Pathway for theoretical physics

In summary, the conversation is about the speaker's plan to go to grad school in theoretical physics and the different pathways they are considering to strengthen their mathematical skills. The speaker is concerned about not having a strong enough math background and potentially having to take extra courses or spend a lot of time studying. However, the other person reassures them that their current math background is sufficient for most grad programs and they can always pick up additional math skills along the way. They also suggest a few advanced topics that may be helpful for certain areas of theoretical physics.
  • #1
cesaruelas
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I want to go to grad. school in theoretical physics after I'm done with undergrad (aiming quite high: Perimeter Institue, Cambridge's DAMTP, MIT, etc. I know it's hard but I want to keep optimistic about it). Which pathway would be more appropiate/realistic?

route 1: I self study math courses online from mit ocw or something like that with, possibly, help from a professor who would encourage me and help me out every now and then or on my own and asking questions online etc. (we don't have a math undergrad program so, even though there is a math department, the courses stop at linear algebra/partial diff. eqs. and the rest is primarily external industry research) I have my mind on analysis 1 (both the one with proof introduction and then the other one), analysis 2, algebra 1, differential geometry, Fourier analysis and introduction to functional analysis (from the mit ocw page, that is: http://ocw.mit.edu/courses/mathematics/).

route 2: I self study one or several mathematical physics book (I can get my hands on hassani, byron & fuller, morse & feshbach, courant & hilbert, that sort of books). I'm guessing a professor from the physics department would be more willing to help me out on this one, probably.

route 3: I stop worrying about it and stick to my curriculum (we cover practically all of arfken and of boas over the course of a year except for probability and other chapters that we should already know).

I just don't want to go to grad school and have to take "catching-up" courses or simply have to study a relatively HUGE amount of time because I don't know my maths.

Some background: I'm an engineering physics major, sophomore year, taking math methods 1 this semester (covering Fourier analysis, tensor analysis, series solutions of ode's, pde's and calculus of variations (not necessarily in that order )). Will cover functions of a complex variable, special functions, basic group theory, and basic operator theory next semester. I've already taken calculus 1-3, ode's, and linear algebra.

There is also the concern that I'll burn out after a while or, even worse, just as I'm off to grad school. I also work 20 hours a week, I'm involved in a research project, help out rural high school kids through an online program and do amateur triathlon training (I could cut the triathlon and stop working but I'd rather not if possible).

Opinions? Experiences? Advice?

Thank you.
 
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  • #2
cesaruelas said:
I just don't want to go to grad school and have to take "catching-up" courses or simply have to study a relatively HUGE amount of time because I don't know my maths.

This is probably not going to happen. If you're smart enough to get into a top tier physics grad program for theory, you can probably pick up any maths you need along the way quite quickly. But realistically, what you need is not far beyond the standard undergrad math curriculum. The only real example where you might want to study an extra book would be something like Nakahara's text "Geometry, Topology, And Physics" if you were planning on taking a serious crack at string theory. Otherwise, the advanced topics like group theory, Fourier analysis, algebra, and even differential geometry are covered along with physics material with a strong emphasis on what is relevant to the physicist.
 

1. What is theoretical physics?

Theoretical physics is a branch of physics that deals with the development of mathematical models and theories to explain and predict physical phenomena. It is concerned with understanding the fundamental laws and principles that govern the behavior of the universe at the smallest and largest scales.

2. What are some common career paths for theoretical physicists?

Theoretical physicists can pursue careers in academia, research institutions, government agencies, and private companies. They can work as university professors, researchers, consultants, or science writers. Some also choose to work in interdisciplinary fields such as engineering, computer science, or finance.

3. What skills are necessary to become a successful theoretical physicist?

Successful theoretical physicists possess strong analytical and mathematical skills, creativity, critical thinking, and problem-solving abilities. They also need to have a deep understanding of physics concepts and theories, as well as proficiency in programming and data analysis.

4. How do theoretical physicists conduct research?

Theoretical physicists use a combination of mathematical tools, computer simulations, and experiments to develop and test their theories. They use mathematical equations and models to make predictions about physical phenomena and compare them to experimental data to validate or refine their theories.

5. What are some current areas of research in theoretical physics?

Some current areas of research in theoretical physics include quantum mechanics, general relativity, cosmology, particle physics, and condensed matter physics. Other emerging fields include quantum computing, string theory, and computational physics.

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