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\noindent\shadowbox{\begin{minipage}{\textwidth}
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{\LARGE\bf Math 124: Elementary Number Theory}\vspace{1ex}\\
\large 
{\tt http://modular.fas.harvard.edu/124}\vspace{1ex}\\
{\sc At Harvard University\\
MWF 11--12 in Science Center 103B}\vspace{1ex}\\
{\bf OFFICE HOURS: Monday 5--6 and Tuesday 2--3}\vspace{1ex}\\
\large 
Instructor: William Stein ({\sf was@math.harvard.edu})
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\section{Topics}
The main ideas of the course are prime numbers, arithmetic modulo~$n$,
public-key cryptosystems, quadratic forms, continued fractions, and
elliptic curves.  This course is {\bf unusual} for an introductory number
theory course in that we will go more deeply into elliptic curves than
usual, we will learn more about using computers to do number
theory, and we will read a novel.



\section{Prerequisites}
You must already be comfortable reading and writing {\bf proofs}.  I
will assume you are familiar with abelian groups, commutative rings,
and fields.  For the elliptic curve part of the course, I will use
some basic complex analysis.  You might want to attend a few of the
Math 113 (complex analysis) lectures, though this isn't essential.


\section{Texts}
Doxiadis's little novel {\em Uncle Petros \& Goldbach's Conjecture} 
is required.  I selected Niven, Zuckerman, and Montgomery's {\em An Introduction to the Theory
of Numbers} as the primary course textbook because it was highly recommended
to me.  I've hardly looked at it.  {\bf The primary text will be
the book I'm writing}, which you can download from the course web page and
print, as it is written.  I will probably select some homework problems from
Niven, Zuckerman, and Montgomery, and you might benefit from
their alternative exposition of many of the topics we will cover.

\section{Evaluation}
\begin{center}
\begin{tabular}{|l|l|}\hline
Weekly Homework & 30\%\\\hline
Project  & 20\%\\\hline
Take-Home Midterm  & 20\%\\\hline
Take-Home Final Exam & 30\%\\\hline
\end{tabular}
\end{center}

\subsection{Homework}
There will be one homework assignment per week, and these may involve
using a computer.  Homework will be assigned on Wednesday and due the
following Wednesday.  The course assistant will not accept any late
homework, but I will drop your two lowest homework grades.
\begin{center}
{\bf Please work together on homework problems!}
\end{center}
Write up your solutions individually and acknowledge those people and
other sources that helped you.

\subsection{Project} 
There will be a project that might be related to Doxiadis's novel, or
the recent deterministic polynomial-time primality test, or something
else number theoretic that appeals to you.  This project will be due
{\bf December 4}, which is the Wednesday after the Thanksgiving break.

\subsection{Exams}
There will be a take-home midterm exam and, subject to university
approval, the final will also be take-home.  You must work on both
exams by yourself.  

The take-home midterm will be assigned on {\bf Wednesday, October 16}, you
will return it on Friday, October 18, and you will know your grade by
October 21, which is the add/drop deadline. The midterm will be
similar to what I would give as a one-hour in class exam. 

\subsection{Attendance}
If you come to class less than half the time, you will not receive a
passing grade in the course, even if you do passing work on the
homework, project, and exams.  Don't take this course if you don't
plan to attend.

\section{Office Hours}
My office is Science Center 515, which is right up the stairs from the
Math Department common area.  I will be available to talk with you
Monday 5--6, Tuesday 2--3, by appointment, or whenever you drop by.

\section{Computing}
I'll give lectures on techniques for using computers to
do experiments in number theory, and create homework problems that
involve computation.

In class I will demonstrate how to do computations using the computer
algebra system MAGMA.  This is not a free program, but I have a
license to use it in our course, so I can give you a copy that runs on
either Windows, Linux, or Mac OS\thinspace{}X.  Also, if you want
access to a powerful computer with MAGMA pre-installed, I can give you
an account on the MECCAH cluster.  



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