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\begin{document}
\title{Analysis Seminar: Assignment 7}
\maketitle
\begin{enumerate}
\item  Read section 23.  As used on page 201 the word discrete''
has the following meaning.
\begin{defn}
A subset $$S$$ of a metric space is discrete if it has no cluster
points.
\end{defn}
You should note that this is stronger than saying that $$S$$
consists entirely of isolated points.

\end{enumerate}
\section*{Doing}  In each case I list what is a reasonable
prioritization.  Your own priorities may differ a bit from mine.
\begin{enumerate}
\item All the problems at the end of section 23 are worth doing.  If
you are not confused by the reading, I would prioritize them in
order: 3, 6, 5, 4, 2, 1.  If you are confused by the reading, I would
prioritize them in order: 1, 2, 3, 4, 5, 6.  Do at least two or three

\item  Problems 3--6 at the end of section 24 are all applications
of the theorem in problem 2.  You may wish to do these before proving
the result in 2.   If you are comfortable with the
material in this section I prioritize the problems: 2, 5, 6, 3, 4,
1.  If not, 1, 3, 5, 4, 6, 2.  Again, do at least two or three of

\item  The problems at the end of section 25 are mostly interesting,
but only 4 and 8 involve the real material of the chapter more than
other sorts of cleverness.  I would prioritize them as follows:  8,
4, 3, 1, 2, 5, 6, 7.  Do at least one or two of your high priority problems.

\end{enumerate}

\section*{Writing}
Expertly write up at least one page of work you are proud of from this
week.
Hand this in no
later than than noon on Tuesday following Break.
\section*{Presentations}
\begin{pres}[Tom]
The definition of manifold and an example or two.
\end{pres}
\begin{pres}[Rob]
Theorem 24.4 and either solution or confusion involving problem 24.2
\begin{pres}[Mike]
The definition of integral and the lemmas involved in showing that
the integral is well-defined.
\end{pres}

\end{document}