On March 27 and 28, 2009, Noah Prince took eight students to the 26th annual Rose-Hulman Undergraduate Mathematics Conference at the Rose-Hulman Institute of Technology in Terre Haute, Indiana.
The students (Dawna Bagherian, Bonny Jain, Alina Kononov, Vlad Kontsevoi, Santina Lin, Zack Maril, Peter Nebres, and John Wang) listened to and presented talks in advanced mathematics, met other students from midwestern colleges and universities, talked to mathematics faculty, and raised a minimal amount of Cain across southwestern Indiana.
Despite being the only high school in attendance, the IMSA delegation had more student participants (8) and more student speakers (5) than any other school.
The titles and abstracts of the talks by IMSA students are listed below.
Bonny Jain
On the Embedding of Degree Sequences on the Projective Plane and Torus
Abstract: The degree sequence of a graph is the list of its vertex degrees
counted with multiplicity (usually given in nonincreasing order). A graphic
realization of a sequence S is a graph with degree sequence S. An embedding
of a graph is a drawing of its edges and vertices on a surface such that no
edges cross. The problem of determining which degree sequences have the
property that every graphic realization is planar was addressed by Prince
and Wenger (2008). This raised the question of which degree sequences have
every realization embed on other surfaces, namely the projective plane and
the torus. In this talk we discuss joint work with Prince regarding the
embedding of realizations of degree sequences on the projective plane and torus.
Santina Lin
Origami Axiom 6: Solving Cubic Equations and Trisecting Angles
Abstract: The Huzita-Hatori axioms are a set of rules of the
mathematical principles of origami. They describe the operations on
the Euclidean plane that can be made when folding a piece of paper.
Each one of the seven axioms could be visualized mathematically and
by folding paper. One of the axioms, Axiom 6, states that, given two
points p1 and p2 and two lines
l1 and l2, there is
a fold that places p1 onto l1 and
p2 onto l2. This
axiom is practical in solving cubic equation and thus angle trisection.
In this talk, I will present the seven axioms and how origami can be
used to trisect an angle.
John Wang
The Educational Black-White Achievement Gap: Significant Factors in a Static State Intergenerational Model
Abstract: The black-white achievement gap is a robust empirical phenomenon in economics. Since the early
1960s, researchers have found that black students score consistently worse on tests than white students. This
presentation explores the factors that cause such a gap and attempts to understand the determinants of lower
test scores for blacks. We develop a model that exhibits a static state variation of Neal's (2005)
intergenerational achievement gap model. Then, we proceed to analyze data from two cohorts of middle
schoolers with multivariate regression analysis-one in Philadelphia and a randomized sample that comes from
the Tennessee Star Project. We find that a statistically significant portion of the residual gap persists and
cannot be fully explained with the set of covariates available. We conclude that school effort and study skills
are the primary determinants of worse academic performance, but that these may be linked to other exogenous
variables, such as socioeconomic status or school quality.
Peter Nebres
Lattice Geometry
Abstract: Consider the two-dimensional integer lattice Z2,
where the vertical and horizontal distance between consecutive
lattice points is 1 unit. A lattice shape is a polygon that can
be drawn so that its vertices are all on the lattice points. There
are many polygons that are not lattice shapes. In this talk, I will
show why certain shapes, such as equilateral triangles, are not
lattice shapes.
Vlad Kontsevoi
Problem Solving in Elementary Mathematics: The IMO and Putnam Competition
Abstract: The International Mathematical Olympiad (IMO), open to six high
school students from each country and held since 1959, and the William Lowell Putnam
Mathematical Competition, held since 1927 are arguably the two most prestigious
competitions in mathematics available to secondary school students and undergraduates,
respectively. Each competition offers contestants the opportunity to solve problems by
chiefly elementary methods (with the Putnam Competition requiring knowledge of
analysis), but success in either competition requires ingenuity in creative problem
solving. In this talk, I will present applications of fundamental mathematical ideas
such as invariance, symmetry, and induction to problems from the IMO and from the
Putnam Competition.