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Math Applied math MS/PhD jobs

  1. Dec 26, 2010 #1
    Many schools advertise their applied math graduate programs by answering the question "what kind of job does a mathematician do?" The answers all essentially say the same thing--something like "you can [strike]teach[/strike], work for a government agency, or work in industry." They are very bad at explaining in what roles, how, and how many.

    Can anyone help answer these questions? I am not interested in answers from people who are unqualified to give them--i.e. people who have no experience with this issue themselves. By visiting school websites, I've already gotten such answers.

    My undergraduate advisor is totally useless, by the way.

    Is it pointless to seek a job in industry unless I go to grad school for some kind of engineering?

    For instance, what roles in finance are realistic for someone with an applied math M.S. from a non-top10 school?

    What other industries come to mind, supposing I have 1.5-3.5 years' experience with C, C++, Python, and MATLAB, and did my research primarily in machine learning?

    Personal stories get 50 bonus points.
  2. jcsd
  3. Dec 27, 2010 #2
    Unfortunately, those aren't realistic questions to ask. Your undergraduate degree is about the skills that you learn, in math you gain lots of problem solving and technical skills. So it doesn't need to be about whether or not your real analysis is any good, it's about the fact that you're comfortable with something that's very complicated. This means mathematicians and physicists alike are sought after for many technical positions. In general, big companies don't mind training you from scratch in the work that they do.

    What do you mean? Either way you'll still be in a job in industry. My answer is 'no'. You might be able to progress higher with a PhD, but you might not - lots of industry roles are about experience. When you arrive as a raw graduate you'll get taught up to industry standard and work from there. The funny thing about PhD/academic research is that it can be completely different and so far removed from the real world it would be amusing if it wasn't so disastrous. For example, academic research in biocompatible materials is a huge area nowadays - there are hundreds of researchers working on new materials for implantation, testing methods and design methods. There are hundreds of new candidate materials. However, in the real world - because it is so difficult and expensive to reliably approve new materials, industry is still making and marketing the same materials that were around 20 years ago. This is a pretty extreme example, but it's just to highlight that academic research isn't always necessary for industry applications.

    Have a look at something like: http://www.quantfinancejobs.com/

    You'll find most of them ask for PhDs.

    Your programming experience is less relevant than what you actually want to do. In applied math, things like continuum mechanics in industry (go work for hewlett packard on liquid crystal modelling to develop next-gen displays), PME (population modelling and epidemiology) for research labs or government bodies (you can look at, say, models of disease or drug addicts to try and work out how government initiatives might improve the situation), network analysis (you could analyse social networks in a research setting, telecommunications networks in industry, biological networks, protein-protein interaction networks in research).
  4. Dec 27, 2010 #3
    But this still leaves me asking... what roles are applied mathematicians hired for? Some examples would be fantastic. Personal anecdotes would be better. How many applied mathematicians are hired each year outside of academia? Are there numbers out there for specific industries? And is the market for those jobs as saturated as the market for academic jobs? And still importantly... how do you go for them?

    But, for example, on QuantNet, I've seen it said that first of all, those job listings are "bogus," and second of all, a PhD is NOT the way to go for such jobs (in spite of the fact that these and similar listings say so). Who is telling the truth?
  5. Dec 27, 2010 #4


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    Here are a few concrete examples:

    1) Actuary

    These people are basically "business mathematicians" that work mostly in financial services and insurance companies.

    Their job is akin to an engineer. They have the professional and the legal responsibility to sign off on things that are required by specific bodies like prudential bodies and other regulatory bodies.

    So what exactly do they do?

    They do quite a lot.

    They do all the required analysis when designing insurance products which involves simulations (statistical and Monte Carlo) and present results to business executives that are not as math inclined as they are.

    They also have to make sure that the insurance company remains solvent and that covers a lot of different areas including statistics, finance, economics, accounting, investments and the connections between these fields.

    With regard to investments, they have to pass courses that are both computational and conceptual. Since a lot of premiums are invested straight away, they need to understand a lot about investments, but they are not legally allowed to sign off on those things because it requires another certification.

    Like most applied mathematicians, they basically solve problems within some domain, and do presentations that show a concise analysis of a problem, with recommendations for the top brass to make. They may have some responsibilities themselves, but for a lot of applied mathematicians, they are giving recommendations for people with a higher amount of responsibility to make a decision.
  6. Dec 27, 2010 #5


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    Also I'll give a personal anecdote for video game design programmer.

    While it wasn't a "mathematician" job, you have to know a lot of math to actually do your job.

    Here's an example.

