Department of Mathematics
http://hdl.handle.net/1957/13737
2017-06-27T06:41:22ZKACZMARZ AND RANDOMIZED KACZMARZ METHOD
http://hdl.handle.net/1957/61479
KACZMARZ AND RANDOMIZED KACZMARZ METHOD
Abubakari, Nurideen
2017
2017-06-20T00:00:00ZA New Algorithm for Computing the Veech Group of a Translation Surface
http://hdl.handle.net/1957/60633
A New Algorithm for Computing the Veech Group of a Translation Surface
Edwards, Brandon (Brandon Gary)
We give a new characterization of elements in the Veech group of a translation surface. This provides a computational test for Veech group membership. We use this computational test in an algorithm that detects when the Veech group is a lattice (has co-finite area), and in this case computes a fundamental polygon for the action of the Veech group on the hyperbolic plane. A standard result, essentially due to Poincaré, provides that a complete set of generators for the Veech group can then be obtained from the side pairings associated to this fundamental polygon.
Our approach introduces a new computational framework used to formulate a membership criterion for the Veech group of a compact translation surface (X,ω). We represent (X,ω) on a certain non-compact translation surface O that can be used to represent any translation surface within the SL(2,ℝ) orbit of the translation equivalence class of (X,ω). The surface O has an easily computed SL(2,ℝ)-action. When this action is restricted to the translation surface representations mentioned above, it corresponds to the usual SL(2,ℝ)-action on the set of equivalence classes of translation surfaces. The Veech group of a compact translation surface is therefore the stabilizer of its representation on O.
Graduation date: 2017
2017-03-17T00:00:00ZQuantitative Study of Math Excel Calculus Courses
http://hdl.handle.net/1957/60588
Quantitative Study of Math Excel Calculus Courses
Watkins, Christopher H.
About twenty years ago, a large, rural, doctoral granting institution with an undergraduate population of approximately 24,000 in the pacific northwest of the United States established the Math Excel program. Students would attend lectures three times a week for 50 minutes like a traditional course, and they would also attend two workshops per week that are two hours each, in contrast to traditional courses with a 50 minute recitation once per week. For several years the university would offer a few sections of Math Excel for several 100- and 200-level mathematics courses each term. During the 2013-2014 academic year, the university dedicated all sections of Math Excel to a particular section of calculus and implemented a Math Excel section of a calculus every quarter with the sequence of courses consisting of differential calculus, integral calculus, and vector calculus. A Math Excel version of differential calculus, integral calculus, and vector calculus were offered during fall term, winter term, and spring term respectively. The purpose of this thesis is to investigate how students in the Math Excel calculus courses performed compared to students in traditional calculus courses. First, a logistic regression model will be used
to model the relationship between pass rates and enrollment in a Math Excel calculus course after controlling for predictor variables and a two-sample t-test will be performed to compare pass rates of students in a Math Excel calculus course and a traditional calculus course. Next, a linear regression model will be used to model the relationship between grade points and enrollment in a Math Excel calculus course and a two-sample t-test will be performed to compare grade points of students in a Math Excel calculus course and a traditional calculus course. Finally, a two-sample t-test will be performed to examine if there is a difference in average grade earned for students that took a Math Excel calculus course in the previous term and students that did not. In each of these cases I found that there is not significant evidence that the Math Excel program has a greater effect on student pass rates, grades, or future grades in calculus courses than traditional versions of the calculus courses. Based on these results, I suggest that more data is gathered to see if there is a change in the results, an in depth analysis of students’ demographics and activities outside the classroom, and looking at the instructor effect and execution in the classroom in order to understand how and whether the Math Excel program benefits students in different ways.
Graduation date: 2017
2017-02-28T00:00:00ZVariations of Mathematics in College Algebra Instruction : An Investigation Through the Lenses
of Three Observation Protocols
http://hdl.handle.net/1957/60045
Variations of Mathematics in College Algebra Instruction : An Investigation Through the Lenses
of Three Observation Protocols
Gibbons, Claire J.
College Algebra is a prerequisite for calculus and is thus an important stepping stone in the careers of STEM-intending undergraduates. However, College Algebra has low pass rates across the United States, interrupting students’ pathways to success. To address this concern, a research-oriented university in the Northwest United States restructured its College Algebra course to increase student engagement and active learning practices. Despite a new common curriculum, wide variation in the mathematical content that is presented by instructors was observed. Through the lenses of three observation protocols applied to video recordings of College Algebra classrooms, this thesis investigates the mathematical content present in lessons covering two mathematical concepts, evaluates the protocols for their ability to capture the variation in mathematics, and synthesizes these results to offer ideas for future research in College Algebra instruction.
Graduation date: 2017
2016-12-06T00:00:00Z