Graduate-level analysis vs. second-year physics

[PieceOfPi]

Hi,

I am a math major who will be a senior in my undergraduate career. I will be applying to graduate schools in mathematics.

I still have not decided which courses to take in my senior year. So far, I have taken most of the undergraduate math courses, including real analysis, complex analysis, abstract algebra, and advanced linear algebra. I am certainly going to take topology (2 quarters) and differential geometry (1 quarter), and possibly probability theory (2 quarters) next year, but I might also be able to take additional class, so I am debating whether to take the graduate-level analysis sequence or the second-year physics sequence.

It probably makes a lot of sense to take the graduate analysis sequence (3 quarters) if I am planning to go to a graduate school in math. The textbook for this course is Big Rudin (of course!). I really enjoyed my analysis classes (both real and complex) here, and I think it would be wonderful to learn more about it. It would also help my chance of getting into more selective graduate schools as well. However, while I did enjoy analysis, I wasn't really a superstar in my classes--while I did get A's in my complex analysis sequence, I only did reasonably well in my real analysis sequence (B+/A- level), so I'm not so sure if I would be able to handle a graduate level course. Furthermore, I will be preparing my thesis through my senior year, so topology and thesis might be enough for my senior year. I did, however, talked to a few professors, including the one who I had for real analysis, and the one who will be teaching the graduate analysis next year, and most of them seemed positive about that idea, except for one.

Now, some of you might be wondering why in the world I would ever want to take a physics class. I took a first-year physics in my sophomore year, but I was only semi-interested in the subject back then, so I didn't study physics further. But recently, I took a seminar course that studied a little bit of nonlinear dynamics and quantum physics (It wasn't really like a physics class, since the seminar was also accessible to non-science majors... so no heavy math was involved), and I thought the topics were very interesting, which made me regret for not studying more physics. So I thought that while it is too late to major in physics now, I can at least learn a little more so that I can study physics during my free time, or even better, consider studying mathematical physics in grad school (warning: I don't really know what this is; I only mentioned because it involves "math" and "physics"). The first quarter of the second-year physics sequence that I'm considering to take discusses modern physics (i.e. special relativity, light, quantum mechanics, atomic and nuclear physics), and the remaining two quarters will discuss thermodynamics and statistical mechanics. If I'm lucky, I might be able to get a minor in physics, but that's not really necessary.

So yeah, I was wondering what people on here think about this. It's too bad that they are both offered at the same time, because otherwise I would try out both of these courses during the first week and stay in the one I feel more interested. Ask me if you have any question about my background.

Thanks

 

[flemmyd]

the physics course you are describing sounds likes a "modern physics" course. Conceptually, I'm sure you'll be introduced to a lot of topics you are interested in, but the mathematics will probably be fairly dull for you.
I might recommend the junior level e&m sequence instead. It has a lot of great theories and great math.

But then you have to compare this e&m class to graduate analysis, which i probably can't do...

Keep in mind though: when you go to mathematics graduate school, you'll probably have to (or be offered the chance) to take Graduate Analysis with Rudin. I'm doubtful you'll get the chance to take any physics classes.

 

[PieceOfPi]

Thanks for your reply! I was kind of giving up on getting any reply on this post, but I guess waiting helps.

the physics course you are describing sounds likes a "modern physics" course. Conceptually, I'm sure you'll be introduced to a lot of topics you are interested in, but the mathematics will probably be fairly dull for you.
I might recommend the junior level e&m sequence instead. It has a lot of great theories and great math.

The physics class I mentioned is probably like the one you described; it is a "modern physics" course. The textbook for that physics class is likely going to be Giancoli's Physics for Scientists and Engineers, so most of the math for that class is probably limited to calculus (for thermodynamics and statistical mechanics, however, I believe they use Kittel's Thermal Physics).

I do however have the option to take the E&M class as well, and it's actually offered at the different time slot from the analysis and modern physics. It might be worth attending that class for a first couple of lectures.

