Teaching yourself modern physics

AI Thread Summary
A software engineer expresses a desire to self-study modern physics and recognizes the need for a strong mathematical foundation. They are comfortable with calculus and linear algebra but seek guidance on additional mathematical topics essential for a deeper understanding of physics. Key mathematical areas mentioned include vector calculus, differential geometry, matrices, group theory, real analysis, complex analysis, and probability and statistics, emphasizing that a physicist's knowledge of mathematics is crucial for their work. A helpful resource link is shared to aid in their studies.
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Hello everyone,

I am a software engineer by profession. However, I would love to teach myself Physics and would like to gain a deeper understanding of modern physics. I know it is quit a daunting tasks but I am determined to make it happen, even if it takes a few many years!

I understand that I will need to build a very extensive mathematical foundation for this. I am pretty comfortable with calculus, linear algebra but am not a Mathematician and would probably struggle (on very good days!) with some of the math involved.

So, my question to you guys is, what are the mathematical topics that one should be comfortable with before trying to study physics in some depth? What is the progression of the Mathematical topics that I should cover?

Thanks,

Luca
 
Physics news on Phys.org
Hi Luca, welcome to PF.

Calculus of course is a main one. Vector calculus, differential geometry, matrices, group theory, real analysis, complex analysis, probability and statistics.. the list goes on.
A physicist can never know enough mathematics, mathematics is like a physicists toolbox.

edit : Just found this, http://www.superstringtheory.com/math/math1.html
 
Great! Thanks for that link. Time to get cracking then :)

Luca
 
No problem!
Good luck! :wink:
 
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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