Honors Theses Open Access
 
Filters: Department: "Mathematics" Collection: "ir_htoa" Year Start: 2019
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CreatorTitleDescriptionSubjectDate
1 Martin, IsaacA result concerning the F-Signature and the torsion divisors of strongly F-Regular singularitiesPolstra showed that the cardinality of the torsion subgroup of the divisor class group of a local strongly F-regular ring is finite. In this thesis, we first provide an expository introduction to the field of F-singularities before improving upon Polstra's result by proving that the reciprocal of th...2021
2 Samuelson-Lynn, MosesThe classification of surfaces2024
3 Baker, JustinDesigned Swarming Behavior Using Optimal Transportation NewworksModels of swarming behavior aid in disaster planning, direct the actions of ware- house robots, and can map the foraging characteristics of insects. These mod- els use the optimal behavior of individual agents to determine the behavior of the larger population. Optimal transportation is one such mod...2019
4 Verhaaren, MollyDouble-checking: a statistical analysis of twenty-first century U.S. election recountsElection recounts are an integral part of voting history in the United States. Initiated by the political jurisdiction or by the candidate, they have the power to overturn previously decided election results and have done so on more than one occasion. However, that power may not be worth its price a...2021
5 Fischer, PaulHigh-Performance Computing Performance Metric AnalysisAt present, a signi#12;cant amount of ongoing scienti#12;c research relies on computational models. High-performance computing (HPC) resources are often required to obtain results in a reasonable amount of time. However, as physical and practical limitations constrain the performance progression of ...2019
6 Tang, AnnaMathematical model of drug resistance in ER+ breast Cancer: the role of the microenvironmentOne of the main obstacles to treating cancer is its ability to evolve and resist treatment. In this project, we are primarily interested mathematically modeling how the cancer microenvironment interacts with cancer cells and affects cancer's response to therapy. We aim to develop the mathematical mo...2023
7 Youatt, Catherine C.Mathematics in Visual Art and BalletCultures all over the globe utilize both mathematics and ballet to understand the world and to express their distinct realities. In this way, mathematics and art interact, both with math creating new visual art fields, like fractal artworks, and with art influencing mathematics, as with Renaissance ...2019
8 Johnson, DylanModular forms, Elliptic Curves, and Their Connection to Fermat's Last TheoremFermat's Last Theorem (FLT) states that if n is an integer greater than three, the equation xn + yn = zn has no integer solutions with xyz 6= 0. This incredible statement eluded proof for over three-hundred years: in that time, mathematicians developed numerous tools which finally proved FLT in 1995...2020
9 Kroll, TylerNumerical floating-point code: precision-independence, base-independence, and other programming considerationsThe knowledge and skills of the floating-point-literate mathematician are seldom lauded, though central to the art of translating the world of mathematics into the language of computers. This thesis highlights the importance of floatingpoint literacy through various high-utility techniques relevant ...2020
10 Halberg, CharlesOn causality in machine learningAlthough the studies of causal inference and machine learning arose independently, there are emerging intersections which are proving fruitful for both fields. One of the major modern challenges in AI is to develop robust, generalizable models which can perform across a number of different tasks wit...2022
11 Copinga, AidanOptimal transport and applications in partial differential equationsIn the 18th century, Gaspard Monge created a mathematical framework to find the best way to describe the optimal way to rearrange the dirt dug out from the land into castle walls or other desired shapes. More recently, in the 20th century, Leonid Kantorovich explored infinite dimensional optimizatio...2022
12 Thomas, J PaytonStability of genetic oscillators with distributed delayed feedbackGenetic oscillators govern periodic phenomena in biology including circadian rhythms and are also the basis of biological clocks used in the design of synthetic genetic circuits. Models of genetic oscillators tend to neglect biological detail, however, because biological systems tend to be too compl...2023
13 Bull, August JohnStudying Galois Representations Using Elliptic CurvesDiophantine equations and their solution sets are prominent subjects of study in number theory. These equations are often studied modulo prime numbers or prime ideals in field extensions. Galois Theory is well-suited to study field extensions, but Galois groups are often mysterious. To remedy this, ...2020
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