More than twelve years ago, a talk on "Ducci games"
delivered jointly by two Ohio Northern University students at the 2001
Ohio MAA Spring meeting initiated a fairly long streak of
undergraduate research in the area of number theory at our school.
Since then, Ohio Northern University students presented 40 talks and
posters in the broad area of number theory at various mathematics
meetings, and were co-authors of 11 research articles in number theory
which appeared in peer-reviewed mathematics journals. We were
especially pleased to see our research on "greatest prime factor
sequences" (published in Fibonacci Quarterly in 2010) featured
alongside other "noteworthy variations on the Fibonacci numbers" in
the keynote talk at the 15th International Conference on Fibonacci
Numbers held in Budapest (June 25-30, 2012), and cited in various
other journals. In the light of the speaker's experience as an
undergraduate research advisor, we will try to address some issues of
interest regarding the impact of undergraduate research in the outside
mathematical community. This "impact" may be viewed as a long-sought
fulfillment or closure of the combined efforts of faculty and students
engaged in undergraduate research, which ultimately takes a life of
its own. We will explore open-ended difficult questions such as: What
does it mean to make an impact? Are there specific strategies for
smaller schools? Can presentations make an impact? What is the
relationship between undergraduate research and faculty research? Is
it harder for pure mathematics?
My talk (abstract) at the 2013 RMS-AMS Special Session of Discrete Mathematics and Theoretical Computer Science
in Alba Iulia: Uniform distribution for a class of
k-paradoxical oriented graphs By using estimates for incomplete character sums with polynomial arguments, we provide uniform distribution results for the
dominating sets in a class of
k-paradoxical regular oriented graphs, including the Paley tournaments. Moreover, we will explore a
method of quasi-random tournament generation from fi nite sets of natural numbers, by using the greatest prime factor function.