\documentclass{article}[11 pts] 
\begin{document}

\centerline{\bf THEORY OF NUMBERS, Math 115 B}
\centerline{\bf Some Suggested projects }
\vskip 5pt

\begin{enumerate}

\item Write a program that counts the number of lattice points inside
planar simple polygons.

\item Write an essay on the Riemann Hypothesis. What is it and why is
it important.

\item Explain how the knapsack cyphering method can be broken (work by
Shamir and Zippel).

\item Discuss what are pseudorandom numbers and how one can obtained
them using number theory. Why are pseudorandom numbers important?

\item Write a computer program that implements a simple version of
the RSA encryption method.

\item Discuss the problem of representing integer numbers in terms
of quadratic forms.

\item which numbers are the sum of 5 nonzero squares?

\item Discuss all you can about the LLL algorithm to find the shortest
vector of a lattice. Explain connections to cryptographic systems.

\item choose a famous sequence of integers (e.g Fibonacci numbers,
binomial coefficients, etc) and investigate all you can about it.

\item What are Elliptic curves and why are they interesting for
computer applications.

\item Write an essay on the life and work of Minkowski, Gauss, Euler
Wiles, or any other famous number theorist. Discuss in detail one
theorem of your choice.
 

\end{enumerate}

\end{document}





