Neccessary Math before going for a PhD

[Thinker301]

Hello everyone,

How much math should I know like the back of my hand before I go to grad school, so that I am not barred from a field because I don't know enough math.

I am not sure what field of physics I want to go into. I will probably be in theory though. (I am doing research in theory right now and really enjoying it, but I am planning to do an reu in experiment because when else will I have the time)

Thanks

 

[Dr. Courtney]

Algebra and trig (high school). Calc 1, 2, and 3. Diff Eq.

These all need to be mastered. Depending on what field, you may need to master other aspects of undergrad math also.

 

[Thinker301]

Awesome, I have got those down. Say I want to go into HEP/CondensedMatter/Astro/Nuclear (all theory)?

 

[Dishsoap]

Also linear algebra.

 

[Thinker301]

I am learning that now! It's rather interesting!

What about Real Analysis, Complex Analysis, Abstract Algebra, Lie Theory, Differential Geometry, Calculus of Variations,etc?

 

[Student100]

I am learning that now! It's rather interesting!

What about Real Analysis, Complex Analysis, Abstract Algebra, Lie Theory, Differential Geometry, Calculus of Variations,etc?

Work through Mary boas book. Then in graduate school take a mathematical methods course. That will introduce you to many topics that are applicable to your physics study. Once you've started research in a particular field, you can pick up what else you need to know. It can depend on many things, and the fields you've listed are quite different in terms of mathematics.

 

[radium]

For CMT it is highly dependent on the specific area but based on recent topics of interest, I would say topology, continuous and discrete groups, representation theory/projective representations, complex analysis, asymptotic methods (stationary phase, saddle point approximations), differential geometry especially in the context of holography.