Math for Theoretical Physics: Undergrad Pursuit, Rigor & Proofs

[glueball8]

What types of mathematics is needed for a undergrad pursue theoretical physics? How rigorous does it have to be and how much proofs is there?

 

[flyingpig]

My advice is, do not take what is just NEEDED, take what you feel is NEEDED.

 

[Klockan3]

It is really hard to study too much maths, study as much of it as you can without compromising your selection of physics courses. Abstract algebra, functional analysis and differential geometry are examples of maths that are used a lot in higher end physics. But every ounce of maths is good even though you might not use all of it in your actual physics but it helps you understand better what things are.

 

[MathematicalPhysicist]

"How much math should a theoretical physicist know?
More!"

[:-D]

 

[kakarotyjn]

as much as you can,i think

 

[glueball8]

How rigorous does the mathematics has to be? I'm trying to decide if I should take a very rigorous math course or a course that has less proofs but learn basically the same material. (Less proofs course might has more application based problems.)

 

[Dr Transport]

less rigor the better in my opinion for a theoretician working outside of string theory...

 

[glueball8]

less rigor the better in my opinion for a theoretician working outside of string theory...

why is that?

 

[Nabeshin]

In my opinion, as long as you can handle it, the more rigor the better.

 

[Klockan3]

In my opinion, as long as you can handle it, the more rigor the better.

This, you get enough of the non rigorous stuff when you study physics. Of course it is easier to do courses that just do the computational parts but that would be just to make the physics courses easier rather than learning anything in itself.

 

[Landau]

If you learn your math too rigorously, you'll end up being frustrated with your physics teachers and depressed by physics textbooks ;)

 

[Klockan3]

If you learn your math too rigorously, you'll end up being frustrated with your physics teachers and depressed by physics textbooks ;)

Nah, only if you start loving the rigorous side of maths too much, but then what are you doing in physics?

 

[Landau]

Yeah, that's why I probably won't continue with physics next year.

 

[MathematicalPhysicist]

If you learn your math too rigorously, you'll end up being frustrated with your physics teachers and depressed by physics textbooks ;)

It depends which books you are using, most of the physics textbooks prefer physical intuition
over mathematical rigoursness and they will include experimental data and appratus, because physics is an empirical science, obviously.

 

[WhoWee]

It depends which books you are using, most of the physics textbooks prefer physical intuition
over mathematical rigoursness and they will include experimental data and appratus, because physics is an empirical science, obviously.

Obviously!

 

[wengsee]

I am poor in mathematics .Can I study applied physics well?And what should I do first?

 

[Monocles]

Do you mean pursue research in theoretical physics as an undergrad?

You may be surprised to know that you don't need to know that much, especially if you want to do computational work. I have several undergraduate friends working in computational astrophysics that haven't taken any math beyond differential equations.

However, if you want to work in something more analytical, that may not be enough. I'm an undergrad working in mathematical physics, and I've had to learn a decent amount of abstract algebra, topology, algebraic topology, and differential geometry to even get to the point that I was able to start reading papers. However, that doesn't mean you need to TAKE all of these classes - math classes are more rigorous than you need to start getting your hands dirty. The only one of those classes I've taken is abstract algebra, I've just picked up everything else as I've went along from one of the many texts on math for physicists. I'm a double major in math, so I'll be taking them all eventually, but the point is that you don't have to sit around taking math classes for 2 years before you ask a professor to advise you.

 

[kuahji]

In my opinion, as long as you can handle it, the more rigor the better.

I have to agree with this. However, most people can only take so much of it...

 

[glueball8]

In my school there's Specialist, Major or Minor. I'm doing physics specialist for sure, I'm not sure if I should do a Math Specialist or Major. I want to be basically prepared for nearly any math that is within theoretical physics.

For most schools does people need a double major (physics and math) to do quite math based theoretical physics(like string theory I guess)?