Teach me about Applied Math
January 1, 2013 1:28 PM   Subscribe

I'm interested in a Masters in Applied Mathematics in the NYC area. Help me research further.

I love dissecting complicated systems and understanding how things work. I am 27 years old, currently working on Wall Street. I have spent a lot of time thinking about graduate school. I am very interested in moving in a different direction. I am interested in pursuing a program that would allow me to further develop my quantitative skills and would be willing to let it lead me where it may. I think that a Masters in Applied Mathematics might be what I am looking for, although I have also thought about perhaps a Masters in Comp Sci or Statistics.

I graduated with a 3.50 GPA in Economics from a top college. My GPA was thrown off by a poor freshman year. I believe excluding my freshman year that my GPA would have been closer to a 3.80. Working against me is the fact that I did not take much math in undergrad. I believe that my only real math courses were two prerequisite semesters of calculus. Additional quantitative courses were Intro to Stats, Econometrics, and what was taught in my upper level econ courses (some exposure to linear algebra, Laplace transforms, etc.). Obviously these courses aren't as rigorous as what would be taught in an undergrad math program.

My questions:

I would like to know how to research this further. I know that graduate schools often like for their students to have diverse backgrounds. However I also know that most programs would require that I have a strong understanding of undergraduate mathematics, which I lack. I'm wondering whether any schools would be willing to admit me on a provisional basis, based upon my ability to make up any prerequisite coursework. Or barring that, I would be interested a learning plan of what courses I would need to take prior to applying.

If I did need to take additional coursework before applying, how many semesters realistically would this coursework take to complete?

Would it be acceptable for me to informally reach out to professors in the Applied Math departments?

Perhaps most importantly, am I being unrealistic?
posted by prunes to Education (7 answers total) 4 users marked this as a favorite
I am in a similar place to you. This fall I took my first graduate course in applied math in a competitive program. Given the course material and the work expected of me, I would consider these to be an (almost) absolute prerequisite:
  • a basic understanding of proof-writing
  • a full sequence of undergraduate calculus, including a strong grasp of vector calculus
  • substantial exposure to (real) analysis at an undergraduate level
  • differential equations, including a basic grasp of PDE
  • a good basic grasp of abstract linear algebra (i.e., more than just solving Ax = b)
As you can see, this is quite a bit more than two semesters of undergraduate calculus can provide. This was also my undergraduate preparation. I've spent a good chunk of the last three years trying to make up for my lack of math coursework. All told, I managed to do reasonably well last semester. I think I'd have doubts about an applied math program that would admit applicants without a major part of the background I outlined. If it's at all an option for you, try to get your employer to fund a two-course sequence in undergraduate analysis, see how well you like it. Numerical analysis material in an applied math program will start approximately where the analysis sequence leaves off.
posted by Nomyte at 1:45 PM on January 1, 2013 [2 favorites]

I should add that it's taken me three years because I've been taking 1-2 courses a semester and I have a fairly demanding job. If you had more time to devote to developing your foundation, you could probably take the required courses in 3-4 semesters, maybe less. On the other hand, it won't be easy taking more than 2 rigorous math courses in a single semester.
posted by Nomyte at 1:50 PM on January 1, 2013

This is somewhat tangential to your question, but you may want to take a look at a couple of books to help you get a feel for which topics you need to refresh/learn. You may be able to plan courses out from there.

1. Advanced Engineering Mathematics by Kreyszig -- Good overview of lots of applied mathematics: ODEs, Linear Algebra, Vector Calculus, Fourier Analysis and PDEs, Complex Analysis, Numerical Methods, Optimization, Graphs, and Prob/Stats. If it looks helpful to you, try some of the exercises. One must do math to really learn it. nswers to odd exercises are on in the back.

2. All the Mathematics You Missed: But Need to Know for Graduate School by Garrity -- This is designed for pure math students, rather than applied, but it's got some good tips and short overviews of everything. It's beyond what you need, but certainly interesting to view the scope of mathematics. If you can find it at a library or can take a look at a bookstore, take a brief look.

