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Ill be going into my first year of college fairly soon, with a prominent interest in studying and researching (as a career) pure/theoretical mathematics (especially number theory). However, the college I'll be entering only offers an "Applied Mathematics" major, which I understand may be more suitable for engineers, economists, physicists, etc (but my perception on that point may be incorrect). Given this conflict, I have been considering transferring to another university.

My question is: Is an Applied Mathematics major still satisfactory for my interests in pure math, or should I transfer to pursue a major more closely connected with these interests?

Thank you kindly!

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  • I graduated from an "Applied Mathematics" program, but the name was almost completely for historical reasons. Indeed, the classes I took aligned with a standard "Pure Mathematics" curriculum. It is certainly worth asking any (math) advisers at the college whether your interests will be met. The people there are in the best position to answer your questions. Commented Jul 19, 2016 at 21:48
  • I have a correlated concern. Most (though not all - good but not exceptional engineering schools are a prominent exception) schools with only applied mathematics departments don't have very good students. This means, unless the school is small, professors probably will not be able to challenge you sufficiently for you to develop into someone who can get into the top grad school where professors can challenge grad students enough to develop most of them into mathematicians competitive in the current job market. There are late bloomers, but they are an exception, not the rule. Commented Jul 20, 2016 at 1:09

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For undergraduate math, programs tend to be really similar. You do calculus, then multivariable calculus, then linear algebra and differential equations, and you move on to an elementary analysis course and abstract algebra. These are usually what a student does through their freshman year for any math degree (and many for sophomore year depending on how prepared you were).

After you go through these, there will be upper division courses in PDEs, dynamical systems, manifolds/geometry, complex analysis, numerical analysis, etc. I assume that the main difference would be that an undergraduate program with only applied math would have less algebra courses (more courses in ring theory, Galois theory, etc.), one or maybe no upper division number theory course (except maybe a cryptography course in a CS department), and more courses based in modeling, numerics, and differential equations (numerical linear algebra, finite element methods, etc.).

But there's really one way to know for sure: look at the courses they offer. It's always online. Don't look at just one year since the upper division courses tend to be every other year, so look at maybe the last 3 or 4 years. Look at what they offer and ask "are there 3-4 courses a quarter here that interest me?". Look at some syllabuses, crack open some books, look through Wikipedia. Then do the same for places you are wishing to transfer to.

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  • The undergraduate Applied Math programs I'm familiar with offer zero abstract algebra. But you're right that looking at the courses online is the way to go.
    – user37208
    Commented Jul 20, 2016 at 1:04
  • And possibly even zero elementary analysis, if by that you mean a course that involves proofs to a significant degree. Commented Jul 20, 2016 at 1:11
  • I am going on this example, this example, and this example. I can't (quickly) find a program which only has applied math, but if they don't make you take algebra, it seems they usually recommend it. Same with analysis. But the best way to know for sure is look at your exact case. Commented Jul 20, 2016 at 1:18
  • I'm thinking more like this. You're pointing at programs at (very) selective institutions. I don't think that's what's going on here. Commented Jul 20, 2016 at 7:44
  • Well if you look at the courses, it's still all there. Abstract Algebra is applied abstract algebra, but look like it has the same stuff. Analysis isn't required but it's there. As expected, there's tons of modeling, numerical analysis, and differential equations / dynamical systems. There's just no number theory course. Commented Jul 20, 2016 at 15:38
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Applied math is basically applications of pure math. That is, it is the math that is used in "field research" rather than theory.

This shouldn't be an issue for you until at least your junior or senior year. If there are advantages to the applied math program (e.g. it is cheaper), I wouldn't worry about it now. The time to "jump" is one (or at most two) years before you would go to graduate school, when you'll want more pure math in preparation.

Alternatively, take the applied math degree and take a few courses in pure math elsewhere as a "special student" before grad school.

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    This isn't technically wrong, but I think it is still wrong. While, technically speaking, the courses that are specific to pure mathematics are upper division courses meant for juniors and seniors, most people who end up in mathematics as a career take them "early" and end up either with a wider variety of advanced undergraduate courses beyond the minimal requirements or with some graduate courses taken as undergraduates. Reading and writing proofs takes a different kind of thinking, and the earlier and more frequently you are exposed to it, the better off you will be. Commented Jul 19, 2016 at 21:56
  • (cont) - If your aim is to be a research mathematician, you need to aim to get into a top-40 graduate school, and ideally a top-5 graduate school, because the market is extremely competitive and the quality of your fellow graduate students makes a big difference in your own development. See for example, math.stackexchange.com/questions/94861/… Commented Jul 19, 2016 at 22:01

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