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