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\LARGE Math 129: Topics in Number Theory (Spring 2005)\\
{\sf http://modular.fas.harvard.edu/129-05}\\
Course: TuTh 10-11:30\\
Office Hours: TuTh 3--4\vspace{1em}\\
\large
William Stein ({\sf was@math.harvard.edu})
\end{center}
\section{Textbooks}
The main text for this course are the notes that I've written and will
be handing out. There are also many other books on algebraic number theory
and elliptic curves, and I encourage you to look at some of them. For
example, there is a book by Marcus that is popular with students.
\section{Course Topics}
\begin{itemize}
\item{}{[\bf Algebraic Number Theory]} The foundations of algebraic number theory, including unique
factorization, finiteness of the class group, and Dirichlet's unit
theorem.
\item{}{[\bf Elliptic Curves]} My goal will be to give a complete proof of finite
generatedness of the Mordell-Weil group of elliptic curves over
number fields. This theorem mostly reduces to an application of the main
results of algebraic number theory from the first part of the
course. After we prove the Mordell-Weil theorem, I will talk about
the Birch and Swinnerton-Dyer conjecture.
\item{}{[\bf Computation]} How to compute the objects we will encounter
in the course, both in theory and practice (i.e., with actual software).
\end{itemize}
\section{Prerequisites}
\begin{itemize}
\item Math 122 -- Groups, rings, fields, etc.
\item Ability to follow and create nontrivial mathematical arguments.
\end{itemize}
\section{Grade}
Your grade will be determined as follows:
\begin{itemize}
\item 25\% take-home midterm
\item 25\% final project
\item 50\% homework
\end{itemize}
In particular, note that there will be no in-class exams (subject to
university approval). If you get 90\% of points you'll get at least
an A-, 80\% will give you at least a B-, and 70\% at least a C-.
\section{Homework}
There will be one HW assignment per week. It will be assigned on
Thursday, and due the next Thursday. Though I will not accept
late homework, your lowest homework grade will be dropped.
\begin{center}
{\bf You are allowed to work together on homework problems!}
\end{center}
BUT, write up your solutions individually, and carefully
acknowledge the people and other sources that helped you.
\section{Office Hours}
My office is Science Center 515, and I will be there on {\bf Tuesday
and Thursday, 3:00--4:00pm} (except on Feb 10). You can also make
an appointment with me if you want to see me outside of my
office hours. My office phone number is 617-495-1790.
\section{Dining}
Faculty members are granted unlimited meals in undergraduate houses
when accompanied by a student. So please invite me to dine at your
house.
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