    The level designers come to you and say they want you to add a tool that given a volume, you use that volume to create nodes that the AI can use in path building (A*) for navigating around the level.

    So my one was a general solution:

    1) Take the polytype and project it on to the world
    2) Find the planes that it was projected on to.
    3) For each plane build a convex hull by rotating the plane to a standard XY plane and then using minimization of angle to form the hull
    4) For each hull triangulate using the definition of the hull
    5) Use triangle interpolation (barycentric coordinates) to fill each triangle with points given some density parameter
    6) Rotate each point plane that has been filled with points back to its position and add a z offset so that the points are above and close to the plane

    Note that the rotated plane in 6) refers to the points created from the real plane definition.

    So there's some computational geometry at work to solve a problem.
  7. Dec 30, 2010 #6
    it could be said 'with a degree in mathematics, you can do anything except mathematics'. 'you like statistics? be an actuary! that uses mathematics!' or 'you like to program, be a programmer! that uses mathematics!' and on...but you're not going to get a job with the title 'mathematician'.
  8. Jan 1, 2011 #7
    I must disagree with you here. There are many jobs that will all you to do mathematics. You cited two examples that happen to be pretty far out of the reach of pure maths, but there are others that I can think of that would allow a mathematician exercise his talents. For example: cryptography & cryptanalysis, applied fields in industry and government development, quantitative finance etc...

    Also, I suppose this depends on your definition of "mathematician". I would consider anyone who has a degree in mathematics (or related field) and actively works with mathematical methods -- either to solve problems or to investigate, and improve upon said methods -- a mathematician.
  9. Jan 1, 2011 #8
    Why wouldn't the same stringent requirements for "physicist" also apply to "mathematician"?
  10. Jan 1, 2011 #9
    I think physicists and mathematicians are two fundamentally different people, so to speak. I think it's the nature of their respective work that sets them apart.

    Mathematics seems to be a more general field, especially where career opportunities are concerned. Also, there's the question of persons who are physicists by training, but work as mathematicians (or computer scientists, chemists etc...); for example, some quants. And in those cases, I think the work of the individual determines his/her job title. I don't think there are many physics trained-quants actually doing any physics on Wall Street, but there's certainly physics trained-quants doing stochastic calculus. To me, that would make them employed as applied mathematicians. By the same token, I'm pretty sure there are mathematicians who work primarily as computer scientists; however, I'm not sure that there's any mathematicians working in experimental fields in government labs. It's just the nature of the beast.

    In the interest of full disclosure, I'm not a working mathematician or physicists. I aspire to be a working mathematician, and those aspirations have led me to a lot of reading on career paths. Perhaps someone with experience in industry, government or finance could give a deeper, more meaningful insight.
  11. Jan 1, 2011 #10
    algorithms is always big. companies like amazon, netflix, google or facebook. the first two rely on algorithms to make recommendations to their customers. the last two rely on them to direct ads to their users.
  12. Jan 3, 2011 #11
    not really disagreeing, but its far more likely you're going to be looking for a job in industry or government that applies the ideas you've learned for your degree in mathematics but you're not going to have the title 'mathematician'. you're a 'cryptologist' you're a 'quantitative analyst'.

    worse, the car industry for example doesn't really hire 'mathematicians', they hire 'engineers' who have been specifically trained for that type of job. similarly for other jobs that use mathematics, 'programmer', 'actuary', they require specialisiation within the field of mathematics which a generalist mathematician might have difficulty proving can do.
  13. Jan 3, 2011 #12
    Okay, sure. But I would definitely consider a cryptographer or a quant a mathematician.

    This is a bit different. I would not consider a programmer or an actuary a mathematician. These jobs are not equivalent to those of cryptographers or quantitative analysts.
  14. Jan 3, 2011 #13
    it is said the 'statictians' also reject being labeled as 'mathematician'. but i'm not sure what criteria you or they are using.
  15. Jan 4, 2011 #14
    Saying a quant is a mathematician but a programmer isn't is just weird. I think there's a lot more variety in these occupations than people are giving credit for.
  16. Jan 5, 2011 #15
    And also there isn't any need to label someone specifically a 'mathematician' or otherwise. Who decides the pigeon holes, and why? Does it matter? I would say no.

    The important thing for this thread is that applied math opens up hundreds of different job opportunities. It isn't about which jobs consider themselves to be mathematicians or not, but which jobs in which the skills a mathematician has are valuable. And by skills, we mean things like problem solving, technical writing, etc, not just "can do calculus.". It's the fact that you're the kind of person that can learn calculus that is interesting to many employers.
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