Frustated by the lack of mathematical rigour in physics topics

[Theorem.]

Go for it! Who knows, maybe you'll switch back to physics :p

Haha I doubt that I really love the stuff I am working on : ) but it could never hurt to learn

 

[George Jones]

How important is rigor in undergraduate learning?

Using rigourous mathematics to teach physics courses in: quantum mechanics would be insane; quantum field theory would be impossible.

Should it be emphasized more?

Possibly a little more; also more formality. For example, Dirac's quantum mechanics book is formal, but is not rigourous

why aren't there more accessible undergraduate textbooks that share the same level of rigor as is taught in undergraduate mathematics?

Because, while physics uses mathematics, physics isn't mathematics.

Adding in the rigorous math might make some things more lucid but it is a HUGE time consuming task to teach rigorous math to undergraduate physics students on top of the (more important) physics that has to be taught. Of course this has never stopped physics students who want a rigorous math background from taking rigorous math classes regardless.

Yes.

To understand the rigourous mathematics in such textbooks, physics students might have to take more pure mathematics than they want to, i.e., they are physics students, and have to take loads of physics courses. Either that, or develop the rigourous mathematics in the physics texts, in which case there would not be room in the book or time in course to cover the physics material that a typical physics department wants included in a typical physics course.

Don't get me wrong; I think such physics texts are both useful and interesting, but I don't think that they should be used as texts for standard physics courses.

I recall taking E&M and having my prof "teach" vector calculus in 2 days, no student had yet been exposed to the topic and the result was horrible.

I agree. Unfortunately, this happens all too often.

It wasn't until I actually took the mathematics that developed vector calculus that I was able to reflect on what had really happened. Unfortunately most other students that took the class with me are still puzzled.

Don't physics student have to take vector calculus (eventually)? If so, why did they remain puzzled?

 

[Theorem.]

Because, while physics uses mathematics, physics isn't mathematics.

I agree with you here up to a certain extent. In many instances understanding the mathematics can go hand in hand with understanding the physics. This can, at least in some cases, involve the development of the maths itself. I know that going through rigorous development really helped me understand what was actually going on in the math used, and consequentially the physics. Although, I am not saying that this should make rigour mandatory- simply stressing that it can have huge advantages (and as it has been mentioned, there are also some big negatives).

Don't physics student have to take vector calculus (eventually)? If so, why did they remain puzzled?

Yes I believe so, but I think by the time it was done much of the essence of the course was lost. It was definitely an odd ordering. Quite unfortunate! Part of that is, of course, the students responsibility.