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\begin{document}

\title{Math 18.100B/C, Spring 2012 - Problem Set \# 10}

\maketitle



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\textbf{Professors:} Roman Bezrukavnikov and Jared Speck  \
\\
\begin{center}
{\large \textbf{Due: by 3pm on 5-11-12} (in the Undergraduate Math Office: Room 2-108)}
\end{center}
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}


\bigskip

\textbf{Instructions:} Write your name and whether you
are registered for 18.100B or 18.100C. Students registered for 18.100C are expected to typeset all of their solutions using LaTex.

Collaboration is permitted but you are advised to first attempt
solving the problems yourself, and you must write up the solutions
independently and mention your collaborators and other sources
in your paper.

As always in this course (unless stated otherwise) an answer must be
accompanied by a proof.

\bigskip

\begin{enumerate}

\item (15 points) Problem  4 on page 165.

\item (15 points) Problem  6 on page 166.

\item (15 points) Problem  7 on page 166. 

\item (15 points) Problem  15 on page 168.

\item (15 points) Problem  16 on page 168. 

\item (15 points) Problem  19 on page 168

\item (10 points) Problem  20 on page 169.

\end{enumerate}

\end{document}