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For someone who is more interested in applied mathematics than abstract, which degree should one pursue in order to have a career in applied mathematics, considering he/she has pursued an MS in abstract mathematics? Is it advisable, considering that the person does not know much of the basics of applied mathematics?

  • Just a note, but abstract mathematics can certainly be applied (or at least applicable). See, for instance, the work of Robert Ghrist on applied topology. – J W Jun 23 '15 at 19:57
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    As @JW suggests, the labels "abstract" and "applied" are not now, and maybe never were, "opposites" or to be put in contrast. To answer your question meaningfully, you might tell what you mean by "applied math", not to justify the label, but to explain what mathematics you are putting it on, so that people can respond to that. (Yes, there is a tradition that "applied math" means numerical or heuristic solution of PDE, but... much more math than that was and is applied, and solving PDEs has to count as pretty abstract, in the first place!) – paul garrett Jun 23 '15 at 20:04
  • brightknowledge.org/knowledge-bank/science-and-maths/… .... such links made me ask this question here (i am sure to get clear answers here). – Harsh Pruthi Jun 23 '15 at 20:09
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    That alleged difference in content, expressed in your link to quora, is a naive and simplistic opinion. Yes, it has appeal because it answers a question in simple (but false) terms. It is more relevant to say whether you'd aim to work in academe, or in industry. Whether you'd like to collaborate with scientists in non-math departments. Whether you want to be "part of a team", versus choosing your own projects. – paul garrett Jun 23 '15 at 21:08
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    You may also find it valuable to browse the Society for Industrial and Applied Mathematics' career pages. – J W Jun 23 '15 at 21:14
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If you already have a Master's degree in mathematics, you should be capable of learning additional mathematics topics yourself. If you are interested in a particular field in which mathematics is applied, you can always spend some time becoming acquainted with that field and the mathematics involved. The Society for Industrial and Applied Mathematics (http://www.siam.org/) is one resource to get an idea of what's out there. You might look for a smallish project to test the water and pick up some experience in mathematical modeling and, if relevant, computational mathematics. Years ago as a student, I did a summer project on modeling measles epidemics using difference equations. It was a valuable experience and taught me more than merely reading about mathematical modeling in a book or on a website.

You may also wish to bear in mind that seemingly pure mathematics can often end up being very applicable, so you may be able to have the best of both worlds. For instance, Bernd Sturmfels has used algebraic geometry in statistics and computational biology and Robert Ghrist has applied algebraic topology to signal processing and sensor networks.

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