Computer algebra systems

Some of you are familiar with systems like Wolfram|Alpha which can automatically do many computations in calculus. Homework problems will sometimes be just a computation which could be done by a computer, and since we're using Webassign, there's no way to check that you've actually done the computation yourself. So, I'll rely on you to be honest about it. Of course it's in your best interest to work out these problems yourself! Without working through examples yourself you won't really understand what's happening, and more immediately, exams will not go well.

That said, the fact that computers can do these things means it doesn't make sense for me to have you do tons of them, so I won't. It also means that it's well worth learning how to use a computer algebra system, and I encourage you to do that, for example to check your answers. One place in this course where they're especially useful is visualizing mathematical objects in 3 dimensions, something that's not easy for many people (including me).

If you do want to use a computer algebra system (CAS), I recommend Sage. I won't give any regular assignments which require a computer (possibly extra credit?), so you can use whatever you want or nothing at all, but Sage has some advantages compared to say, Wolfram|Alpha or Matlab or etc.

• It's free and open-source.
• It can be used online.
• Unlike Wolfram|Alpha, you can create and save whole documents in the Sage notebook, not just single computations.
• The lead developer is a professor in the math department at UW (William Stein), so many people here are familiar with it; you may well take a future course where Sage appears.
• If you want to do something more than one-line computations with a CAS, you'll need to know whatever programming language it uses. Mathematica, Matlab, Maple, etc. all use their own proprietary languages which are used nowhere else. Sage uses Python, which is very popular and which you may already know.

Using Sage

To use Sage, go to uw.sagenb.org and follow the instructions to sign up for an account. If you like you can install it on your own computer, or even build it from source, but uw.sagenb.org lets you run Sage remotely without having to download or install anything. There are many other Sage servers besides uw.sagenb.org (the main public server is in fact sagenb.org), so if it's going slow you could try another one on this list.

Here are some worksheets I've made to explain how you can use Sage to help with various things in this course; this list will grow as the quarter goes on.

• Plotting