Hello all. So, let me explain my situation. Originally, I signed up for an Engineering major, figuring it was what I should do, since I liked math. So, I signed up for my classes, and it was all good. However, a lot of things happened over the summer. Things that've changed my views on the matter. I've realized now that trying to appeal to my love for math through Engineering was not smart and that I should change now while I can. Luckily, most of the classes are similar, so I only had to drop two classes (I was doing a double major so I had the math classes in already). Currently, I have credit for Calc 1 and 2. I feel I have a strong base in these two from math competitions and the likes. However, I also understand that REAL Calculus it's not something you really learn from a book like Stewart, so I've been reading up Spivak's "Calculus" in order to reinforce my Calculus knowledge. Currently, I'm signed up for Calculus III offered by the school's Engineering department. It's very technology based (lot of Mathematica) using the book "Vector Calculus" by Tromba and Marsden. I know the text is slightly more rigorous than others, but I still feel the class won't be as rigorous as I need it to be. Now, at my school, there is an honors track, but within the honors, they also have a side-track for Multivariable, a very rigorous treatment. Now, currently, I got screwed over through my application and didn't make it into honors college. However, I found out that you can sign up for honors classes if you obtain permission. For this particular class, however, you also need permission from the department as it requires "mathematical talent". In a sense, this worries me since my proof skills are a bit weak, and my exposure to rigorous math only goes as far as I've gotten in Spivak and some studying for things like the AMC or Mu Alpha Theta. And I don't want to go jump over multiple loops to obtain such a hard permission only to get owned and get a C. I checked the book used by the class. It is "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach" by Hubbard. This text itself was recommended to me if I wanted to pick up a more rigorous treatment of Multivariable, so the fact that it is the text for the class makes it seem perfect. So, I suppose the question is, should I try to get the permission and take the class? Should I just stick with what I have? Or should I take what I have currently and maybe switch later? The last option seems good since it'd give me time to prove I have the "mathematical talent" (if I have it), but I don't know if I'd miss too much by the time I got in already. So, what should I do?