Would pure mathematics benefit an undergrad physics student?

[u/Novel_Variation495]

Hey, everyone.
I thought about studying a textbook called "An Infinite Descent into Pure Mathematics by Clive Newstead" as I'm really into abstract math and thinking about learning coding as a skill for the future. But I think I'm wasting my time because it seems really hard to follow and requires a lot of discipline.

What do you think?

[u/InsuranceSad1754]

You can get a PhD in physics (theoretical, experimental, doesn't matter) without an undergrad math degree.

You also can double major in math and physics -- it is very hard and not required, but you can do it if you are super motivated and find both interesting.

So is it "useful?" Well, especially if you do more theoretical physics, learning more math will provide a more solid foundation for the math you need, so sure that can be useful. But often physicists are more interested in calculating or approximating what happens in specific examples and less interested in generality and formal proof, so the two fields are not the same and you will need to appreciate that you need to think about math problems and physics problems differently.

I think it is less a matter of whether it is "useful" but whether the tradeoff you will make to spend time and effort you could use for other things on pure math is worth it for you. No one can answer that question for you. We can only give you pros and cons and you have to decide what you want to do.

[u/SoSweetAndTasty]

You could take an introductory proofs course and see how much you like it. It'll be easier than reading a textbook and knowing how proofs work can be extremely helpful.

[u/Novel_Variation495 → u/SoSweetAndTasty]

That's actually a really good idea! Thank you!

[u/Interesting_Hyena805]

As long as you take a series of very rigorous linear algebra courses, and some real and complex analysis throughout your degree, these should give you the mathematical maturity to be able to start understanding some more advanced topics in pure math. For example, I’d never done pure math unit taught by the math department, but I have now done two pure math units taught by the physics department, namely Group & Representation Theory and Differential Geometry. If i didnt have such a rigorous linear algebra and analysis background I would have been absolutely screwed

[u/TheBacon240 → u/Interesting_Hyena805]

Its very funny how a lot of these "(insert math topic) for physicists" actually lowkey require a math background thats not a given for physics majors/even some masters programs.

[u/Interesting_Hyena805 → u/TheBacon240]

yeah at first i started trying to use textbooks more catered ‘to physicists’ but they just slap you with definitions that you dont have the background to understand, dont prove any theorems, and then go into complicated stuff.

In my differential geometry course I’ve just starting using Tu’s Introduction to Manifolds and its been a game-changer.