Swapping courses.

College Life
1

<p>Hello all.</p>

<p>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). </p>

<p>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. </p>

<p>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. </p>

<p>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? </p>

<p>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. </p>

<p>So, what should I do?</p>

2

<p>“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.”</p>

<p>I think you answered your question right there.</p>

3

<p>I know, but I don’t want to end up in a weak class and pay for it later. For example, the only Analysis classes offered at my school are in the honors department, and if these honors kids take these classes, then how am I going to compete against them in analysis? Eventually, I’ll have to face rigorous math, so it’s not like I can avoid it forever.</p>

4

<p>I took a proof-based multivariable calculus class and I wish I hadn’t. I have seen proofs of the Inverse Function Theorem and Stokes Theorem, but I still don’t understand what they mean. Nor do I know how to do any computations. My gaps in multivariable calculus are giving me a really hard time now (especially in differential geometry and differential topology) because all the math professors assume that we are comfortable with computational calculus if nothing else. </p>

<p>And I can assure you that no one in the class really understood what we did because it went over everyone’s head. Sure, we could do the silly little proof exercises but we all had a really hard time translating the formal math back into geometric intuition and computational algorithms. That is a skill that is much more naturally picked up in Real Analysis than Multivariable Calculus. Real Analysis starts with very familiar topics from single-variable calc and slowly moves into areas we have less intuition about. Multivariable calculus on the other hand throws you into waters you have probably never encountered before, and that is rather painful for your first rigorous math class. I think it makes much more sense to learn multivariable calculus on the intuitive/geometric/computational level first and worry about the proofs once you have taken Real Analysis.</p>

<p>Just for the record, I had taken several rigorous math classes before I took honors multivariable calculus and I did fine in those. The main difference is that they were all algebraic (linear algebra, abstract algebra, number theory). The algebraic classes were easier in the sense that we did not have to extract geometric intuition from a rigorous mathematical statement. That is a very hard (but important) skill to learn for most math majors.</p>

<p>At my college the students in Real Analysis who had taken honors multivariable calc did not have an advantage over the students who had taken the regular version. But at least the regular students understood multivariable calculus which the honors students did not. If multivariable calc and real analysis at your college are anything like the classes at mine, I would strongly recommend you take the regular version, in particular because you say that you have a hard time writing proofs. Real analysis or linear algebra are much gentler introductions to rigorous math.</p>