Appreciating p-adics, the Fake Numbers

66 p.What does the phrase “Fake Numbers” mean? For me, the origins are in the semantics of food. If you will bear with me for a moment, please consider the term real food and its implied opposite, fake food. Taken literally fake food would refer to a plastic apple. However, that is not the comparison that is being made when real food is brought up. It references healthy food, natural food, or perhaps the food that people have been eating for most of history. Therefore, we know that the implied fake food is the modern, in this case processed and industrialized food. However, we can note that the latter is still edible. It still has calories, and by most definitions would qualify as food. Let this then inform our understanding of “fake numbers”. Much of the early if not full mathematical journey of many of my peers has been to learn about the real numbers (R). I content the p-adic numbers are the implied, albeit often omitted, fake number counterpart to R. A more modern construction, one with quite the overlap and enticing features that fake food has, yet not necessarily a full substitute for the original and all of its properties. With some semantics and analogies over with, we can discuss the layout what this paper and what we wish to accomplish over its duration. On a personal level it has been the culmination of my undergraduate experience with mathematics. A chance for me to appreciate much of what I have learned, apply past concepts to new landscapes, finally get my head around some key ideas, left me with a clearer picture of how little I know, and has been a continued exploration my newly kindled love of seeing math1. Therefore, I have a goal for us to accomplish. We will enjoy looking into the interesting, weirdly shaped, sometimes counterintuitive, yet also very accessible world of the p-adics. Along the way we will make several comparisons with R. We should also not believe in the above analogy so much as to begin viewing the p-adics as unhealthy or as a full replacement for R. To accomplish this goal, we will start at the beginning, what are the p-adics

Between the Lines and the Lens : The Sensory Experience of Memory, Trauma, and Adaptation in Gillian Flynn and Jean Marc Vallées Sharp Objects

x, 38 p.This idea of analyzing adaptation as a dialogue across mediums was the driving force of how I chose to structure the form and content of my SIP. I opted to structure each section around how both literary and filmic mediums complemented the story and themes of Sharp Objects. In my SIP, I structured my analysis thematically rather than simply chronologically, which was a direct result of how each version of Sharp Objects invites the audience to feel the story before they fully understand the overall plot. I used subheadings to create sections wherein I analyze the novel and how it presents its themes, and then a section on the TV series and how it translates those ideas to the screen. Moreover, both sections heavily focus on the sensory impact of each form. This organization allowed me to explore how the two texts are working in tandem, and why Sharp Objects is a prime example of adaptation done right. Akin to the story itself, I let emotional resonance guide the organization and tone of my writing, aiming to capture how adaptation can amplify meaning through aesthetic choices. Ultimately, this approach allowed me to exemplify how the plot of Sharp Objects itself was not the sole focus of my thesis, but the perfect case study in the power of storytelling across mediums

Towards the Synthesis of Mn(II) Complexes with Carbene Ligands

vii, 16 p.Catalysis allows access to chemical reactions that are slow or challenging, saving both time and energy. Photoredox catalysis uses a transition metal complex that absorbs visible light, accessing an excited state that can transfer electrons to an organic substrate to start a reaction. Photoactive complexes of ruthenium (II) and iridium (III) are commonly used as photocatalysts due to their high efficiency. However, Ru and Ir are scarce, expensive, and toxic. Abundant firstrow transition metals, such as manganese, serve as cheap, nontoxic alternatives to these metals. This project focuses on making Mn(II) complexes with tridentate N-heterocyclic carbene ligands. The target complex is [Mn(BbimMe)2]2+, where BbimMe is 2,6-bis(3-methylbenzimidazole- 2-ylidene)pyridine. In this paper, we report the synthesis of the ligand and work towards its optimization, as well as progress towards the synthesis of the corresponding Mn(II) complex

Art SIP

15 p.Six pieces that represent the artist's home, family, and heritage

Progress Toward the Synthesis of Manganese (II) Coordination Complexes with Tridentate Imine Ligands

iii, 18 p.Replacing fossil fuel energy sources is desirable because of the harmful carbon emissions to Earth’s atmosphere. Currently, some clean energy options, like dye-sensitized solar cells (DSSCs), are used to harness energy from the sun. These DSSCs use expensive and unabundant metals such as Ir, Os, Re, and Ru, making them unsustainable. Our group is using manganese to solve this issue due to its low cost, high abundance, many oxidation states, and low toxicity. The goal of this project is to synthesize [Mn(Ph-IAPP)2]2+ (Ph-IAPP is [(E)-{4-phenyl-6-[(phenylimino)methyl]-2-pyridyl}methyleneamino]benzene). The synthetic route for Ph-IAPP consists of five steps; this project focuses on the optimization of the first three steps, starting from dimethyl-4-chloropyridine-2,6-dicarboxylate. Plans to coordinate Ph-IAPP to Mn(II) are also discussed

