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I have read other threads along similar lines but I am looking for slightly different advise. And I am posting this anonymous because I would rather my current employer not find out my intentions !

So, I have a bachelors and a masters degree in computer engineering and currently work in one of the top microprocessor companies, which would otherwise be considered the "dream job" for someone with my degrees. However, every day I realize how much I miss Math and really want to go back and have an opportunity to work more with math, particularly in the field of numerical analysis, scientific computing, matrix algebra and the like.

Supporting factors -

  • I have always done well in math. I can get great recommendation letters from math professors I have taken courses with.
  • I am a CRLA level 3 certified math tutor. I used to be one when in undergrad.
  • I am preparing for Math GRE and am confident I can do well in it.
  • Good undergrad math and engineering GPA
  • My masters thesis involved quite a bit of dealing with numbers, since I worked with various LINPACK benchmarks and linear algebra solvers.

Negative factors -

  • I am not from a very highly reputed school.
  • I have not published any papers, even though I did write a thesis for my MS in Computer Engineering.
  • My math courses are the basic math courses engineering students take, along with graduate level math courses in numerical analysis, scientific computing and the like.

How do I go about getting a PhD admit in a reputed Math graduate school? How do I begin to convince professors / hiring committees that I am capable of doing a PhD in Math? I am only looking at quitting my company and switching to PhD around either of Fall 2013 or Fall 2014, so I have the time. What are some extra-curricular 'outside my day job' activities I can pursue that would further solidify my application in the mean time?

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Please consider registering you account. This will give you the ability to post comments to your own questions, so you can actually reply to answers instead of posting your response as a new answer. Commenting (as opposed to posting a new answer) will notify the person who posted the answer so he/she can address any additional questions you may have. –  Willie Wong Apr 10 '12 at 9:13
    
There are programs where you can go for a summer or a year and learn some of the math you will need to start grad school, like real analysis and abstract algebra. I know of people who have done these but I don't know anything about them personally. But, at the same time, at my school you can get a PhD in applied math and that would involve taking linear algebra and numerical analysis and applied math classes. You can get by without taking measure theory (graduate real analysis) or abstract algebra. But, you would need to understand the undergrad levels of these classes. No need to publish –  Graphth Apr 10 '12 at 13:39
    
A possibility you may want to consider is getting into an applied mathematics M.A. program somewhere. Spend the roughly two years getting as much background as you can and be as impressive as you can in the course work. Then use this to springboard into a decent Ph.D. program in (presumably) applied and/or computational mathematics. –  Dave L. Renfro Apr 10 '12 at 15:46
    
I'm going to migrate this question to the academia.SE site. There will be a link that appears below the question here that you can follow to the new location of your question. If you need help associating an account on academia.SE, you can flag your question for moderator attention, and someone over there will help out. –  Zev Chonoles Apr 13 '12 at 18:37
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migrated from math.stackexchange.com Apr 13 '12 at 18:38

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3 Answers

A concern (raised by your background) that occurs to me is that do you really have a clear idea what graduate programs in math are all about? I don't think that any reputable grad school would allow you to study numerical analysis alone ... [Edit taking note of Willie's remark] within a graduate program in pure math - the scene is markedly different if you are applying into a program in applied and/or computational math. I apologize for not knowing that such possibilities exist. My smalltown background left me with the false impression that math and applied math always come together. Such programs may be better suited for you![/Edit] (continued rant) ... For the simple reason that doing research in math requires familiarity with a variety of tools and theories from adjacent, nearby and occasionally relatively remote areas of mathematics.

Is entering a computer science/computer engineering graduate program not an option? Probably you can specialize in scientific computing/numerical analysis in such a program. It may actually be easier to find an advisor in such a topic at a CS department? I don't know for sure, but it sounds like such a plan would entail less risk.

Our resident experts on numerical analysis/scientific computing can give you more useful advice. Below I will say my bit.


