Research by Undergraduates in Mathematics Boston University Symposium 2007
Poster Presenters: Students
Presenter: David Hansen, Brown University, Class 2010
Faculty Sponsor: Steven J. Miller
Title: The Sato-Tate Conjecture 'on average'
The Sato-Tate conjecture is a beautiful and deceptively simple
statement on the arithmetic of elliptic curves over finite fields, with
surprising links to many other deep results in number theory. Recently the
Sato-Tate conjecture was proven for a wide class of elliptic curves. I will
explicate this conjecture (with numerical examples and motivation), and
explain why it is easy to prove 'on average' in certain situations.
Presenter: Marc Kelechava, CAS 2008, Boston University
Faculty Sponsor: Emmma Previato
Title: On Lattice Path Enumeration and Epidemiology
ABSTRACT: We explore an application of lattice path enumeration to a problem
in epidemiology, the study of the spread of diseases within human populations.
An epidemiologist, Dr. D. Ozonoff, discovered equivalence between this problem
and a problem in lattice path enumeration, a branch of enumerative
combinatorics. A geometric interpretation allows us to compute the number of
underdiagonal paths that touch the diagonal line a fixed number of times. We
derive a formula encapsulating information about the sub-lattices, and then we
deduce the probability that a path is underdiagonal.
We have found one-to-one correspondences with well-known number sequences and the number of underdiagonal paths that touch the diagonal once.
Poster Presenters: Special Career Presentations
Recruitment Director, New England
Teach For America
ABSTRACT [by Emily Berman, SMG 2009, Campus Campaign Coordinator]:
As math concentrators/majors, let me throw some numbers at you:
1 in 10.
Of the 13 million children growing up in poverty in the United States, only
50% on average will graduate from high school. If they graduate, they do so
at an 8th grade reading and math skill set. Only 1 in 10 of these 13
millionwill graduate from a four-year college. That's only
1.3 million. (Source: National Assessment of Educational Progress, 2005,
cited on www.teachforamerica.org)
Teach For America, a nonprofit organization committed to closing the
achievement gap, recruits seniors to teach in low-income schools across the
nation for a two year period. It is a full salary job in which you can
impact the life of low-income students, giving them educational
opportunities that they do not have based upon their socioeconomic
Registering on the website
gives you access to look at the application at no consequences.
Glenn H. Stevens
(Department of Mathematics and Statistics, Boston University,
Program Director, Focus on Mathematics)
Do you like doing challenging mathematics? Do you enjoy sharing ideas with others? If so, then Boston University's Noyce Scholars Program may be the perfect opportunity for you.
With funding from the National Science Foundation, Boston University offers full scholarships for outstanding graduating math majors to our MAT program in Mathematics Education.
The Noyce Program features a number of unusual elements -- focusing on significant mathematics and developing applications to classrooms in high need school settings.
This presentation will describe the Noyce Program in detail and will offer sample mathematics activities for everyone to enjoy.