Mathematics
http://hdl.handle.net/10211.3/141103
2018-03-19T01:05:28ZDecompositions of bivariate order polynomials
http://hdl.handle.net/10211.3/199750
Decompositions of bivariate order polynomials
Karunaratne, Gina
We study bivariate order polynomials on bicolored posets. Richard Stanley first
introduced univariate order polynomials in 1970. Recently, Sandra Zuniga Ruiz
extended his work to bicolored posets and took a look at strict order polynomials
on those posets. We continue her work by exploring what happens with weak as
well as strict order polynomials on bicolored posets. Our main theorem decomposes
bivariate weak order polynomials into a sum of type-ic order polynomials. We also
prove a reciprocity theorem between weak and strict order polynomials.
2017-01-01T00:00:00ZGraduate teaching assistants' enactment of pedagogical techniques in developmental mathematics college courses
http://hdl.handle.net/10211.3/199679
Graduate teaching assistants' enactment of pedagogical techniques in developmental mathematics college courses
Haro, Javier Alejandro
Entry level college mathematics courses are frequently taught by graduate students
in the math department. Educational researchers advocate for these classes to
be taught using group activities, investigations, and student presentations. However,
most graduate teaching assistants (GTAs) have little to no prior teacher training or
teaching experience. At San Francisco State University, a large urban public university,
graduate students are required to take a semester course, Math 700, in teaching
concurrent with their first semester as a GTA. This study investigated the promoted
Math 700 teaching practices that were and were not maintained and developed by
the GTAs in subsequent semesters of teaching. Analysis of classroom observations,
surveys, and interviews reveal how the GTAs were implementing student-centered
pedagogical strategies and where they could benefit from additional professional development.
Results show that all of the GTAs continued to use group work as a
large part of class instruction, even several semesters after completing their Math
700 class. They show greater variation in the opportunities for students to share
their thinking through presentations or explanations in response to teacher questioning.
Implications included the importance of highly developed curricular materials that support student-centered teaching and the need for ongoing support for the
GTAs with questioning and curriculum planning.
2017-01-01T00:00:00ZThe Minkowski continued fraction algorithm from a dynamics perspective
http://hdl.handle.net/10211.3/199634
The Minkowski continued fraction algorithm from a dynamics perspective
Graham, Jon
The Littlewood Conjecture is an open problem in simultaneous Diophantine
approximation. It and the stronger Margulis Conjecture, a proof of
which would imply Littlewood, are currently viewed using dynamic systems.
In this paper we will look at the space o f ’’triple points” , also known
as the domain for the Minkowski continued fraction algorithm, using a
dynamics perspective. We will look at ’’maximal boxes” and associated
’’uniquely” maximal systole cubes with their related lattice configurations
from different perspectives. We will explore possible indexes for these
related lattices. This will be done to attempt to shed some light on the
configuration space of triple points.
2017-01-01T00:00:00ZEffective Wedderburn and applications
http://hdl.handle.net/10211.3/199553
Effective Wedderburn and applications
Fong, Justin
We propose a new algorithmic proof of the classical Wedderburn’s theorem in the
representation theory of finite abelian groups. Namely, the algebra isomorphisms,
known to exist from the classical theory, are explicitly found. This leads to a new
succinct resolution of the well-known isomorphism problem for group rings and an
alternative description of the automorphisms of these algebras. Employing ideas
from algebraic geometry, the global variety of all representations of fixed dimension
for a finite group is introduced and its geometric properties are explored. The last
step involves an extensive computer assisted analysis of the resulting high dimensional
polynomial ideals.
2017-01-01T00:00:00Z