This is an example of how to do some simple typesetting in \TeX.  If
you already know how to do this, you can do it however you feel
comfortable.

To finish question 2 on this problem set, do the following.

Edit a .tex file (like this one); let's say you've called it question2.tex.

Compile it.  On Athena, you can compile it by typing: tex question2

Check the results by typing: xdvi question2

Repeat until done.

There are a number of online resources to help you learn to do the
basics.  (Michael Doob's ``A Gentle Introduction to \TeX'' is a good
example.)  There is also Donald Knuth's \TeX book if you feel like
spending money or raiding the library.

\vskip 0.5in


The main point is to be able to enter some mathematics equations.

To typeset a mathematics equation in the middle of a line, you enclose
it in dollar signs, like so: $x + y = 4$.  If you want it to get its
own line, enclose it in double dollar signs.
$$
x + y = 1
$$
You can add superscripts:
$$
x^2 + y^2 = 1
$$
Or subscripts:
$$
x_1 + x_2 + x_3 = 1
$$
Or superscripts and subscripts:
$$
x_1^2 + x_2^2 + x_3^2 = 1
$$
If you want a larger formula in a superscript or subscript, enclose it
in braces:
$$
a_{i,j} = x^{i+j}
$$
Fractions:
$$
{1 \over p} + {1 \over q} = 1 
$$
$$
{1 - p^2 \over 1 - p} = 1 + p
$$
Uppercase and lowercase Greek letters:
$$
\alpha + \beta + \gamma + \delta = \Lambda
$$
Other miscellaneous mathematical symbols:
$$
\in, \cdot, \times, \ast, \le, \ge, \exists, \forall, \langle,
\rangle, \sim, \ldots
$$
Sums:
$$
\langle \chi, 1 \rangle = {1 \over |G|} \sum_{g \in G} \chi(g)
$$
Et cetera, et cetera.

\end