Before you burn your boats I would recommend, as an extra-curricular activity, that you take a look at what the obligatory 1st year courses of math programs have in store for you. The core math at a typical US grad school (for 1st year grad students) contains at lest topology, abstract algebra, real analysis (sorry the link is only to measure theory, couldn't find a more fitting Wikipedia article at this time) and complex analysis. Some places would offer/recommend/require also mathematical logic. After the first year, you are expected to display a working understanding of the theories and results that those articles link to, and be able to reproduce their proofs on demand (ok, the committees will likely give you some slack on the more esoteric proofs, but don't count on it). The depth of those course probably depends on how much ivy the school has. I cannot give details on that for the simple reason that my experience is from a reputable but not top notch grad school, and I have only heard rumors about the others :-).

Only after having covered those basics can you start specializing on a topic that interests you the most.

I don't want to dampen your enthusiasm. I just had a few fellow grad students who were surprised by the graduate curriculum, and either dropped out or had a hard time making through the 1st year. My concern is that you may not fully appreciate how limited your exposure to math actually is (given your background). GRE is a joke, but it does test that you can speedily pick the correct calculus concept/theorem off the shelf in your brains and apply it.

So if going through those links just makes you hungry to learn more, then 'full steam ahead!', but otherwise you may want to reconsider.

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Good point. I do understand what you are saying, and the only reason I mentioned numerical analysis was because it was also a part of my computer engineering masters. I did take courses on more core mathematical topics as my undergrad electives. I even took a couple of independent study courses during my undergrad as well. As a matter of fact, I don't even want to "decide" on one particular topic as a topic that interests me the most. If anything, Math in general (and I mean the "able to reproduce proofs on demand and display working understanding") fascinates me and I would like to get more i –  NeedPhdApplicationAdvise Apr 10 '12 at 8:38
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"I don't think that any reputable grad school would allow you to study numerical analysis alone." That's not entirely true. If the OP is willing to consider programs in applied and computational mathematics, there are certainly reputable schools where one can focus on, say, numerical analysis + discrete methods + optimization. –  Willie Wong Apr 10 '12 at 11:35
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Pure mathematics isn't your only choice for a PhD, and may not be the best fit with a computer engineering background.

I'm currently a masters student in a MS/PhD program in computational engineering after getting a B.S. in applied math. Computational engineering is very different from computer engineering. It is a field which combines numerical analysis, linear algebra and parallel programming to solve engineering problems which are typically modeled as coupled systems of partial differential (or integral) equations.

In my program, the focus is on fluid dynamics, but there are others that focus on geophysics, structural dynamics, electromagnetics, etc. One of the advantages of this program is that it brings together people from mathematics, engineering and computer science, both in faculty and students, so you get a different perspective on problems than you would working strictly with other mathematicians.

If this sounds interesting, you may want to check out the Computational Science board here on Stack Exchange.

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I don't know howto respond individually, so I am just going to respond here all together.

@Willie, thanks, I have registered an account now. @Zev, thanks for migrating to academia. I didn't know this site even existed till now, and I am hooked. I will be posting with my regular SO account here :)

@Tonymac, computational engineering would be ideal. That's exactly the kind of thing I am looking for as well, and that's precisely what excited me during my undergrad days and motivated me to take a lot of math grad courses as electives in my undergrad program.

Coming back, let me re-emphasize. I am currently employed, just moved to Austin, Tx. I am only going to be applying for Fall 2014 for the most part, and that gives me an year to prepare. My question is, how do I "best" use the time till then? There are some advise I have seen on here that say "use your time productively". What would "productively" be in this case? What are the things I could do in the meanwhile to improve my application when I do apply?

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When many people start a PhD program, they struggle with the pace of the classes. One way to prepare for this pitfall is to have seen much of the material before. I recommend that you get the syllabus for one or two of the classes you expect to take during your first semester, and work through all of the material on your own (perhaps from the books commonly used for those courses at schools where you're planning to apply). Generally, the students who do best in first year classes are the ones who have already seen much of the material. –  Dan C Jun 19 '12 at 4:25
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