Here is my situation: I am a pure mathematician finishing Ph.D., working in Riemann surfaces, Teichmueller theory and differential geometry (with published papers in decent journals), having backgrounds in these topics and some PDE and topology and have some introductory knowledge about programming. I have been wanting to switch to little more applied areas (described below) because: 1) I believe getting posts and grants are slightly easier in there, 2) my postdoc hunting in pure mathematics have resulted in vein (despite getting shortlisted twice in Europe). I wanted to switch later anyway but reason 2) is forcing me to think of it now.
Since I have not published any single papers in those applied areas, or haven't had any formal training in them, what are my chances of getting a postdoc in these areas, being a pure mathematician all my life so far? If any of you have done so before, or are working in these applied areas, I would very much appreciate if you inform me! By informal communication with some people (who are Ph.D. students) working in these areas, I was informed that my backgrounds are good, but one or two professors I have contacted already mentioned that they want somebody with actual research experience in say imaging, which I do not have. So, I am not sure where I stand compared to other applicants. Your responses and honest opinion (even though not in my favor) will be highly appreciated! Thanks a lot in advance!
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Students can use at most one of CAS MA 411 and CAS MA 511 to fulfill the requirements of this specialty. Students planning to go to graduate school in a related field are strongly encouraged to take CAS MA 412, CAS MA 511, and CAS MA 512, as well as a numerics course. A major advisor can approve one roughly equivalent upper-level course, either inside or outside the Department of Mathematics & Statistics, as a substitute for one of the courses in one focus area. The Probability and Mathematical Statistics track is meant for students working in mathematics and related applied fields who are looking to use the fundamental tools of probability and statistics in their field of study. Students who plan to pursue graduate study or a career in statistics should, in consultation with their major advisor, consider pursuing the Specialty in Statistics.
When I got to Harvard as a first-year student, I had some idea of what I wanted to study. I was a STEM-oriented student, but I was also a music lover and open to learning about new disciplines. Math was a subject I was planning on continuing so I could have a solid foundation in science classes. I then learned that there were two types of math I could study: pure mathematics and applied mathematics. Initially, I felt slightly overwhelmed because I had never heard of the distinction before; I thought math was just math! Luckily, both the Math and Applied Mathematics departments have very helpful and kind people who are here to help students.
Logistically, pure mathematics requires 12 courses (48 credits), of which 8 are in the math department and four are in math or related subjects. Applied mathematics requires 14-15 courses, including five courses in a chosen application area. Happily, if you are not sure which to choose, but you do know you want to study mathematics, many courses overlap and will count for both concentration requirements.
In terms of what differs between the two concentrations, it is actually pretty intuitive! Essentially, pure mathematics focuses on abstract and theoretical concepts in math working to prove theorems and research and discover new realms of math. Pure math courses are heavily proof-based and deal with theoretical possibilities of math. On the other hand, applied mathematics focuses on ways to use math. This is why all students choose a specific application area within their applied math concentration. For example, many students choose economics as their application area and take courses learning the mechanics of how to use math in economic situations.
With regard to Mathematics degrees, most universities do not require Further Mathematics, and may incorporate foundation math modules or offer "catch-up" classes covering any additional content. Exceptions are the University of Warwick,[2] the University of Cambridge which requires Further Mathematics to at least AS level; University College London requires or recommends an A2 in Further Maths for its maths courses; Imperial College requires an A in A level Further Maths, while other universities may recommend it or may promise lower offers in return. Some schools and colleges may not offer Further mathematics, but online resources are available [3]Although the subject has about 60% of its cohort obtaining "A" grades,[4] students choosing the subject are assumed to be more proficient in mathematics, and there is much more overlap of topics compared to base mathematics courses at A level.
There are numerous sources of support for both teachers and students. The AMSP (formerly FMSP) is a government-funded organisation that offers professional development, enrichment activities and is a source of additional materials via its website. Registering with AMSP gives access to Integral, another source of both teaching and learning materials hosted by Mathematics Education Innovation (MEI). Underground Mathematics is another resource in active development which reflects the emphasis on problem solving and reasoning in the UK curriculum. A collection of tasks for post-16 mathematics can be also found on the NRICH site.
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