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I am still in the process of choosing which major in the SEAS of my school I should pursue.

I want to go into an applied math PhD program after undegrad, so must I choose applied mathematics as my major? Or can I pursue electrical engineering or mechanical engineering? A double major isn't an option.

Any thoughts?

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    If you're just choosing your major now, how do you know you want to do a PhD in applied math? Or a PhD at all? – JeffE Dec 31 '13 at 6:36
  • I'm actually pursuing a 3-2 program so I'm an upperclassman math major and going to another college soon to complete a second major as a student in seas. I just wanted to simplify the question. – Alex Dec 31 '13 at 6:41
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    SEAS = School of Engineering and Applied Sciences? – Paul Dec 31 '13 at 22:36
  • Paul yes that's correct – Alex Jan 1 '14 at 1:42
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    Look at this link:Where possible, undergraduate students interested in applications should seek a broad scientific background. Understanding problems from the viewpoint of more than one specialty or application can help lead to a deeper mathematical understanding as well. The Courant Institute welcomes applicants with undergraduate degrees in other science fields, such as physics, biology, or engineering.math.nyu.edu/degree/phd/application.html – John Hass Jan 1 '14 at 14:56
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I don't mean to be rude but JeffE's answer (which I cannot comment on-site as I don't have the necessary reputation)

Whatever. Your major won't matter as much as your demonstrated potential for research in applied mathematics, which you can develop in almost(?) any engineering discipline.

is so off-base, it's like saying that majoring in English gives you license to do a PhD in any field that involves writing in the English language.

Engineering is certainly not a substitute for applied mathematics, and the transition can be very harsh.

  1. First of all, you need to localize yourself. Applied mathematics in the US is different from applied mathematics in the UK, which is different from applied mathematics in France. Similarly, applied mathematics at Harvard (which would not be with mathematics, but SEAS) would be different from applied mathematics at Courant at NYU or in the Mathematics department at Princeton (who don't have an applied mathematics department, but rather a Program)

  2. In any case, you will be expected to know all the core mathematics curriculum that pure mathematicians take in their first two years. From here, it will depend on what subfield of applied mathematics you're interested in. For example, if you are applying to a subfield that involves the classical mathematical physics (like solid or fluid mechanics), then you would need classes on those.

  3. Engineering classes are vastly different from mathematics classes in almost all the mathematical topics. There might be some overlap in terms of, for example, fluid mechanics, but even then there is a big distinction between engineering fluid mechanics and mathematical fluid mechanics. For instance, mathematical fluid mechanics would involve more rigorous reductions and derivations of the Navier-Stokes equations (exploring techniques in asymptotic analysis, for instance).

  4. There is some possibility of jumping from an engineering degree to an applied mathematics PhD, but again, this would depend on the country and the university and the department. If you want to examine the difference, look at the applied mathematics department at Cambridge University and compare to the applied mathematics group at the Courant Institute in NYU. Also, examine the PhDs of current faculty.

  • Thanks, it seems like an applied math major would be most appropriate for me. – Alex Dec 31 '13 at 15:50
  • Nothing prevents you, as an engineering major, from taking mathematics classes or doing mathematics research, either pure or applied. Except time. – JeffE Dec 31 '13 at 23:46
  • @JeffE: Technically, this is true of any field, but it is probably least true of engineering just because engineers are almost always constrained by a very strict schedule. The course structure is different between engineering mathematics and pure mathematics. For example, engineers will typically take a first matrix course that goes over things like solving matrix equations. Mathematicians will be doing 'similar' course but first dealing with vector spaces and their axioms. In theory, an engineer can do both. In practice, I don't know how many would care to, given their tight schedules. – TSGM Jan 1 '14 at 3:18
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    In addition, I did teach a professional engineer who went back to get an applied mathematics degree 'for fun'. It took him a little over two years of extra coursework, I believe. – TSGM Jan 1 '14 at 3:21
  • As far as I can see (and I did go back and check some admission requirements), as @JeffE said, nothing says that you need a math degree to pursue a PhD in applied math. Heck, if you decide that you like math after getting a BA in English, and if you have good reasons to let grad schools believe that you are capable of math research, that is perfectly fine, too (and your papers would be so well-written!) – user10269 Jan 1 '14 at 16:01
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Whatever.

