I will recommend two computational resources for this course. The first is Wolfram|Alpha, which allows you to do quick, one line computations without worrying really at all about exactly how you type your command. For example:

The second resource is a free and open-source language called SageMath (or Sage, as it used to be known). The computational investigations I include in the course notes will be in Sage. Sage can also be run in-browser, at sagecell.sagemath.org. A more full-featured browser-based experience is available at SageMathCloud, and nowadays you can also install Sage on your computer relatively painlessly, thanks to installation binaries the developers have made available.

The advantage of Sage is that you can run blocks of code; the disadvantage is that your code has to be correct. Wolfram|Alpha will try to guess what you mean, whereas Sage does exactly what you tell it to do.

See the official SageMath caluclus tutorial for help getting started with Sage.