Exploring High-Performance Python Using Concurrency and Different Interpreters

vii, 44 p.Python has established itself as one of the top programming languages in the last decade, thanks to its ease of learning and versatility across various fields. Its community spans both academia and industry, including areas such as data science, machine learning, web development, and scripting. As the demand for Python continues to grow, there is a strong push to discover methods for enhancing its performance in safe and effective ways. However, this convenience comes with a limitation, the Global Interpreter Lock (GIL), which is a builtin mechanism to synchronize the execution of threads. This feature makes code writing in Python much more user-friendly but restricts Python’s capabilities in distributed and parallel computing. In this SIP, I will study the ways to achieve high-performance Python from coding style to libraries and interpreters. All the code used in this paper can be found at https:// github.com/chauta03/python-parallel.git

Processing Compressed Genetic Data Using Hybrid Parallelism and High Performance Computing

vii, 22 p.FASTQ files are a common file structure used to store DNA sequence information and the quality scores for the associated DNA reads. These files are stored in a plain text format, so it is advantageous to compress these files to minimize the storage used. Dr. Sandino Vargas- Pérez performed previous research to develop a hybrid parallel algorithm called phyNGSC. This algorithm allows for fast compression and decompression of FASTQ files using distributed and shared memory programming models utilizing the MPI and OpenMP libraries. This research expands on this algorithm by introducing in compresso, an approach using hybrid parallelism with MPI and OpenMP that allows for the processing of genetic data without the need for total data decompression. This technique greatly reduces the storage needed to work with these genetic datasets and offers significant performance increases relative to comparable algorithms. This SIP showcases in compresso data processing for DNA sequence pattern finding and FASTQ to FASTA format conversion. The code for this implementation is available at [1]

Between the Pages : German American Identity Formation in Late 19th Century Milwaukee using the Germania Newspaper

65 p.Newspaper analysis can offer insight into communities, their world views, and how the companies perceived them. Germania served as one of those newspapers for a community of German Americans in Milwaukee from the late 19th century. A newspaper company titled Germania Wöchenliche was bought by George Brumder in 1873, creating one of Wisconsin’s most popular German-language newspapers leading into the 20th century. Located in downtown Milwaukee, the Germania publishing company building was a staple in printing news regarding national and international affairs, while also–with less emphasis–reporting on local events happening in Wisconsin. The publishing company would enjoy an ever-increasing German American population, quoted by Robert C. Nesbit stating how, "In 1850, Wisconsin had 38,064 German-born in a total population of 305,391. […] In 1870, with a population of 1,054,670 and 364,448 foreign-born, the percentage was 34.6. [...] By 1880, the foreign-born population in Wisconsin was approximately one-third of the total population"1 The German American community was large enough in Milwaukee for the city to earn the nick-name Deutsch Athen, translated as German Athens. Milwaukee received that name from the German immigrants arriving in Milwaukee at the time.2 It was not as if George Brumder’s work was insignificant either, as he would eventually buy out all the local newspapers in Milwaukee and grow Germania into one of the biggest German language newspapers in the 1890s

The Consequences of Nuclear Testing on a Nation: Lasting Impacts on Human Health and Identity in Semipalatinsk, Kazakhstan

13 p.Entitled “The Consequences of Nuclear Testing on a Nation: Lasting Impacts on Human Health and Identity in Semipalatinsk, Kazakhstan,” this piece will examine the impacts of the Soviet Union’s nuclear program on Kazakhstanis living in or around Kazakhstan’s Semipalatinsk Test Site, now called Semey, wherein hundreds of nuclear explosions occurred in the name of scientific development from 1949 to 1989. This is the Science essay winner of the 2025 Voynovich Essay Competition

"How I Learned What I Learned" Senior Integrated Project

11 p.For my senior integrated project, I wanted to do a theatrical piece showing what I have learned about during my time as a student here. More importantly, I wanted to express my art in a way that would get people’s attention by doing something I would not have even thought of if I was back in Tennessee. That was to do a theatrical piece that touched on racism, which no one wants to talk about. At Kalamazoo College, they push to be active in the community and to be social justice leaders. A topic that is going on today is schools in the United States are trying to ban critical race theory from their curriculum. My state was one of the 44 states since January 2021 to introduce bills or take other steps to restrict critical race theory or censor how teachers can lecture about racism and sexism