Level of mathematical rigor needed for physics

[IAmLoco]

How much mathematical rigor do you need to have good understanding of physics? My professor for multivar calc this year isn't really that good(that or I'm not good enough to keep up) so I've resorted to reading and working through Stewart on my own and I'm wondering if that's enough since Stewart gets so much criticism for lack of rigor and thoroughness, should I get something like Spivak?

I don't think I'll end up in theoretical physics even though I want to but I still want to study and understand physics on a more theoretical level so I want to make sure I'm well equipped in the math department.

Sorry if this is post actually belongs somewhere else, I'm still getting myself familiar with the forum.

 

[Orodruin]

This is very dependent on the meaning you put into the phrase ”good understanding of physics”.

 

[IAmLoco]

This is very dependent on the meaning you put into the phrase ”good understanding of physics”.

After thinking about it maybe I should have asked this instead: how much mathematical rigor do you need in theoretical physics. I think I'm simply worried about whether the text I'm using for calculus right now will prepare me well for theoretical physics.If that's still too general of a question maybe my worry is misguided or I need to think about what I want/need a bit more.

 

[gmax137]

I don't think there is anything wrong with first learning how to do calculus - solving rate problems etc. and then later on learning why it really works. In other words, practical application followed by more rigor. In fact that's a pretty normal progression.

 

[RPinPA]

Conversation I had with a colleague, a mathematician, early in my career. I went to him trying to understand a rather math-heavy book on Fourier Theory I was reading.

Him: Have you ever had a math course? I teach a course on Real Analysis at the night school.
Me: I did undergrad and graduate work in physics. I've had the standard calculus, mathematical physics, probability and statistics (listed a few more)...
Him: You've never had a math course. Take my course.

He was right. That kind of rigorous thinking (and Real Analysis was a good place to start with it) was not part of my physics education. Now, I did not pursue a heavy theoretical route, but I don't think anybody I knew who did took very many graduate courses in the math department. They got the math they needed in their physics courses, and it was "just rigorous enough".

Still, if you want to see what rigorous proof looks like and get used to a totally different mode of thinking, I'd recommend taking an Analysis course.