What sort of mathematics for mathematical physics?

AI Thread Summary
In pursuing mathematical or theoretical physics, a strong foundation in mathematics is essential, with a recommendation to focus more on math courses than physics. The discussion highlights the dilemma between specializing in algebra or analysis, with varying opinions on their relevance. Analysis is generally considered more useful, especially for advanced topics in physics like Quantum Mechanics, while algebra also plays a significant role, particularly in areas like linear algebra and functional analysis. Ultimately, the choice should align with personal interest and aptitude, as both fields are interconnected and beneficial for a comprehensive understanding of physics. It is emphasized that a solid grasp of both algebra and analysis is necessary for advanced studies, with specific areas like differential geometry and lie algebra being particularly relevant in mathematical physics.
mitcho
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I am hoping to do mathematical or theoretical physics after my undergraduate science degree. I have been advised to do more maths subjects than physics subjects in order to achieve this. I am double majoring in maths and physics and I am just wondering what area of maths I should be focusing on more. my concern is that I want to leave the door for pure maths open. This means I have the choice of algebra or analysis... Does anyone have any advice on which is more useful in modern mathematical/theoretical physics?
Thanks
 
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mitcho said:
I am hoping to do mathematical or theoretical physics after my undergraduate science degree. I have been advised to do more maths subjects than physics subjects in order to achieve this. I am double majoring in maths and physics and I am just wondering what area of maths I should be focusing on more. my concern is that I want to leave the door for pure maths open. This means I have the choice of algebra or analysis... Does anyone have any advice on which is more useful in modern mathematical/theoretical physics?
Thanks

How the hell would we be able to answer this?

I can think of 30 reasons for why you should pick either one. I suppose it will come down to what you are best at. If you hate analysis and that scares you then drop it.

Personally algebra would be less use if you want to go into Quantum Mechanics. Even then do Matrix analysis or advanced linear algebra stuff if you can. Analysis overall is probably more useful. Saying that decide which you are at best at or what interests you and then do that. Don't be thinking that it won't be use later on or something is more useful.

Problems usually have multiple ways to attack it. Which, makes your choices not important.
 
If you can only pick one of the two, Analysis or Algebra you should pick the one that you think you'll enjoy more.

P.S
You'll need to know both at least as far as Bsc studies goes in order to procceed to advanced studies.

I have taken courses in Functional Analysis and Differential Geometry, there are always algebraic structures luring there.
(be it Ideals in FA or tensors in DG).
 
You will probably find analysis, geometry, and linear algebra most useful for a long time. You should learn some algebra eventually too, however. For much of classroom-based physics, your instructor will introduce ideas as necessary.
 
you need lie algebra for mathematical physics.
 

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