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I need and request some advice on selecting the area for my research. In particular, I want to know the about job prospects of Applied Mathematics Versus Pure Mathematics in Academia. I understand that Applied Mathematics would give an edge for industrial jobs. But is this a disadvantage for getting academic jobs. Ideally one should select the research area based on ones interest. My first preference is to get an academic job after Phd and do research in Pure Mathematics. And this was my plan when I joined this Phd Program (Turning down an offer of Phd in Computer Science). However, now I find, most of my seniors, who are about to graduate, are struggling to get an academic job.Therefore my reasoning is that if with applied maths I have almost similar kind of job prospects in landing an academic job then I should go for it. Once, if I am fortunate enough to get an academic job, then I could work on whatever area that interests me. And in the worst case scenario, I would have more options in getting an Industrial Job. Do you find this logic OK or naive? Please advice.

I am providing some more information about my circumstances.

I am a first year international student pursuing PhD from a Public University(Group II -Old AMS Classification) in USA. I am already 32 years old. I am married and I have a kid. After obtaining my undergraduate degree in Electrical Engineering I have worked for about 10 years in my home country and then I left my well settled job and comfortable life to pursue mathematics. I know programming and have experience of working in Big IT companies. I am hard working, motivated and reasonably good at maths (GPA - 4.0) but of course by no means an exceptionally intelligent/ genius as is evident from my profile. I am also not from a Top 20 maths department in USA. Although many past students of my University got academic jobs,I understand that getting academic job in USA is difficult (especially for International Students).

Some probable broad research areas that come to my mind are - 1) Algebraic Topology 2) Algebra and Number theory 3) Graph Theory / Combinatorics 4) Algorithms 5) Mathematical Optimization 6) Fluid Mechanics / Aerodynamics. 7) Control System

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Why the downvote? –  Git Gud Mar 17 '13 at 22:14
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academia.stackexchange.com would be a more appropriate SE for this question, IMO. –  JB King Mar 17 '13 at 22:18
    
Computer Science and Algorithms are synonyms, sez D.E.Knuth... and your range of topics of interest sounds awfully wide (to me, a complete outsider). –  vonbrand Mar 18 '13 at 3:24
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4 Answers

Here is what I believe:

First of all, do not abandon your dream of doing research in pure math. This is a long road and you can build it slowly and consistently. For this reason, and since you have a family to support, I recommend you solve first the survival problem, i.e., get a well-paying job e.g. in an applied math department or in an electrical engineering department. This will provide you with the psychological strength to pursue research directions you wish, without having much pressure. Note that pressure might turn your love for math into a nightmare. Finally, since you are only 32, you could achieve a position in a pure math department later in your career. I think Weierstrass did not become a professor until his forties :)

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Thanks for your reply and encouragement.I am a graduate teaching assistant. Although we have to live very frugally but I have a very supportive family and survival is not an issue right now. This is about what would be a wise choice considering future job prospects. –  Samal Mar 17 '13 at 22:26
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Do what you like best, anything else is just self-torture. If you are good at it, you'll succeed. As Manos' answer says, just make sure you have work near the area of ultimate interest. Look for a position not only in the US, there are plenty of good universities elsewhere.

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I think that you should follow your plan to get a PhD in pure math and work in academia. Not because the chances are particularly high that you will end up doing this, but rather because it is much easier to gracefully switch from this plan to another plan than vice versa. As long as you work fairly hard and maintain a reasonable outlook, the worst that will happen is that you might decide after some small number of years that math research isn't for you, at which point you might choose to graduate with a master's degree and look for work in industry. That would still not be a bad position to be in.

That being said, I think you should also make sure to ask some PhD students who left academia, in order to get more balanced advice.

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I'll be the cynical response. Give it up. You have very low probability of gaining a full time research position in pure simply because online education is going to be making radical changes with how education is administered. Realistically you should aim to industry. A PhD can train you to be quite excellent in areas outside research math.

Research positions come from folks with lots of publications, so say you finish at 33, you will need to publish great works, each work takes 1-2 years. So 3 publications puts you around 6 years of work; now that is around 40 years of age. In the mean time you will live frugally. That is a tough shot there. I argue to aim more well-balanced, and aim more realistically by questioning your expectations and responsibilities and work/life balance.
If you deny my cynicism and pursue your advanced research, but then start to notice 1)marriage tension 2) neglecting time with child 3) inner / emotional tension

then it is time to refocus on a balanced life.

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