Is Formal Math Necessary for Physics Success?

[cochemuacos]

hi everyone, I am not sure if this is the right place to ask you guys for your opinios, any way. I am a freshman in college and my calculus course is a very formal one, i mean we do all this things with deltas and episilon proofs and definitions, i enjoy it, but i was wondering if it has any usefulness in physics. I am not talking about usefulness of calculus of course, I am talking more about the rigorous side of it, is it really necessary to learn all that as a physicist?

 

[paulfr]

Depends on how good of a Physicist you want to be.

 

[dextercioby]

You may need to understand the formal proofs in functional analysis, if you wish to get behind the mathematics of quantum physics (quantum mechanics or rigorous quantum field theory).

You shoud keep these proofs for reference, because, in my perspective, there's nothing worse to see in a physics book than: <one knows from mathematics that non-compact Lie groups don't have any finite dimensional linear representations, other than the trivial one>.

 

[Avatrin]

Yes... Calculus is the math of change, and mechanics are entirely about change:
Speed is the change in position. Acceleration is the change in speed.

Thus, mechanics, both classical and quantum, have the same basic framework as calculus. Therefore, they also share definitions and theorems.

You will encounter practical calculus problems early on (especially differential equations). Newtons laws are based on calculus, and thus, you will not have to wait for quantum physics before calculus problems show up.

 

[HallsofIvy]

Of course, you could apply Calculus formulas without knowing all that "epsilon- delta" stuff! But paulfr's "Depends on how good of a Physicist you want to be." is very relevant. The best physicists will need to use mathematics in new and different ways (as, for example, Riemann surfaces in relativity and group theory in quantum mechanics). In order to do that, you have to know the basic theories very well so you will know if what you are doing is still valid or if how you can alter the theories to do what you want.