1.  BUT FIRST: A lightning introduction to Mathematica - double click on the far right of this line to open this subsection

Mathematica is a program known as a   Computer Algebra System.  It can do some amazing number crunching, create cool graphics, create Java applets, even play sounds.  First, let's look at some freaky fractions.  To "compile" a piece of Mathematica code, you will have to press enter while holding down the shift key.  Do so on the next line, which defines the fraction "f1".  SO click with your mouse anywhere in the next line, then press shift-enter:

If that worked properly, you will see an input indication and an output indication.

Now we request the numerical value of this fraction, to, say, 100 digits.  So press shift-enter on the next line:

If we want f1 to 700 digits,we can just go back up, and change the 100 to 700, then press shift-enter.  Do so now.  Are you surprised by the digits in the fraction?

Find the numerical value of f2 to 150 digits.  You will have to shift-enter on f2, then insert your own line of "code"...

Similarly, find the numerical value of f3 to 50 digits.  I have changed the font size now and then to show you that it can be done (in case you are curious, just use the format menu option above...).  What familiar digits arise in the decimal expansion of f3?

As an example of the graphics capability, we will spend a few minutes on...