Start an exercise set with \exercises and end it with \endexercises. Begin each exercise with \exercise and end it with \endexercise. To list parts of an exercise, use \beginlist and \endlist, and use \item for each part. You may also use \exercises* to begin; this does not insert the heading "Exercises''. You may want to do this, for example, if the exercises form an entire section. Here's a brief sample:

\exercises

You may begin with some remarks or instructions.

\exercise Consider the function $f\colon[0,\infty)\to \R$ 
defined by $f(x)=(x-2)/(x+3)$. Prove that $f$ is a 
one-to-one function.
\endexercise

\exercise Let $A$, $B$, and $C$ be nonempty sets and let
$f\colon A\to B$ and $g\colon B\to C$ be two
functions.  The composition of $g$ with $f$, denoted
by $g\circ f$, is the function $g\circ f\colon A\to
C$ defined by $g\circ f(x)=g(f(x))$.

\beginlist

\item{a)} Suppose that $f$ and $g$ are one-to-one.
Prove that $g\circ f$ is one-to-one.

\item{b)} Suppose that $f$ and $g$ are onto.  Prove
that $g\circ f$ is onto.

\endlist
\endexercise

\remark{Remark} You may insert a remark between exercises just 
as you do in ordinary text. Note that the result is different.

\endremark

\exercise For each real number $x$, let $f(x)$ be the
distance from $x$ to the nearest integer.  Show that
this defines a function $f\colon\R\to \R$ and sketch
the graph of this function.
\endexercise

\endexercises

This produces:

Exercises 3.

You may begin with some remarks or instructions.

Ex 3..1 Consider the function $f\colon[0,\infty)\to \R$ defined by $f(x)=(x-2)/(x+3)$. Prove that $f$ is a one-to-one function.

Ex 3..2 Let $A$, $B$, and $C$ be nonempty sets and let $f\colon A\to B$ and $g\colon B\to C$ be two functions. The composition of $g$ with $f$, denoted by $g\circ f$, is the function $g\circ f\colon A\to C$ defined by $g\circ f(x)=g(f(x))$.

a) Suppose that $f$ and $g$ are one-to-one. Prove that $g\circ f$ is one-to-one.

b) Suppose that $f$ and $g$ are onto. Prove that $g\circ f$ is onto.

Ex 3..3 For each real number $x$, let $f(x)$ be the distance from $x$ to the nearest integer. Show that this defines a function $f\colon\R\to \R$ and sketch the graph of this function.