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...
This thesis is an exploration of writing a music album from a singer-song writer perspective. It contains the process of writing lyrics and music, inspiration from other artists, as well as performance. It goes through the emotional ebbs and flows of creative writing, ground work for recording an album and...
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 will study certain generalizations of the classical Shannon Sampling Theorem, which allows for the reconstruction of a pi-band-limited, square-integrable function from its samples on the integers. J. R. Higgins provided a generalization where the integers can be perturbed by less than 1/4, which includes nonuniform and...
We present an analysis of the relationship between spectral lag and luminosity in time-resolved segments of long gamma-ray bursts detected by BATSE, an experiment aboard the Compton Gamma Ray Observatory satellite. For full bursts, there is a well-established correlation between the lag, which is easily computed, and the total burst...
In this work we consider two multiscale applications with tremendous computational complexity at the lower scale. First, we examine a model for charge transport in semicon- ductor structures with heterojunction interfaces. Due to the complex physical phenomena at the interface, the model at the design scale is unable to adequately...
Translation surfaces can be viewed as polygons with parallel and equal sides identified. An affine homeomorphism φ from a translation surface to itself is called pseudo-Anosov when its derivative is a constant matrix in SL₂(R) whose trace is larger than 2 in absolute value. In this setting, the eigendirections of...
In this thesis we construct compatible discretizations of Maxwell's equations. We use the term compatible to describe numerical methods for Maxwell's equations which obey many properties of vector Calculus in a discrete setting. Compatible discretizations preserve the exterior Calculus ensuring that the divergence of the curl and the curl of...
Robotic global navigation is often based on the assumption that the world is static. It assumes that obstacles present in maps will be there later and new obstacles will be dealt with by a local planning algorithm. When robots interact in an environment inhabited by people, this assumption does not...
Markov chains, discovered over one hundred years ago by Andrey Markov in an
attempt to analyze the distribution of vowels and consonants in Russian poetry, have
evolved in multiple fields over the last century to become a mainstay of statistical
modeling and computation. maRkov is a package of software to...