Will Physics Proofs Prepare Me for Math Proofs?

[Jack21222]

Math proofs vs physics "proofs"

I'm a senior level physics major interested in taking a 400-level class in the math department for which I do not meet a prereq for (Graph Theory requires Intro to Abstract Math). I emailed the professor, and he stressed to me that a very important part of the class is doing math proofs, and that a physics major might not have the "mathematical sophistication" necessary to do well.

Now, I have seen a lot of derivations in my upper level physics classes, but I have no idea how they compare to math proofs, or if they're even close to the same thing.

For those that have taken both upper level physics and upper level math classes, will any of the skills translate from physics to math? Will the class be completely alien to me, or will I have a chance to understand it with some hard work?

 

[nonequilibrium]

What math classes have you taken so far?

 

[Jorriss]

A lot of proofs in a quantum mechanics class are akin to the proofs in a math course but it's not the same. The language and attitude is vastly different. I wouldn't recommend it myself.

 

[Jack21222]

What math classes have you taken so far?

Calc 1-3, elementary linear algebra, probability theory, and I'll be taking an advanced calc class at the same time (fourier analysis).

 

[homeomorphic]

Why not just look at a math book and see if you understand it?

You can find Diestel's graph theory book online, for example. Just google it. It doesn't really have many prerequisites, other than some comfort level with proofs and maybe some really basic set theory.

It's better to start doing proofs in a more gentle environment, rather than just jumping in, which is the reason for the "intro to abstract math" class. A lot of people, even those who are successful at other somewhat mathematical majors, find it pretty difficult. It's just hard to predict what will happen. I imagine some people could jump right in and feel right at home. To some extent, that's what happened to me, and that's why I changed majors to math pretty quickly after I took real analysis.

I switched majors from EE to math and the EE experience did help a lot, I think, mainly just with understanding the ideas intuitively, which allowed me to come up with the proofs. That's the main thing. But if you're not used to doing proofs, it could take some getting used to.

Some math classes are taught in sort of an intimidating way, but more so if it's graduate level or an honors class. The fact that he is warning you could be an indication that it might be taught that way, but on the other, it's an undergraduate class.

 

[Jack21222]

I met with the professor of the class today. He showed me the book that is being used as well as last year's copy of the first exam. None of it looked intimidating at all. 70% of the exam is definition stuff and computation, and the other 30% is proofs. But, only 10% of the exam in the "proofs" section is a hardcore abstract proof, the other are more like "show that if..."

Furthermore, the only proofs he puts on his exam are ones that are seen either in the problem sets or done in class, and before the exam, he tells us which proofs we'll need to know how to do.

I'm very optimistic about this class.

 

[genericusrnme]

The main difference you'll see between the two are
Physics proofs - Intuition and handwaving
Maths proofs - Rigor and sets

Combine the two and you'll get some intuitive, rigorous, setty crossover called mathematical physics