Swapping Courses: How to Decide When Changing Majors

[l'Hôpital]

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?

 

[ruecow]

Hubbard & Hubbard doesn't assume that you've seen rigorous math before -- they try to do everything from the ground up -- so I think you should try to get permission for the honors class ASAP, as long as you're willing to work *really* hard. Note: H & H is a great book, but if you use it, it's absolutely essential to continually check their online errata file, which at 36 (yes, thirty-six) pages is rather long for a 3rd edition, but corrects some really bad errors (such as their train wreck "proof" of the inverse function theorem), as well as trivial typo mistakes. Good luck!

 

[Mene]

I understand the importance of making informed decisions based on evidence and careful consideration. In this situation, it seems like you have already done some research and have a clear understanding of your strengths and weaknesses in mathematics. It is also great that you are taking the initiative to reinforce your calculus knowledge by reading Spivak's "Calculus."

Based on the information provided, it seems like you have a strong foundation in calculus and are looking for a more rigorous treatment in multivariable calculus. I would suggest exploring all of your options and gathering more information before making a decision. This could include talking to your academic advisor, speaking with students who have taken the honors track for multivariable calculus, or even reaching out to the professor teaching the class to get a better understanding of the expectations and content covered.

Additionally, it may be helpful to consider your long-term goals and how switching to the honors track for multivariable calculus may impact your academic and career plans. Will it provide you with a more challenging and rewarding academic experience? Will it open up potential opportunities for graduate school or certain careers? These are all important factors to consider.

Ultimately, the decision is yours and it's important to weigh all of your options carefully. Don't be afraid to seek guidance and advice from others, but ultimately trust your own judgement and what you feel will be the best fit for you. Good luck with your decision!