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How would I find and select a PhD program in Computer Science, or Computer Science combined with Mathematics? Since I am not a traditional candidate, I am unable to seek relevant advice from professors and fellow student. I am not too concerned about school ranking.

Some background about me and my circumstances may help frame the question and better focus the answer.

I have substantial experience in software engineering (over 20 years), including analysis, requirements, architecture, design, (extensive) hands-on development, testing, systems, team leadership, mentoring, management, and process. Many colleagues have said that I am really good at explaining concepts. I could continue working in software development.

I have a BS Mathematics and Computer Science minor, earned prior to my software career. And I am halfway through a MS Computer Science (part-time). Grades are solid (3.8 undergrad, 4.0 grad), the schools are good, and GRE scores are good enough (>160).

I would either return to my career or I would seek a position teaching at the college level. I am not concerned about about tenure or reputation, nor do I expect to become wealthy. I am willing to TA, and would probably enjoy it.

closed as off-topic by Brian Borchers, Buzz, Enthusiastic Engineer, gman, user3209815 Jan 29 '18 at 7:59

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • ""Shopping" questions, which seek recommendations or lists of individual universities, academic programs, publishers, journals, research topics or similar as an answer or seek an assessment or comparison of such, are off-topic here. (See this discussion for more information.)" – Brian Borchers, Buzz, gman, user3209815
If this question can be reworded to fit the rules in the help center, please edit the question.

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    Why do you want a PhD? That matters quite a lot in identifying appropriate programs to apply to. – ff524 Jan 26 '18 at 4:54
  • Career options, teaching, bucket list - is it ever a single answer? – ChuckCottrill Jan 26 '18 at 4:58
  • Have you checked which universities have offers at the moment? Once you have that list - you may be able to shorten the list... – Solar Mike Jan 26 '18 at 6:57
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    I strongly disagree with the close vote. OP is not asking which departments to apply to, but rather how to decide which departments to apply to. This is not a shopping question, but a "how to shop" question. – JeffE Jan 26 '18 at 15:21
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    How are you not traditional? Why are you unable to seek relevant advice from professors and fellow student? – paparazzo Jan 26 '18 at 16:24
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Since I am not a traditional candidate, I am unable to seek relevant advice from professors and fellow student. — Nonsense. Of course you can seek relevant advice from professors and fellow students. Yes, you're a non-traditional student, but you're not so non-traditional that "traditional" advice doesn't apply to you.

You need answers to the following questions, not necessarily in the following order:

  • What kind of research do you want to do? — Are you interested in doing research in algebra, algorithms, analysis (real or complex), animation, architecture, artificial intelligence,...? Which subfield(s) of mathematics and/or computer science do you enjoy working in, and which subfields are you actually good at? This is not the same question as "Why kind of classes you you want to take?" A PhD is a research degree; admissions committees will be looking for your interests and potential as a researcher. It's perfectly fine not to know precisely which subfield you want to work in, but you should at least have some explicit priorities.

  • Who does the kind of research you want to do? — Who are your potential advisors? Your advisor and your other faculty mentors/collaborators have at least as big an effect on your success (and enjoyment) as a PhD student as the department you apply to. Look for departments that have at least two or three people who are active and successful in your target subfield(s). You don't want to find yourself in a department where nobody does what you care about, or more subtly, where only one professor does anything you care about, but the two of you don't get along for some reason.

  • What are other strengths and weaknesses of the departments? — Now that you know who you'd like to work with, and where those people work, other factors come into play. How strong is the overall department? What are the course requirements? Given your past record (and likely recommendation letters), how likely are you to be admitted? How likely are you to get funding? What is the expected workload for teaching assistants? Are there many other nontraditional students? Again, you don't need firm answers to every question about every department, and some questions can only be answered by a physical visit after being admitted.

  • Can you see yourself living there for five years? Is the department in a big city/small town? What's the weather like? What's the traffic like? What are the local politics? How good is the local food/coffee/beer? Any good nearby farmer's markets / museums / hiking / judo / frisbee golf / hip-hop / swing dancing / fishing / rock-climbing / maker spaces / improv / underwater hockey / SCUBA / musical theater / Zen centers? How close are your family and friends? If you're married: Are there opportunities for your spouse? If you have kids: How good are the schools?

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On the how part, generally you shop around like you would for a car. Some really good resources you might utilize are at your local university's academic advising offices (you mention you are in a MS program right now, your department may already have one check your school's website). As some I've seen, there are generally department specific academic advisors that can field questions as to what programs suit x,y,z interests. Many times they can and will field questions from prospective students, even if you don't actually end up applying (you are prospective if you are looking around).

Web searches for your program of interest is also a very viable and strong way to find prospective degrees and programs. For instance, a quick web search of "PhD Computational Mathematics" brings up quite a few programs Princeton, Caltech, etc. These are going to be ofcourse the big schools that get returned first, but once you get the idea of what specific type of program you might want to pursue, you can then go to your local schools and ask: What do you have in Applied Math? What do you have in Computer Science? Is it theoretical or applied? Is there departmental funding for students or will I need to seek my own funds (big one)? and so on.

A third option is a bit more involved, expensive, and time consuming. You might find it useful to go to your local university and see if you can enroll as either a non-degree or second degree undergrad. I would recommend second degree, even if you don't plan on completing it, as it helps with signing up for classes. This way you can take some time getting to know what is out there now and where your interests really lie, and get prospective recommended classes out of the way before you tack on graduate fees.

Now as for prospective degrees if you want to combine CS and Math, then you may want to check out applied and computational math programs. Generally you will probably find this type of degree (US) in a school's Applied Mathematics department. This list of Computational Math Ph.D. Programs might be useful to you. When I first went through school this type of program really didn't exist in the schools I attended when I attended. I recently decided to take some refresher courses in calculus and it was through attending a local university for these courses that I found the applied math department. This then led to the Computation Mathematics with Physics dual program that I will ultimately pursue.

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