the committee members at my department, they're not really looking for well-rounded students or people who have a diversity of interests. They care about how good you are at physics. So doing well in your physics classes is the best way to get into grad school. Maybe you should take just one advanced math course at first and see how you do (most physics BS degrees require an advanced math elective anyway). But if you need to start skimping on physics to get a math degree, then it probably isn't worth it.

Also, you said that grad programs offer mathematical physics courses which cover basically any math that I would ever need as a physicist. This sounds like something for me because like I said, I am interested in math as it applies to physics, but not for the sake of math itself. Sure, I can enjoy a beautiful proof, but I'm not sure this gives me reason enough to take an extra year.

Well, my department does this anyway (I can't speak for all departments, but I'd imagine they're much the same). Most of the first years take the math methods for physicists class offered by the math department. And as I already said, the physics department itself offers group theory. And then there's quantum mechanics, where you simply can't get away without learning a whole bunch of linear algebra. Since you don't like proofs, it seems to me like you may just want to skip the math major and just wait until (physics) grad school to further your math education.

2Tesla, you said that it would be helpful to know diff geom, complex analysis, group theory, etc before starting grad school. How difficult is it to self-study this math over the summer, say, as opposed to taking courses? Are there texts I can use which are aimed directly at physicists, that don't require going through an ocean of proofs?

This differs from my experience, but 2Tesla's undergrad or grad departments may simply be different from mine. I took differential geometry my sophomore year of undergrad. It was heavily proofs oriented, and did virtually nothing forme when I took cosmology as a senior. 2Tesla also mentioned field theory. I imagine that field theory requires quite a bit of math (I wouldn't know, as an astrophysics student I'll never have to take it), including complex analysis and group theory. So he's right to recommend it to someone who would take this course as a first year. But field theory is quite an advanced course, and most people only take it their second or third year of grad school. I can't imagine who would want to torture themselves by taking field theory first year. It might help if you have an idea of what kind of subfield you want to go into. If you're interested in high energy or condensed matter theory, you'll need a lot of mathematical skills. But if you're interested in astrophysics, space physics, biophysics, etc., you don't need all that much math beyond what you probably already know.

 

[Asphodel]

Yeah, that was why I never went past a math minor. Anything specific I want to learn will either come through physics courses or through independent study, and the time consumption was increasing far beyond what I considered reasonable (in large part because of inaccurate assumptions about prior knowledge that didn't consider the material covered in the prerequisite classes adequately, which was just plain annoying to boot).

 

[physucsc11]

Arunma, you said that "It might help if you have an idea of what kind of subfield you want to go into. If you're interested in high energy or condensed matter theory, you'll need a lot of mathematical skills."

This is actually another question I've been debating. I find many different subfields interesting, especially condensed matter and biophysics. On that note, I realized that biophysics probably doesn't entail as much advanced physics or mathematics as I would like, so it is certainly not a career goal for me. My general tendency is to get a solid foundation in physics and mathematics, and later on specialize. That way I would be able to study high energy physics or anything else for that matter even if my interests changed later on.

When did you figure out you wanted to study astrophysics?

 

[mgiddy911]

Is it possible to take some summer classes? maybe free up enough time that you can get those math courses in without the extra semester?

 

[arunma]

Arunma, you said that "It might help if you have an idea of what kind of subfield you want to go into. If you're interested in high energy or condensed matter theory, you'll need a lot of mathematical skills."

This is actually another question I've been debating. I find many different subfields interesting, especially condensed matter and biophysics. On that note, I realized that biophysics probably doesn't entail as much advanced physics or mathematics as I would like, so it is certainly not a career goal for me. My general tendency is to get a solid foundation in physics and mathematics, and later on specialize. That way I would be able to study high energy physics or anything else for that matter even if my interests changed later on.

When did you figure out you wanted to study astrophysics?

Heh, that's an interesting question. Actually it happened by accident. Originally I wanted to do experimental condensed matter or high energy. After I got into grad school, I started emailing a bunch of professors asking if I could work for them the summer before I started. One of the professors I emailed was into high energy astrophysics. I looked at the group's web page, and noticed that working for him would give me a good chance to learn about instrumentation and electronics (which I figure is a good skill to have). He ended up responding, and I did a summer with the particle astro group. Eventually I just liked it too much to switch. I'm not much of an astronomy person (I never took a single astro course in undergrad except cosmology), but my advisor's research is almost entirely physics-based. In fact technically, I'm going to be getting my PhD in physics, and not astrophysics. But basically, I didn't end up going into a subfield until my first year of grad school.

Incidentally, if you want to go into a mathematically rigorous subject, I'd suggest condensed matter. You an always do a postdoc in biophysics (which is considered "soft condensed matter") afterwards if you want. But this will let you study all kinds of fun mathematical things. In fact my only gripe being in particle astro is that I don't get to take stuff like field theory or solid state physics.

 

[2Tesla]

I'm all for waiting as long as possible to specialize, but as a soon-to-be 1st year grad student... it's getting to be time. Not that you can't study other subjects, but how hard you need to work on math right now and your 1st-year courses really do depend on what field you'll work in.

I'll say that if you're planning on taking field theory (that is, if you're thinking of high-energy or theoretical condensed matter), or GR (not a cosmology class, but a whole semester just about GR), in your first year, then I would highly recommend studying up on some suitable math before starting. Not that some students don't, but they tend to be the ones that learn just enough to do the problem sets and never quite grasp the subject, in my experience, because they're so caught up in learning the math that they miss out on the physics. This is just my opinion, of course.

As for taking GR or field theory in your first semester, again that's up to what kind/s of physics you're interested in. In my department (which, yes, tends toward the torture-prone :) those thinking of high-energy or (theoretical) condensed matter generally take field theory in the first year, and those thinking of cosmology or high-energy or astrophysics take GR in the first year, as well as some other students. This is because they need these subjects for almost all of the other courses in their fields.

So, there you go. As for self-teaching books, for GR there is a big list here:

http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html#background

or try these:
"A relativistic toolkit" by Eric Poisson
"Elements of Diff. Geometry" by Millman and Parker
http://people.hofstra.edu/faculty/Stefan_Waner/diff_geom/tc.html
math appendices in Sean Carroll's "Spacetime and Geometry"

for field theory, pick up an undergrad complex analysis book and make sure you understand contour integrals. "QFT in a Nutshell" is also great to read before your first QFT class, as it has lower-level explanations of both the physics and the math.

Good luck! (And QFT is not as hard as you think, don't let it intimidate you :)