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Transitioning from computational maths to computer science?


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Hi guys, I am going through a mini existential crisis. I am really hoping I can get some good advice here.

I did a BS in mechanical engineering, and started getting involved in research right from my sophomore year. It became very apparent to me that I liked research and was cut out for an academic career. I spent my sophomore year and junior years working mostly on computational fluid dynamics (CFD), which I found very cool at that time. Essentially applying computing tools to solve PDEs, but I slowly started realizing that I was interested in the algorithmic and computational aspects of the field as opposed to the problems itself. For example, I wasn't interested in understanding the physics behind lava flowing or how fluids close to hot media behave. I was fascinated more with what sort of discretization scheme must be used, which data structure will help me update values easily in an iterative manner, how can I tweak the solution scheme to get a parallel implementation etc.

I thought computational maths or scientific computing (CM/SC) PhD programs would be the solution to all my woes with mechanical engineering and the "physics" of the problems. I applied last December and met with reasonable success - I had offers from multiple top 10 programs. At the same time (Fall of 2014), I was taking classes and was starting to get into Artificial Intelligence - particularly applications of optimization in planning, learning, control etc. I was always interested in optimization and had taken multiple courses on it (it's very important to CFD). I started realizing that AI and signal processing were much more fun and closer to my taste. I liked the whole paradigm shift - use computers to *do* something (a decision support system, a web application, robotics etc.); as opposed to use computers for *understanding* a physical phenomena.

I tried to see if I can do AI and more CS type work sitting in CM/SC programs, but I wasn't very happy or convinced with the work. The cultural difference was apparent, and people were strictly using computers as a means to understand physical phenomena. A few professors were working on the algorithmic aspects, but still their interests were in studying PDEs or monte carlo methods for computational chemistry. I was expected to go through the applied math sequence (mostly PDEs) and have an adviser formally affiliated with the applied math department (ruling out working with CS/AI professors). This made me sort of go through a mini-depression, and was not at all excited by the offers I had in hand. I finally decided against joining and decided to defer one program as backup (I told them I will seek out other programs too, and they were OK with it). I can now clearly see that I am cut out for work in AI - from a CS (algorithms, computation) perspective.

Question: What are my chances of admission in CS, given that I did have good success last time, in a closely related discipline? I would love to join the CS programs of places where I got admission, but I gather that CS admissions are more competitive than applied math. However, given that a red carpet was literally rolled out for me (multi-year fellowships) at the best of places, I don't want to settle for a lower ranked school (not in top 20?) or pay my way through a masters first, just to get into a CS PhD program.

Profile: Formal degree in ME, but most courses taken from math or applied math departments from a top school. 1 first author and 1 second author paper broadly related to computational PDEs (application driven problem). Only a few CS courses - data structures & algorithms; AI - planning, ML, control systems. From this year's summer, I have been working with a CS professor in my undergrad school as RA. I have been mostly using this time to read up a lot on AI through online courses and books. I haven't produced any great results on this project yet, but there is a steady progress, and I learning the ropes of working in computer science.

Any advice on how I should approach the situation? Did anyone else go through something similar? Thanks :)

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From what I heard a CS Phd program at a top 20 school is one of the most competitive areas for applications.  If this is indeed true it will be difficult to get in without an elite profile.  I would imagine that atleast some of the SciComp/Comp math programs are more pure than applied.  Are you sure that you didn't overlook anything?

Edited by ace589
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@ace589 yes, I tried hard to pull strings, to see if I can work in AI. But it seems very unlikely. Most places don't have an applied math department, but rather some sort of umbrella program where people from mostly engineering or science (mostly physics and chemistry) departments come together. The CS presence here is minimal, and the objective is to advance science and engg. through use of computers. Look at this link for example: https://www.ices.utexas.edu/about/news/275/

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I see.  Have you considered a graduate certificate?  I would select a safe school with a phd program that is not too difficult to get in.  If you are not admitted then typically you can enroll as nondegree student.  There will be 4 or 6 classes designed for those who want to transition from a different undergraduate major.  After you successfuly complete the certificate with good grades you may reapply for the Phd with better chances.  This almost always works for getting into MS not sure how well it works for gaining admission to Phd

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