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I don't know how to start, truly, but lately I've been involved with some projects in pure mathematics and I've grown frustrated and disappointed. I don't think that pure mathematics is so inspiring; my intent is to move on to study some applied math but most teachers in my department aren't that dedicated to it. All I see are theoretical approaches to problems "that applied sciences may be interested some day".

By talking to a colleague of mine who is seriously considering moving on from Math to Physics, he told me of some engineering departments who might accept someone with a master's degree in their Phd programs. There are some areas I like that might have a connection with what is studied in some Engineering Phd programs, like applied ODE and Dynamical systems and I'd love to put some programming on what I do.

But every teacher I talked about this so far tells me to avoid this kind of migration, since it brings a loss of academic focus and it might be hard for me to find a job later as a teacher. There is no strong tradition in Mathematical Engineering as there is in other countries (I know that such courses exists in Italy and some other European contries).

So I'd like to know some thoughts from more seasoned students and researchers out there. Any advice is welcome.

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migrated from Feb 26 '13 at 3:55

This question came from our site for people studying math at any level and professionals in related fields.

I admit I have huge bias for my profession, my academic titles and my passion, but being in mathematics and passing to engineering on your own volition, without any economical constraints and/or without being threatened with a gun to your head, looks to me like choosing to eat dirt and bugs after begin used to dine only high cuisine plates...I know nothing about mathematical engineering (though it sounds like an oxymoron), but I guess that most engineering schools would be more than happy to have a mathematician (finally!) within their walls. You must try to write to several places... – DonAntonio Feb 26 '13 at 3:39
There's not much difference between modern physics and pure mathematics. – user774025 Feb 26 '13 at 3:41
@DonAntonio, mathematical engineering, as I said, is not to be taken lightly. Take a look: – Gustavo Marra Feb 26 '13 at 3:41
Why not try getting a MS or PhD in Computer Science if you like to code. I'm still an undergraduate student, but all the CS people I know have no trouble finding good paying jobs. – Amateur Math Guy Feb 26 '13 at 3:44
I might like to program but that doesn't mean that I want to make a living out of it. Though I admit that there would be so much easier to find a good paying job, wouldn't it be better just to graduate again in CS? – Gustavo Marra Feb 26 '13 at 3:47
up vote 9 down vote accepted

The only problem with switching to a particular field of engineering is that you'll be missing a core set of knowledge particular to that discipline that will hinder your progress for a while. For instance, you would probably do great in many electrical engineering sub-diciplines, but if you've never taken a circuits or signals course, you're going to be lost for a while before you can learn that material.

If you already have research experience, that will count for a lot, but I would suggest finding an engineering program that would allow you to take a few undergraduate courses during your first year or two in order to get up to speed. If you find a professor that is looking for a mathematics-savvy graduate student to fill in the gaps in his/her lab, that might be the best way to get your foot in the door. You've got skills that could be very valuable to the right lab, and if you use those as leverage to join a particular lab/research team, you'll be able to fill in the missing pieces to your new field and move forward with your own degree.

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The most likely domain of interface for a mathematician with engineering would be in the realm of "computational engineering," in which numerical algorithms are used to study physical and engineering systems. This work is highly interdisciplinary, and requires close collaboration among all of the different researchers involved, as very few are experts in all of the areas with which they are concerned.

However, there is a certain amount of logic to the idea of staying in one's "home" discipline. It makes it easier to figure out "who you are," which can make starting your career a bit easier. One possibility might be to pursue a degree in applied mathematics, in which you study problems relevant to engineering, rather than remaining in "pure" mathematics. This might be a reasonable compromise that keeps you in the mathematics field, while still allowing you to pursue topics in areas that interest you more.

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I second this. Applied math is the way to go. I would look for schools where the two departments (math and applied math) would be separate and then apply for applied math. It will make good use of your pure math background while giving you full opportunity to work with physical/engineering sciences. You get a little bit of taste of everything including plenty of coding. – Fixed Point Feb 26 '13 at 5:41

Most CS graduate programs would be quite happy to admit a math major. It might be tricky early on if you have zero programming experience, but depending on the kind of work you're interested in, you could be in a strong position.

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I have been in your shoes, as I migrated from mathematics to computational engineering. While my math background gave me some advantage, I remember it was difficult to make the transition because I was very unfamiliar with a lot of the key concepts in engineering. What really helped me was watching online courses (MIT, IIT, etc...) in the material I was missing... Of course, I had an entire year to prepare for it. If you have a lot of time to make the transition, by all means do so and you shouldn't have "too much" trouble. But if you're pressed for time to make up for a lack of engineering background, it can be quite overwhelming. It's best to hit the ground running in graduate school.

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