3. Perhaps a Math Subject GRE study book? While you may not need to take the test for grad school, it may help you figure out what you have down and what you need to work on.
posted by wiskunde at 2:28 PM on January 1, 2013 [2 favorites]

What I didn't see in your list of courses you've already taken was an introduction to proofs course, in addition to a missing real analysis course (or two, depending) and PDEs. And an actual linear algebra course. And vector calculus, if you've not had it. (IAAMathProfessor, for what it's worth, although not in an applied field.)

Do you have any sense about what/where a masters would get you? Certainly, in our masters program, students have the option to take some undergraduate courses in the program, but with the previous coursework you outlined, I doubt you would be able to succeed immediately any of the graduate courses. (That is, your sense that you need some prerequisite material is probably accurate.)

On the other hand, it is often possible to go back and get a second bachelor's degree---I know at my institution, students can do this, and you don't have to complete any of the core requirements, only the major requirements, and you would already have at least a couple of the calculus courses out o the way. But you'd have to pay for it, unlike a masters, where you should at least be getting a TA position.

There are a lot of jobs in Statistics, so that might also be a good approach. Again, you don't have the prerequisites, but...you might be missing fewer of them. Look at a catalog for a program you're interested in.

Have you looked at the various professional society web pages for ideas about what you can do with various sorts of math degrees?

Mathematical Association of America

Society of Industrial and Applied Mathematics --- probably the most useful to you

American Mathematical Society

American Society of Statistics

I don't see why emailing some professor in a program you're interested in would be inappropriate. Some big schools have separate graduate advisors you could call, also.
posted by leahwrenn at 3:44 PM on January 1, 2013

I run graduate admissions in a big math department (which includes applied math.)

Here's what you're going to do. You're going to take another math course at a good university. You may be able to do this at night at a place like Hunter College. You are going to excel in this course and you are going to impress the professor, who is going to write you a letter saying "this person doesn't have much background, but they mastered this material incredibly fast and would quickly get up to speed in your graduate program." That letter is what an admissions commiteee will need in order to admit you to their programs with limited coursework.

And if you take this course and that doesn't happen? Well, then you should might want to reconsider how interested you are in doing graduate work in math. Because learning math incredibly fast is what will be expected of you as a graduate student.

Other things:

1. E-mailing professors is fine. I get these e-mails all the time. Write the graduate admissions director or graduate chair, not the chair of the department.
2. You will want to take the math subject GRE and do well on it.
3. You might want to consider applying to Ph.D. programs as well as master's programs. For one thing, Ph.D. programs are funded and master's programs are often very expensive.
4. Your first-year GPA doesn't matter.
posted by escabeche at 5:01 PM on January 1, 2013 [3 favorites]

I don't think an introduction to proofs course is necessary in the sense that people would look askance at you not having one (where I was an undergrad, the course existed but wasn't required--very few people took it). However, if you're coming from a background of no upper level undergrad math, you may want to take such a course to reduce the baptism by fire aspect or be strategic about the order you take classes. For example, as an undergrad the received wisdom was to have your first upper level class be the upper division linear algebra, I guess on the grounds that you'd already done lower division linear algebra (yes, I really spent a year doing linear algebra), and that you definitely shouldn't do real analysis first if you could avoid it. But in some other department, people might normally do real analysis as their first upper level course.

The math GRE is skewed heavily towards calculus, so it may not be that indicative of things you ought to know. (I just checked. It's supposedly 50% calculus. At any rate, I recall very few questions on anything beyond linear algebra--just sort of one question on each broad topic and a hell of a lot of calculus.)
posted by hoyland at 6:01 PM on January 1, 2013

Just another vote for being sure that you know where a Masters will get you. In some fields, that might be a nice qualification, but in others (e.g., academia), it will be worth virtually nothing, so be sure that you know you're going to leverage the degree in some way before you make the investment.
posted by acm at 7:58 AM on January 2, 2013

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