I'm interested in how a MSc in Mathematics, MSc in Applied Mathematics, and MSc in Applied and Computational Mathematics compare in terms of content, but also in terms of how they are perceived and the opportunities they create. Can all three make you a qualified candidate to teach math at the community college level? I would like to keep open the possibility of one day getting into a PhD program in mathematics, how would having a MSc in Applied and Computational Mathematics affect one's chances of being accepted as compared to the other MSc programs?
Here is my perspective as someone who was the Graduate Coordinator in my mathematics department (at University of Georgia), hence principally involved in graduate admission. It is:
I am rather clear on the distinction between mathematics and applied mathematics: the latter is a subset of the former; its complement is "pure mathematics." However one could point to some disputed territories here. I am less clear on the difference between applied mathematics and "applied and computational mathematics." In some areas of mathematics, if you put "computational" in front of it, it need not be applied: this tends to be true in more algebraic areas, e.g. computational number theory. In other areas of mathematics, appending "computational" does seem to make it applied: e.g. computational PDEs is usually considered applied mathematics. In my opinion, this again serves to illustrate that the pure/applied distinction may not mean as much as we think.
How does a master's degree in one of these three areas look? I think all three master's degrees look virtually identical, in particular for trying to get a job at a community college but also for every other purpose I can think of. The distinction between one institution versus another is more important than the name of the degree...and what you actually learned is much more important than both of these.
Mathematics (pure math) implies that the study is to advance mathematics itself. New theories, new areas of study, etc.
Applied mathematics implies that mathematics is being used to solve problems in other domains, business, biology, astronomy, whatever. The list is long and varied. Such study might occasionally lead to advances in math, but that isn't normally the intent.
Computational applied mathematics is like applied math, but uses a fusion of ideas from both math and computing for the solution of problems from, usually, other domains. That might be something like machine learning, for example.
There is a fourth possibility, actually, which is the use of computational techniques to solve problems within math itself. A couple of important theorems were solved at least partially in this way: The Four Color Theorem and work related to Fermat's Last Theorem.
For later doctoral study mathematics itself would probably be best, though there are some departments/universities that have a combined faculty so you can choose. For industry, computational applied math would probably be best since you learn a lot of useful tools for industrial application.
At the community college level any will probably do fine, since the coursework of students in introductory.