What Should I Study to Prepare for Theoretical Physics?

AI Thread Summary
The discussion centers on a junior-level physics student seeking guidance on preparing for graduate studies in theoretical physics. The student expresses a strong preference for theoretical over experimental physics and aims to transition into applied mathematics after graduation. However, they feel unprepared for grad school, lacking direction in their self-study efforts. The student has completed foundational math courses but has not yet tackled advanced topics like analysis, algebra, or complex analysis. They find available resources inadequate, with many books lacking exercises or solutions, and express frustration over unhelpful responses from theorists they've consulted. A link to a resource from Nobel laureate Gerard 't Hooft is shared, offering advice for self-study in theoretical physics, although the student is primarily seeking structured guidance on where to begin their studies. Overall, the student feels overwhelmed and lost, despite having the motivation and discipline to succeed.
ice109
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yes i know there's one right beneath me, and i actually posted in it but my question is a little different than that poster's. I'm actually a physics student at a university at around the junior level and i want to pursue theoretical physics. now i know everyone says this because it sounds so swanky but I've gotten a taste of experimental and i wholly dislike it. anyway after school i'd like to go to industry doing applied math and i figure a theoretical/computational physics background will be the most well rounded where as in applied math i would study just PDEs or SDEs or something like that. plus being a professor some day would be quite enjoyable.

the problem I'm faced with now is that I'm graduating next year tentatively and there's no way i'll be prepared for grad school by then. I'm going to try to push it back another year but barring that there's absolutely no way my classes will prepare me in time. so i'd like to study on my own but I'm having lots of problems.

firstly i have no idea what i should be studying, math wise. I'm halfway through boas' math methods book but i can already tell that will only do exactly what it says, prepare me for undergrad material. there a tiny section on group theory, nothing on differential geometry, nothing on topology etc. secondly most of the books i can grab from the library are , in my opinion, pedagogically flawed. a lot of them are pure math books with no exercises and the ones with proof exercises do not have solutions. i can do proofs but i don't think they teach me how to use tools, only when i can and can't use them. maybe my impression is biased and I'm wrong, I've only done proofs in very elementary classes pure math classes. maybe in the upper level classes you're actually constructing things instead of testing implications.

i just don't know. i would love for someone to give me some advice and what i should be studying and how. note my advisor is an experimentalist, and the theorists I've spoken with have been quite unreceptive. you can consider me at the level of someone who has completed the usual calc sequence, differential eqns and linear algebra and i can write proofs. I'm just finishing a topology class right now but it was terrible and we learned almost nothing. so i haven't had analysis, or algebra, or complex analysis. pdes I'm going to cover on my own within th
i just don't know. i would love for someone to give me some advice and what i should be studying and how. note my advisor is an experimentalist, and the theorists I've spoken with have been quite unreceptive. you can consider me at the level of someone who has completed the usual calc sequence, differential eqns and linear algebra and i can write proofs. I'm just finishing a topology class right now but it was terrible and we learned almost nothing. so i haven't had analysis, or algebra, or complex analysis. pdes I'm going to cover on my own with the month. e month.

honestly, and this is a cry for pity to someone, i feel completely lost and overwhelmed and on the verge of completely failing. i have the desire and even the discipline just no direction.
 
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Here is a link to a page from Nobel laureate t' Hooft: Some advice for studying theoretical physics on your own and LOTS of links to free online ressources. maybe too much stuff for your current situation - if I understand you correctly, you need direction about where to start, but have a look at it anyway.

http://www.phys.uu.nl/~thooft/theorist.html

EDIT: It's sad that the theorists you talked to have not been receptive, I mean isn't it part of their job to give advice to students ? Perhaps you could tell a bit more about what they said to you, maybe they didn't quite get what you wanted to ask them ?
 
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ice109 said:
i'm just finishing a topology class right now but it was terrible and we learned almost nothing. so i haven't had analysis, or algebra, or complex analysis. pdes I'm going to cover on my own within th
You learned nothing new in a topology class? That sounds rather amazing.
 
Defennder said:
You learned nothing new in a topology class? That sounds rather amazing.

it was an exaggeration.

no actually its was a hyperbolic for : it was a ridiculously elementary class
 
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Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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