Advice on Mathematically Intensive Research For a CS major

[monmon_4]

I finished a bachelors in computer science a year ago and now work full-time. I completed calculus I/II, linear algebra, and numerical computing in undergrad and also wrote a brief term paper on numerical computations for PDEs (but only from the computational side).

I want to apply to graduate schools for mathematical sciences in the coming year and I have an opportunity to do physics/math related research with a professor from my alma mater. The nature of the research is mathematically intensive and requires knowledge of partial differential equations.

My question is this: Regarding this type of research, is it possible to proceed with my background while referring to textbooks as appropriate or is the nature of PDEs such that I would need to first take a sequence of courses such as ODE, functional analysis, and finally a course in PDE before I could even start this sort of research?

I took the approach of referring to texts when I wrote my undergrad term paper but, again, that was purely from the computational perspective and not from the mathematical side of PDEs so perhaps more accessible.

 

[MarneMath]

If your desire is to do mathematics at graduate school, you are woefully underprepared. Before we even discuss ODE, functional analysis or PDE, you need calculus III, vector analysis, real analysis I and II, probably modern algebra, and then maybe you can move on towards measure theory.

If you want to do a computer science program with a heavy mathematical framework, you'll find that it becomes harder and harder the more advice the topics become to simply reference a book. It takes some meaningful understanding of the topics, not just a casual comprehensive of the mechanics to really produce anything of value.

 

[monmon_4]

What if my desire is to get a masters degree in mathematics to get those skills in preparation for a phd? Would this endeavor help in that regard?

If your desire is to do mathematics at graduate school, you are woefully underprepared. Before we even discuss ODE, functional analysis or PDE, you need calculus III, vector analysis, real analysis I and II, probably modern algebra, and then maybe you can move on towards measure theory.

If you want to do a computer science program with a heavy mathematical framework, you'll find that it becomes harder and harder the more advice the topics become to simply reference a book. It takes some meaningful understanding of the topics, not just a casual comprehensive of the mechanics to really produce anything of value.

 

[chiro]

What are the requirements for the Masters?

 

[monmon_4]

Three semesters of calculus plus one course in advanced calculus or linear algebra or the equivalent. I would hope that a competent research project would show that I could move straight to a masters program without the third semester of calculus.

 

[MarneMath]

I find it hard to imagine a terminal master program in mathematics that only requires 'advance calculus' OR linear algebra. I would even be bold enough to say that all graduate programs (masters or PhD) would require both and I would be weary of one that doesn't. Now assuming that such a place exist, a lot of programs do allow students to take a few classes they may lack at the undergraduate level during graduate school. However, I think you simply lack too much of the mathematical courses for this to be possible. Keep in mind, mathematics isn't simply about having the course completed or knowing the material, it's knowing how to think like a mathematician and prove statements. Right now, none of the courses demonstrate an ability to prove something as straightforward as Rolle's theorem.

 

[chiro]

I agree that this doesn't sound like enough. Even if you don't have a lot of theoretical background for proofs, you should have enough applied subjects (particular some minimum statistics) for a Masters program.

The applied and stats areas require specific kinds of thinking.

Can you outline what courses you will be doing in the Masters?

 

[monmon_4]

I forgot to mention I've also taken Intro To Statistics offered by the economics department.

In a graduate program, I would like to take Intro to Math Analysis, Real Variables, Linear Algebra II, Basic Probability, Numerical Methods, ODE, and PDE.

From the website: (obviously, this is a bare minimum)
"All applicants must have earned (or be about to complete) a B.A. or B.S. or the equivalent. They must have taken three semesters of college-level calculus, including one semester of advanced calculus or linear algebra or the equivalent. Students who do not have the advanced calculus course may be required to take the course G63.1002 Multivariable Calculus."

For reference, this is NYU's terminal MS program,
http://math.nyu.edu/degree/ms/application.html

So what's my next best course of action? Decline the research and take courses on a non-degree basis until I have sufficient background? If I accept the research project, does it add weight to my application if I do well and receive a positive recommendation in lieu of my having taken two extra courses?

I agree that this doesn't sound like enough. Even if you don't have a lot of theoretical background for proofs, you should have enough applied subjects (particular some minimum statistics) for a Masters program.

The applied and stats areas require specific kinds of thinking.

Can you outline what courses you will be doing in the Masters?

 

[chiro]

If you end up taking the courses that you have listed you want to take, that sounds like a good preparation for further research in applied mathematics.

Note that with research, you will probably have to take more courses anyway while you research to take you to the edge of your field so that you can understand your topic area to take it one step further.

I would caution you though on this: if you want to get into PhD programs of any sort then contact them and find out what they expect.

Some are OK with less pure stuff for applied mathematics research and some want more pure backgrounds. Every one will have particular specialties that they focus on and are influenced by those areas, who they have worked with (and their personalities) as well as the kinds of backgrounds the students have.

If you are going to do a Masters for the purpose of getting into research, you need to know these things. Get a list of schools and find out their specialties, their faculty and past research, and get an idea of what they expect so that you can decide what the best preparation is to get there.

Some professors openly talk about this on their websites (personal pages) but if not, you can always read a personal website and fish around for this sort of information through inference and logic.