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%%%%% In order to set a counter to enumerate and then write and then enumerate again, look at model in 316Final.tex
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\begin{document}

\title{Differential Topology Problem Set \#6}
%
\author{Due: Thursday, May 5}
\date{}
\maketitle

\begin{enumerate}
\item Chapter 2, Section 4, \#1.
\item Chapter 2, Section 4, \#5.
\item Chapter 2, Section 4, \#7.
\item Chapter 2, Section 4, \#8.
\item Chapter 3, Section 2, \#2.
\item Chapter 3, Section 2, \#4.
\item Chapter 3, Section 2, \#14.
\item Chapter 3, Section 3, \#7.
\item Chapter 3, Section 3, \#9.

\newcounter{number}\setcounter{number}{\value{enumi}}
\end{enumerate}

%\begin{enumerate}
%\setcounter{enumi}{\thenumber}
%\item Find a basis of $V\otimes W$ (given a basis of $V$ and of $W$). Find the dimension of $V\otimes W$.
%\setcounter{number}{\value{enumi}}
%\end{enumerate}



\newpage

\begin{center}
{\bf Additional problems for graduate students, or undergraduate extra credit}
\end{center}


\begin{enumerate}
\setcounter{enumi}{\thenumber}

\item Chapter 3, Section 3, \#17. If you want to use other exercises, as is suggested in the hint, be sure to PROVE any of the statements you use.

\item Calculate the Euler characteristic of $S^2$. Calculate the Euler characteristic of the two-torus $T=S^1\times S^1$.

\end{enumerate}

\end{document} 