Your major won't matter as much as your demonstrated potential for research in applied mathematics, which you can develop in almost(?) any engineering discipline.


Note that I did not say that you will automatically develop that potential in any engineering major; I said you can. Research potential is only incidentally related to your required classes. But it's considerably easier in engineering than in, say, English literature.

(Off the top of my head, I can think of applied mathematicians with degrees in computer science, electrical engineering, mechanical engineering, pure mathematics, statistics, ....)

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Almost none of the applied math PhDs in the USA have BS degrees in applied math, because undergraduate degree programs in applied math are very rare (more commonly, one may have a "mathematics" degree but with an emphasis on applied math courses). A large proportion of applied math professors in the USA do not have a Ph.D. in applied math, because most of the applied math doctoral programs only came into existence in the last generation. For instance, my advisor's doctorate is in computer science, but his thesis was in numerical analysis. So the name of the degree program is not key.

I know people who have earned an applied math Ph.D. in the USA with undergraduate majors in engineering, physics, chemistry, computer science, and pure math. The non-math majors were from programs at very good schools with a heavy mathematical emphasis. As a professor at a university that is modelled after US universities, I have supervised successful students and postdocs whose backgrounds are in all those areas, as well as others in mechatronics and operations research. The transition for some was "quite harsh", but they persevered.

I think the quality and rigor of the program is an essential factor. A physics BS from a top school usually knows more mathematics (and can reason better in mathematical terms) than a math BS from a lower-tier school. Some computer science programs are, in fact, applied math programs; others involve very little math. And some engineering programs at lesser schools are virtually devoid of mathematics.

So the bottom line is that you need to know much more about a program than its name in order to determine if it will prepare you well.

I should add that I myself double majored in Physics/Astronomy and Math as an undergrad, then got Applied Math MS and PhD degrees.

  • Thank you for your answer. I find a lot of what you say very logical. But I don't see how it is possible that a physics or engineering major at a top university knows more math than a math major at a less rigorous/prestigious university? The vast majority of physics majors don't take real analysis, abstract algebra, combinatorics, or really any higher level math other than calculus. And engineers have literally zero exposure to proof-based mathematics. – Alex Jan 1 '14 at 1:32
  • @BrandonBakhshai I am not sure about The vast majority of physics majors don't take real analysis, abstract algebra, combinatorics,. I was a undergrad math major. I met a physics major who knew group theory more than I did. – scaaahu Jan 1 '14 at 1:57
  • You can't get a physics degree at any decent program without taking linear algebra, ODEs, and PDEs. In most applied math programs, those are far more essential than abstract algebra or combinatorics. – David Ketcheson Jan 1 '14 at 22:36
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Difficult question, as so much depends on the individual. However, here are 2 questions you might want to ask yourself.

Q1: Are you exceptionally good at math?

If yes, you could consider doing a Master's in an engineering discipline. But if you are not first rate at math, I would suggest doing the Master's in math. Prelims are no joke, and if I knew I wanted to specialize in applied math, then I would take care to learn the basics of real analysis, topology, abstract algebra, and numerical analysis very well. You can always pick up the applications later (or as my advisor who was a mathematician working in biology told me, "It's easier to go down") I worked as a mathematician for EEs for many years and by far, the rate limiting step is always math.

Q2: Do you want to work in industry or academics?

If the latter, then you definitely don't want to do your MS in engineering. If the former, it could be a plus. One the of the biggest obstacles math PhDs face is that they find they often need a secondary field or skill.

The safe bet (for many may reasons) would be to do your Master's in math.

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