2003 Research Experiences for Undergraduates
Computational Number Theory and Combinatorics
Research Projects

Please note that some of these works are still in progress!

Lang-Trotter Conjecture group

This group consisted of Rebecca Bilbro and Eric Manley and was supervised by Kevin James. They implemented algorithms to quickly compute the number of points on a given elliptic curve over a finite field with p elements. They used these algorithms to gather extensive data related to the Lang-Trotter conjecture.

Lang-Trotter Investigation Report

Class Number Group

This group consisted of Brittany Brown and Amy Stout and was supervised by Tim Flowers and Kevin James. They wrote Pari code to compute various sums of Hurwitz-Kronecker class numbers. They studied this data and were led to conjecture formulas for these sums of class numbers. They were then able to prove a couple of these conjectures.

Sums of Class Numbers Report

l-Regular Partition Function Group

This group consisted of Christian Bruun and Chip Swannack and was supervised by Neil Calkin and Kevin James. Christian gathered extensive data on l-regular partition functions and used this data to study various conjectures of Ken Ono and David Penniston.

l-Regular Partitions Report

Coupon Collector Problems Group

This group consisted of Lee Gilman, Natalie Hudson, Rhett Robinson and Dana walker and was supervised by Neil Calkin and Shannon Purvis. They analyzed the probability of collecting c copies of all n baseball cards, assuming uniform distribution, after t trials of collecting r unique cards at a time. They were able to generate some closed formulas based on a combinatorial analysis and are still working on asymptotics.

Coupon Collector Report