Programming is not required in Math 513. Nevertheless, you will likely want to use a computer to play with problems, examples, etc. You are free to use whatever computer software/language you like. This page gives some information about the systems I know about.
WARNING — it is up to you to acquire suitable software to use, to install it on your own computer/tablet/device, and to learn to use it (if you want to use it).
This is a calculator originally designed for researchers in number theory. It is very fast, has all the functionality one could need for this course, and its scripting language is very easy to learn. I use it daily in my own research, so I’m very familiar with it; it is my software of choice for class demonstrations. The downside (for some) is that it is terminal-based; there is no fancy GUI or “worksheet” interface provided.
Available (free) from here.
This is a large computer algebra system that incorporates many mathematical computing packages under one roof. Sage is built on Python and so if you are familiar with the latter you will likely be comfortable with Sage. It has a browser “worksheet” interface that many find comfortable. Sage is also becoming more well-known as an analytical tool in the real world, although at the moment not as much as Mathematica. So knowledge of Sage could be a marketable skill.
Available (free) from here.
Mathematica is one of the oldest computer algebra systems; probably you have used it in other courses. It has extensive support for combinatorics.
Mathematica is not free, but as a UMass student you can get it free. Probably you should do that no matter what.
Mathematica skills are definitely marketable, because it is frequently used in analytical settings. It looks good on your CV.
This is a website that is basically a free front-end to Mathematica. You should be able to do computations there.
MAGMA is a general purpose computer algebra system along the same lines as Mathematica, but it was designed with pure mathematics researchers in mind (unlike Mathematica). I am not as familiar with it, but lots of my colleagues use it.
Available from here.