It is encouraged that you use SAGE to do numerical computations assigned in this course, as well as to get a numerical feel for results covered in class. You can download SAGE if you like at William Stein's website. Of course, that requires you to have a personal computer and be able to work through the installation yourself. Alternatively, you can use the online SAGE notebook. This seems to run a bit slower then if you were to install SAGE directly onto your computer, but has the advantage it can be used anytime on any computer. To access the SAGE notebook, click the following: SAGE Notebook. Though there are instructions on the SAGE notebook homework, below are more detailed instructions for getting started.
1. Go to the page http://www.sagenb.org. This is the main page for the SAGE notebook.
2. In the upper left-hand corner is a box with New Delete Worksheets with a list of worksheets below it. Since we will assume this is the first time you're successfully going to use the notebook, go ahead and click "New".
3. It now asks for a Name: and Password: You can choose anything you like here, say Name: Math573 Password: numbertheory. Once you have entered your name and password, click the add button.
4. Navigate your way down the list of worksheets to find the one named "Math573" and click on it.
5. This opens up your notebook session. It should say "Worksheet: Math573 [locked]. Click the [locked] and enter your password to unlock the worksheet.
6. Move your mouse button just under the "Worksheet: Math573" and you will see a blue line. Click this or just below it. This opens a window where you can type commands.
7. Type your command and hit shift-enter at the same time. A green box will appear showing that SAGE is doing the calculation. Start with something simple like 2+2 to see it is working. This may take time to evaluate, especially at first. I found that it seemed to become faster after I ran a few commands.
8. When you are finished, be sure to delete your worksheet if you do not plan on coming back to it. No reason to clutter up the page.

As the documentation for SAGE is fairly massive, the following link gives "Miscellaneous arithmetic functions", which covers pretty much everything needed in terms of functions in this course.

Miscellaneous arithmetic functions

We will also be using SAGE to do some calculations with elliptic curves. The link to the relevant documentation is given here, though most of the material in the link will be far too advanced for us. I will provide the necessary commands in class as well.

Elliptic curves