Schools Question about math grad school.

[cragar]

Can you go to math grad school and study applied math that focuses on physics. And also study regular math?

 

[chiro]

Can you go to math grad school and study applied math that focuses on physics. And also study regular math?

Hey cragar.

There are certainly applied math PhD programs at many major universities. The requirements for what you need to study if you need to do coursework for your qualifying exams will vary depending on the institutions own requirements.

One example off the top of my head for applied mathematics in direct relation to physics is fluid mechanics. A quick google search turned up these links:

http://cee.stanford.edu/programs/efmh/students/degree.html

http://www.uea.ac.uk/sci/studyscience/researchdegrees/mthres

This was just the first page of results, but I'm sure you could find many more.

The thing though for this would be the specific focus. I'm guessing that engineering PhD programs would have a different focus to say applied mathematics PhD programs so it would be important to get a clear distinction of the focus on the different programs.

 

[cragar]

ok thanks for your reply. I was wondering if they have schools where you study relativity or quantum mechanics from a math point of view. I am also looking for math grad schools on Google that fit this, just wondering if you knew of anything.

 

[chiro]

ok thanks for your reply. I was wondering if they have schools where you study relativity or quantum mechanics from a math point of view. I am also looking for math grad schools on Google that fit this, just wondering if you knew of anything.

There are mathematicians that study the mathematical formalisms for Quantum Mechanics which is based on the work of Von Neumann and his colleagues. If you want to see the first mathematical foundations for Quantum Mechanics, read Von Neumann's original book which was published (I think) in 1935.

The mathematical foundations for these kinds of things are studied in functional analysis, operator algebras and other similar fields.

The thing though is that the above is a pure mathematical field a lot more so than an applied one, which focuses more on generating abstract understanding for the mathematics behind systems in general rather than QM itself.

With regards to relativity, again there are areas of research that deal with geometry extensively as well with things like various kinds of topology and algebra related to the foundational math underpinning relativity.

All of this kind of thing though, is mathematical physics as opposed to applied mathematics and sometimes its hard to really make a distinction between the two.

If you want to look at the theoretical side of physics in a mathematical context, my guess is that you look into mathematical physics. If however you want to look into an applied context, then engineering and related applied programs (in applied math) would make more sense.

If you want to go deep into the theory and construction of systems underlying QM, get a masters or some other equivalent coursework in functional analysis. You will also have to have the other math essentials for higher mathematics including analysis, topology, and algebra, and also end up extended algebra to the study of operator algebras.

I do recall though that a guy at Cambridge is an active researcher in areas where functional analysis and statistics overlap, so that might give you an insight to areas that use this in a more applied context. Here is his web-page:

http://www.statslab.cam.ac.uk/~nickl/Site/_.html

This is statistics though, but the point I'm making is that there are applied areas of research that use things that relate to the same things like QM, but are in a different context and focus which you might want to keep in the back of your mind.

Try a search like this

 

[cragar]

im fine with it being pure math. I just said applied math because I thought that it was more close to physics. Thanks for you help on how to search for those topics.

 

[deRham]

Probably the reason it's hard to make a distinction is that applied mathematics is usually studying "the mathematics of X" where X is some discipline that uses mathematics. And thus, mathematical physics might fit this description, yet the already theoretical nature of theoretical physics might make the field seem significantly more like pure mathematics than other things in so-called applied mathematics.

I tend not to distinguish between the terms pure and applied mathematics for these sorts of reasons, but certainly sometimes it can help someone to have the distinction in words.