This tutorial assumes that the reader already knows the basics of the Python programming language. If you do not, the official Python tutorial is excellent.
This tutorial assumes a decent mathematical background. Most examples require knowledge lower than a calculus level, and some require knowledge at a calculus level. Some of the advanced features require more than this. If you come across a section that uses some mathematical function you are not familiar with, you can probably skip over it, or replace it with a similar one that you are more familiar with. Or look up the function on Wikipedia and learn something new. Some important mathematical concepts that are not common knowledge will be introduced as necessary.
You will need to install SymPy first. See the installation guide.
This tutorial was the basis for a tutorial given at the 2013 SciPy conference in Austin, TX. The website for that tutorial is here. It has links to videos, materials, and IPython notebook exercises. The IPython notebook exercises in particular are recommended to anyone going through this tutorial.