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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