The goal of this paper is to describe the Elliptic Curve Method (ECM), an integer factorization algorithm first proposed by Lenstra. Before describing this algorithm, we first discuss some preliminaries. In Chapter 2, we prove some elementary results from number theory and explicitly describe the RSA algorithm. In Chapter 3,...
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...
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...
We model a fish population in a spatial region comprising a marine protected area and a fishing ground separated by an interface. The model assumes conservation of biomass density and takes the form of a reaction diffusion equation with a logistic reaction term. At the interface, in addition to continuity...
In this thesis we study a numerical analysis problem motivated by the need to simulate an event such as an oil spill in a deep water environment. Numerical simulation can help to mitigate the disastrous effects of such events by aiding the management of risk assessment and recovery efforts.
However,...
In 2012, a university in the north western United States began offering a redesigned college algebra class that had a greater emphasis on active learning. Specifically, two out of four class periods were completely devoted to students working together in small groups on carefully designed worksheets. Two years later, the...
Counting problems are rich in opportunities for students to make meaningful mathematical connections and develop non-algorithmic thinking; their accessible nature and applications to computer science make counting problems a valuable part of mathematics curricula. However, students struggle in various ways with counting, and while previous studies have indicated that listing...
Over several decades, much attention has been paid to the preparation of K-12 teachers. More recently, the body of literature on graduate teaching assistants' preparation for teaching has begun to increase. Since many graduate teaching assistants are hired as community college and university instructors, it is important to understand how...
A teacher's mathematical knowledge for teaching has been shown to have a positive correlation with their students' success (Monk, 1994). So, when half of the students that start out in a STEM major switch out to a non-STEM major before graduation to in large part to instructors pedagogical methods and...
In this work, we provide a detailed analysis of a discrete time regime switching financial market model with jumps. We consider the model under two different scenarios: known and unknown initial regime. For each scenario we investigated conditions that guarantee the model's completeness. We find that the model under consideration...