2002 Research Experiences for Undergraduates
Computational Number Theory and Combinatorics
Research Projects
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Elliptic Curves Group
This group consisted of Jonathan Battista, Johnathan Bayles and Dmitriy
Ivanov. They investigated the Lang-Trotter conjecture and worked
towards proving that the conjecture is true on average for elliptic
curves with various rational torsion subgroups.
Elliptic Curves Report
Partition Function Group
This group consisted of Jimena Davis, Elizabeth Perez and Chip
Swannack.
They developed fast algorithms for computing the coefficients of
the partition function and generated extensive data for this function.
They used this data to study various conjectures related to the
arithmetic of the partition function.
Partition Function Report
Kings Problem Group
This group consisted of Anatoliy Kats, Micah Leamer and Chip Swannack.
They investigated methods for improving known bounds for the Kings
Problem. The group formulated a recurrence using tensor products of
matrices and examined the properties of recurrences of this type.
A generating function was found for the Segre characteristic of Jk tensor
n (where Jk is a Jordan Block of size k).
Kings Problem Report