Theoretical mathmatics for physics phd

[strings235]

hey everyone,

If I plan to pursue a physics phd in quantum theory/string theory do you recommend I get a B.S. in theoretical mathematics as well (with linear pde, Fourier anal, and topology, etc.)?

I'm still not sure whether applied or theoretical math is the better choice.

 

[cristo]

Well, it depends upon what specific courses you will be taking in each degree-- for example, in applied, you may be able to take many of the courses you can in theoretical. I'm not really sure what the content of a "theoretical mathematics" course would be though.

 

[ice109]

jesus christ there's like 5 of these threads already in here

 

[cristo]

jesus christ there's like 5 of these threads already in here

Yea, I thought that. It seems that there are a lot of people keen to become theoretical physicists at the moment.

 

[strings235]

well there actually are categories. I was thinking about discrete mathematics, numerical analysis, dynamical systems, etc. But there are many connections between physics and both applied and theoretical math so I was thinking of taking individual courses and not taking a whole major where I might be studying unnecessary courses.

So are there any specific courses that are needed, useful, or desirable in the fields I mentioned?

 

[cristo]

Well, I presume the first few years of each degree are pretty much the same; i.e. analysis, calculus, algebra, differential equations, linear algebra, basic probability. You could then look into a course in PDE's, complex analysis. Now, if you really want to do a PhD in quantum gravity (let's not call it string theory, since no one knows what will happen in the next few years!) you'll need to know quantum field theory and general relativity. The former requires quantum theory and special relativity, of which the main mathematical techniques you will need to know are linear algebra and differential equations. The latter requires mathematical knowledge of differential geometry and tensor calculus.

I would suggest that you talk to the admissions tutor at the establishemtn where you wish to undertake study and find out, firstly, the difference between the degrees, and secondly, which would be preferential for you selected PhD route.

 

[strings235]

thanks. and I was wondering if mathematics can aid in conceptual thought for research. essentially coming up with new ideas in physics through mathematics.

 

[ice109]

thanks. and I was wondering if mathematics can aid in conceptual thought for research. essentially coming up with new ideas in physics through mathematics.

that it will not do

 

[cristo]

thanks. and I was wondering if mathematics can aid in conceptual thought for research. essentially coming up with new ideas in physics through mathematics.

I wouldn't say that you would be able to "come up with new ideas in physics" using solely mathematics (although, of course, it depends what you mean by "mathematics"-- I learned quantum theory and GR as part of my undergrad maths degree). However, a firm grounding in mathematics is imperative. That's why the researchers in these fields are both strong mathematicians, but have a thorough knowledge of the relevant physics also.