Keep in mind though: when you go to mathematics graduate school, you'll probably have to (or be offered the chance) to take Graduate Analysis with Rudin. I'm doubtful you'll get the chance to take any physics classes.

That is my major dilemma. I love math, and I think the topics that are covered in that analysis sequence should be very interesting (measure theory, some functional analysis, complex analysis), but I can (or as you said, have to) take that class in my graduate school. On the other hand, this will be my last chance to take a class that is offered outside of math department...

 

[nlsherrill]

Thanks for your reply! I was kind of giving up on getting any reply on this post, but I guess waiting helps.



The physics class I mentioned is probably like the one you described; it is a "modern physics" course. The textbook for that physics class is likely going to be Giancoli's Physics for Scientists and Engineers, so most of the math for that class is probably limited to calculus (for thermodynamics and statistical mechanics, however, I believe they use Kittel's Thermal Physics).

I do however have the option to take the E&M class as well, and it's actually offered at the different time slot from the analysis and modern physics. It might be worth attending that class for a first couple of lectures.



That is my major dilemma. I love math, and I think the topics that are covered in that analysis sequence should be very interesting (measure theory, some functional analysis, complex analysis), but I can (or as you said, have to) take that class in my graduate school. On the other hand, this will be my last chance to take a class that is offered outside of math department...

I say you try the physics course out(the modern one not upper level E&M). By what your saying it already sounds like your senior year may be pretty time consuming, and a graduate math class "could" be overkill. I read somewhere that undergraduates in math/physics taking graduate level courses average a full letter grade lower than the graduate students. This, of course, may not hold for you, but I think its noteworthy. You don't want to mess your gpa up your last year in school or anything.

You seem more interested in taking the 3rd part of the calculus based physics sequence. It will probably be easier than a graduate analysis class for you, assuming you still remember your basic physics. So from that we can assume you will probably have a better gpa/less stressful senior year taking something that you can't take after next year. I think the class could really subject you to some of the modern problems/research in physics and just give you some more general knowledge on nature and reality(which you seem interested to learn about in your spare time too).

just sayin'

 

[PieceOfPi]

I say you try the physics course out(the modern one not upper level E&M). By what your saying it already sounds like your senior year may be pretty time consuming, and a graduate math class "could" be overkill. I read somewhere that undergraduates in math/physics taking graduate level courses average a full letter grade lower than the graduate students. This, of course, may not hold for you, but I think its noteworthy. You don't want to mess your gpa up your last year in school or anything.

You seem more interested in taking the 3rd part of the calculus based physics sequence. It will probably be easier than a graduate analysis class for you, assuming you still remember your basic physics. So from that we can assume you will probably have a better gpa/less stressful senior year taking something that you can't take after next year. I think the class could really subject you to some of the modern problems/research in physics and just give you some more general knowledge on nature and reality(which you seem interested to learn about in your spare time too).

just sayin'

Thanks for your reply! I think the physics class would make my schedule easier, since I already know the professor (it's the same guy who taught the 1st year physics, and I got A+'s from him... twice!). While I never take courses for easy A's, I think topology, probability, and thesis project should keep me pretty busy throughout the term (of course, if I take the analysis course, I probably wouldn't be taking probability, since it's more like an elective).

 

[flemmyd]

hmmm... nlsherrill is right
The modern physics class will probably be the most fun as you can focus on the concepts and not have any particularly difficult math. I would go for that, actually the way nlsherrill puts it. just enjoy the concepts and if something catches your interest, talk a little more with the prof about it in office hours.

As for the graduate Rudin class, it really sounds like something you should talk with your professors more about. Also, something to keep in mind: I really can't imagine your admission for math graduate school becoming something like "These two kids are fairly identical... but one did take graduate analysis his senior year and one did not. let's take the one who did". There are so many other factors for admission and can't imagine this one being a huge deal. But I am not familiar with math graduate school, so someone else my correct me.