# Explorations in Computational Number Theory

Number theory is one of the oldest, deepest and most vibrant branches of modern mathematics. It centrally incorporates some of the most sophisticated and profound mathematical ideas that have been developed (witness the recent proof of Fermat's Last Theorem) and yet remains broadly useful in many areas of pure and applied mathematics. It is remarkable how often number theory comes to bear both in other areas of mathematics and in applications. A notable recent example is internet security whose protocols are based on number theoretic problems. Number theory has historically been motivated by the study of properties of integers and solutions to equations in integers, but now includes many other aspects, each with its own flavour and viewpoints. Broadly speaking, these can be divided into Analytic, Algebraic, Diophantine, and Geometric aspects of Number Theory. Research in Number theory today often involves knowledge and expertise from areas such as Algebra, Algebraic Geometry, Analysis, Combinatorics, Probability Theory, Representation Theory, Topology. Connections to applicable fields include Coding Theory and Cryptography. At the IRMACS Centre, we have a strong group in Number Theory which covers the spectrum of Number Theory. Together with the groups at the University of British Columbia and the University of Washington at Seattle, we form one of the largest groups of Number Theory Researchers in North America. The IRMACS Centre has played an important role in hosting the SFU - UBC Number Theory Seminar and Pacific Northwest Number Theory Seminar. The group members are also active participants in the programs and initiatives of the PIMS and MITACS.

### About Project Leader: Drs. Peter Borwein & Stephen Choi

Dr. Peter Borwein is a full professor in the Department of Mathematics of Simon Fraser University and the Founding Director of the IRMACS Centre. After completing a Bachelor of Science in Honours Math at the University of Western Ontario in 1974, he went on to complete an MSc and Ph.D. at the University of British Columbia. He joined the Department of Mathematics at Dalhousie University. While he was there, he, his brother Jonathan Borwein and David H. Bailey of NASA wrote the 1989 paper that showed a proof for computing one billion digits of π. They won the 1993 Chauvenet Prize and Hasse Prize.

Dr. Stephen Choi is an associate professor in the Department of Mathematics of Simon Fraser University. After completing a Bachelor of Science and Masters of Science at the University of of Hong Kong in 1991, he went on to complete a Ph.D. at the University of Texas at Austin in 1996. Dr. Choi's research interests include Diophantine approximations, Diophantine equations, Goldbach-Waring problem, polynomials with restricted coefficients and merit factors of binary sequences.