Mathematics
http://hdl.handle.net/10211.3/141103
2018-07-21T23:08:10ZEquity oriented practices in a college level pre-calculus classroom
http://hdl.handle.net/10211.3/204079
Equity oriented practices in a college level pre-calculus classroom
Zambrano, Diana
Equity-oriented practices have been studied and researched primarily in the K-12
setting (Rubel, 2017). The examples of these practices in college have mostly been
studied in developmental math courses (e.g. Frankenstein, 2014). College instructors
express the concern that topics relating to social justice are too controversial or that
integrating them into math courses will take time and focus away from the mathematics
that students are supposed to learn. In this study, I designed and enacted three lesson
lessons for college pre-calculus, each incorporating different aspects of equity-oriented
pedagogy. The students’ experience in these lessons were compared with student
experience in more standard pre-calculus lessons on the same topics taught by the same
instructor in another section of the course.
Results show that students did have different experiences between the two sections
section using the social justice lessons, with higher rates of feeling supported and that
they belonged as members of the classroom than in the traditional lessons. These
students also indicated more frequently that they found the mathematical content relevant
to their lives. The two classes had a similar distribution of course grades and results on a
common cumulative assessment indicated that that the introduction of equity-oriented
lessons did not hinder students’ mathematical learning. This work indicates that it is
worth continuing to investigate the use of equity-oriented lessons at the college level.
This will require investing in professional development for both instructors and students
to be able to comfortable facilitate and engage in these lessons.
2018-01-01T00:00:00ZGeometric extensions and the 1/3 - 2/3 conjecture
http://hdl.handle.net/10211.3/204003
Geometric extensions and the 1/3 - 2/3 conjecture
Sehayek, Sam
The 1/3—2/3 Conjecture is a famous open problem that deals with partially ordered
sets, called posets. Understanding the linear extensions of a poset can unlock hidden
structure with interesting applications and further questions. The conjecture says
that in every finite poset that is not totally ordered there is a pair x and y, such
that x < y in 1/3 to 2/3 of all the linear extensions. Such pairs are called balanced
pairs. We develop a geometric version of the conjecture, amenable to computational
analysis by considering one dimensions projections of Euclidean realizations of the
poset. We confirm the geometric 1/3—2/3 conjecture for certain classes of posets,
for which the original 1/3—2/3 conjecture is currently out of reach. Ultimately, we
derive quantitative estimates for the number of geometrically balanced pairs for the
hom poset.
2018-01-01T00:00:00ZConvergents and best approximates
http://hdl.handle.net/10211.3/203972
Convergents and best approximates
Santellano, George
Experts agree that if a generalization for finding the convergents of the continued
fraction of a real number existed, the Littlewood conjecture would not remain
unsolved. We will consider two natural generalizations of the convergents of the
continued fraction of a single real number, based on Lagrange’s characterization in
terms of best approximates of the second kind. We consider a generalization of a
convergent using pivots, and a generalization called an TV-best approximate. We
will clarify the relation between these two generalizations by showing that every TVbest
approximate is a convergent. Moreover, we show how the notion of an TV-best
approximate is sensitive to choice of norm TV by exhibiting an example of an TV-best
approximate with respect to one norm which is not an TV-best approximate with
respect to a different norm. Finally, we show TV-best approximates have the nearest
integer property that convergents have by definition.
2018-01-01T00:00:00ZThe dual complex of Mgn in higher genus
http://hdl.handle.net/10211.3/203958
The dual complex of Mgn in higher genus
Quillin, Kyla
In 2016, Giansiracusa proved that a collection of boundary divisors of the moduli
space of genus 0 n-pointed curves has nonempty intersection if and only if all pairs
in the collection have nonempty intersection. We characterize the combinations of
genus and number of marked points for which the analogous statement is true.
2018-01-01T00:00:00Z