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A few years ago finished a physics degree and one of the biggest lessons I learned is that I need to spend some extra time on pure Maths. In fact I almost wish I done a maths degree first as that would have made the physics more fun as I kinda felt that the equations being fed to me where not my first language.

So now I'm wanting to go back and really get stronger at Maths and really get to grips with it. What would be my best course of action? I don't have the desire to enrol in any course.

Part of my motivation is to go on and explore some of the more theoretical side of physics being much more comfortable with the maths. Reading some of the questions on this site makes me realise how much I need to improve to enjoy this wonderful subject.

Many thanks for your advice!

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Mathematical physics is rather broad. Can you at least try to narrow down what you're interested in? For example if you say you're interested in electrodynamics then maybe picking up a book on PDE's is the way to go. –  Alex R. Dec 13 '12 at 23:11
    
Hi Alex! My greatest interest is in Cosmology/Astronomy and Quantum physics. –  Nikos Dec 13 '12 at 23:12
    
Something like Wald's General Relativity would be a good start for learning "rigorous" general relativity. –  Alex R. Dec 13 '12 at 23:31
    
so as I have more time, I could brush up on each area of maths being used in the area of physics in more detail rather than do maths for the sake of maths? –  Nikos Dec 13 '12 at 23:39

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I think you should certainly improve proofing skills and I listed some books on the matter: how to be good at proving?

If you look at the MSC (Mathematical Subject Classification), it imposes some sort of organization in a fairly standard scheme for mathematics. See: How many classification of mathematical topics exists?

This will let you see areas in mathematics for consideration.

I would also think you need to figure which topics would be most helpful and the order for learning those for your specialty in Physics. I would recommend looking at graduate physics programs and seeing which courses they require based on the physics specialty. For example, at Harvard: http://www.physics.harvard.edu/academics/grad/requir.html

Lastly, there is also the Open Course Ware and many universities partake by putting lectures and notes online for free. See http://en.wikipedia.org/wiki/OpenCourseWare

You can audit classes and see if anything floats your boat.

Hope that gives you some items for consideration!

Regards -A

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Ok, thanks Amzoti sounds like good stuff to investigate. –  Nikos Dec 14 '12 at 18:11
    
Great feedback to a great answer! +1 –  amWhy May 14 '13 at 0:50

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