Courses Advice Needed for Course Selection as Math Major

[Sisyphus]

Hello,

I am a high school senior headed off to university in just 4 months or so. I am going to have to select my courses for my first year in the up and coming months, and was hoping to get some advice.

I am pretty dead set on majoring in pure math (consequences be damned ). Just from reading around my math faculty's course calendar and browsing message boards such as this one, I've come to the understanding that pure math majors often make themselves more marketable by supplementing their education via embarking on a double major or taking up a secondary program as a minor. Problem is, I am somewhat torn when it comes to what it is that I want to study in addition to pure math. So far, I've classified my options into: majoring in another area of math, taking up physics, or go with one of the predetermined programs that include pure math studies with focus in other disciplines (finance, electrical engineering electives, or teaching).

I am playing around with the idea of taking up mathematical physics, although I have been somewhat ambivalent in regards to my physics courses this year. I suspect that the case may be that I am simply not adept at physics, despite my interests in the subject. When in physics class, I do not feel the same level of comfort that I feel in math class; I feel out of my element as I try to make sense of all the formulae and laws in a holistic fashion. I don’t think that this is the fault of my teacher, as he’s very smart and talented. I have heard that university physics is largely different than high school physics because it is calculus based. To what extent is it different? I am seriously considering taking up mathematical physics as a double major if I can convince myself that I can succeed in it.

On the other side of the coin, there is the fact that I am going into a largely theoretical discipline, and that complimenting my studies with a more practical major would not be a bad idea to prepare for the future (plans are inevitable to change, and I might find myself in a situation where I need to find employment right out of university). Although I have never been interested in Finance, the finance option, or even the actuarial science program, do offer some peace of mind, especially to my parents, who are not entirely thrilled with the idea of me going into pure mathematics in the first place.

Perhaps the most reasonable option for me would be to simply take up a second major or a minor within the math faculty, such as combinatorics or applied math, that have some overlap between the courses.

This thread ended up being a lot longer than I anticipated (I tend to ramble), but hopefully, I can receive some valuable advice that might help my make up my mind. Thanks.

 

[Stephan Hoyer]

Even the most "pure" math is rarely without any practical applications at all, so even if you major in "pure math" you'll still learn lots of practical math. Linear algebra, vector calculus and differential equations are perhaps the most essential applied math, useful for just about all sciences, and possibly excepting differential equations you'll probably need to take versions of these courses for a pure math major, too. And really, these seem to me as the courses that would be most significant in applied mathematics, as well. I really don't see much of a loss going the "pure" route: in the worst case scenario, you miss an applied topic or two and you take harder versions of the same courses applied math majors would likely take.

The great thing about math is that it shows off your analytical skills in any case, which should make you employable even if the topics were not applied.

However, I still think it's worthwhile to consider other options, possibly in addition to pure math.

If you can handle pure math, I can't see any reason why you could not handle physics. Coursework in physics is basically math with occasional use of physical intuition and slightly fuzzier reasoning (I think this makes it easier, not harder, than math).

I would take the most advanced introductary physics course possible in your first semester. Presuming it's not a firm commitments, you would lose nothing but a single course and you could potentially find you really like physics. I thought physics was so-so in high school since I could get away with patch-work "plug and chug" without much in the way of real understanding. I joked about how I could figure out how to do every problem on a test just from glancing at the formula sheet and guessing the appropriate letters. I even thought chemistry formed a much more cohesive "whole" than physics.

In retrospect, my poor appreciation of physics was basically because the subject matter seemed too "easy" (yes, I'm one of those funny people who will get a worse grade in an easier version of a course) and yet I never really developed an understanding of what I was doing. Algebra based physics is hardly even worthy of being called physics. Calculus brings together and improves physics in countless ways. Mechanics becomes an exercise in remembering F=ma, and well, probably a bit more, but the point is that you don't barely even need equation sheets anymore. That is not to say that the problems are easy: the problems I encountered were harder than anything I had previously dealt with and it took a lot of practice and hard work to understand how to approach them.

My advice is based on my experience with the US university system, but I don't think it's too different in Canada. In the US, it's generally not necessary to determine a definitive major (of any sort) until the middle of the second year, and you can take courses ad-hoc in pretty much any department. In that case, you certainly want to sample courses before prematurely settling on a second

As for back-up plans outside of more strictly academic fields: learn to problem competantly (maybe take some computer science courses) and your analytical skills from math and physics will make you employable in fields like finance, though getting those sought after jobs on wall street could be a trick. Frankly, finance and actuarial science, at least the economic concepts, are a lot easier to learn than the analytical skills you get in physics or math.

This is kind of where I'm at as a second year math and physics major, who plans to go to grad school for a PhD (likely in theoretical physics). If you're smart, confident and deticated, as you seem to be, I don't see how you could really go wrong as an undergraduate.

Disclaimer: I'm still a smart, confident and deticated undergraduate with minimal exposure to the harsh real world . But I've thought a lot about these subjects, so I hope I'm helpful.

 

[Sisyphus]

I think your idea of taking a sampler physics course in my first year seems to be the most reasonable course of action for me. First year in Canada (or at least in the university that I'm attending) tends to work in a manner similar to yours. High school applicants go into faculties, where they generally take some common courses during their first year, and declare their major(s) within their faculty at the beginning of their second year. At least this is how it supposedly works at the school where I'll be next year, so I guess I'll have some freedom to explore some options during my first two semesters.

The way you describe your high school physics experiences are pretty much congruent to my current situation. I am pulling good grades, but they don't really mean anything to me as I don't feel as if I'm learning anything new with the exception of knowing how to solve specific types of questions that may appear on exams by mechanically rearranging variables on the formula sheet with no clear justification. I think that my physics related anxiety pertains to the fact that while I really want to study physics, I feel hesitant to jump into it, having never experienced anything but my high school courses.

As for all the finance stuff: since I really have no particular interest in finance in the first place, I guess that I would be selling myself short if I decide to go into one of these areas simply as a secondary plan to fall back on. I think that I will probably research this option too, and see if I'd enjoy it or not before I make any decisions. I guess if the time comes that I no longer want to go to grad school or whatever, I will still have picked up some valuable skills from my math program anyways (like you mentioned).

Anyways, thanks a lot for your quick and insightful comments.