Maths required for studying intermediate to advance physics

[henry407]

Thanks for all your guys reply. Actually, I am now more confused after the last bit of the discussion..... But, indeed, this is a question without a conclusive answer. So, I'd like to ask the following: sometimes I found the proof in topic of metric space is redundant and unnecessary; the result itself is intuitive and "obvious"( especially those about A map to B and bahbahbah property remains the same). In this case, is this a "good" habit for physicist to ignore the "minor" details of the vigorous proof or a harmful habit which will cause me losing some important knowledge for my future career? Thanks for everyone's contribution to this post !

 

[WannabeNewton]

Most of the time results are not intuitive. So you can either take things for granted and just focus on the physics or take a detour to understand the result more rigorously. It is up to you really. It is a matter of time vs. satisfaction. It doesn't hurt to look at things more rigorously from time to time but if you focus on it too much then you won't get anywhere. It also depends heavily on the subject at hand. If youre learning GR then it doesn't take much time to verify results rigorously because the necessary math is very easy at the learning stage. But if youre learning QFT then you would basically have no choice but to accept all the hand-waving and rug sweeping.

Coming back to the topic at hand, most of the necessary math for a basic foundation in physics you will learn naturally as an undergrad. The only extra stuff which will be absolutely necessary in GR, QFT, EM etc. that you might not be forced to learn as an undergrad and which are usually not taught well in the classes themselves are methods of contour integration and residues, Green's functions, and the physicsts' level of representation theory of Lie groups. If you get that stuff down you'll be just fine. The physics is infinitely more fun than the math so just focus on that and learn what you need as you go along.

 

[porcupine137]

Coming back to the topic at hand, most of the necessary math for a basic foundation in physics you will learn naturally as an undergrad. The only extra stuff which will be absolutely necessary in GR, QFT, EM etc. that you might not be forced to learn as an undergrad and which are usually not taught well in the classes themselves are methods of contour integration and residues, Green's functions,

Sometimes the math department Complex Variable classes do OK by contour integration, residues, analytic continuation, conformal transformations.

 

[porcupine137]

One thing I should also add is that in the more advanced topics of physics like field theory and such that a lot of the stuff, I believe has actually never been rigorously proven yet by anyone in pure math terms so if you try to build it up in pure math terms at a certain level you may find yourself VERY bogged down . If you tried to do that you'd have found yourself left decades behind the guys making all the radical advancements in physics.

 

[WannabeNewton]

Sometimes the math department Complex Variable classes do OK by contour integration, residues, analytic continuation, conformal transformations.

Hi porcupine! I should have been clearer. I meant that said topics are not taught properly in the physics courses in which they predominantly appear.