Physical Sciences and Mathematics Commons^™

College Students’ Images Of Mathematicians And Mathematical Careers, Katrina Piatek-Jimenez, Miranda Nouhan, Michaela Williams

Journal of Humanistic Mathematics

In this paper we report our findings of college students’ images of mathematicians and we reflect on different methodologies used to assess this information. The study reported in this paper was conducted in two stages. During the first stage, we asked 179 college students to “draw a mathematician” and also asked them to list five characteristics and five careers for a mathematician. In the second stage of the study, we conducted four focus group interviews with a total of twelve college students. During the focus group interviews, we showed the students 16 photos of real people and asked them to …

Engaging The Paradoxical: Zeno's Paradoxes In Three Works Of Interactive Fiction, Michael Z. Spivey

Journal of Humanistic Mathematics

For over two millennia thinkers have wrestled with Zeno's paradoxes on space, time, motion, and the nature of infinity. In this article we compare and contrast representations of Zeno's paradoxes in three works of interactive fiction, Beyond Zork, The Chinese Room, and A Beauty Cold and Austere. Each of these works incorporates one of Zeno's paradoxes as part of a puzzle that the player must solve in order to advance and ultimately complete the story. As such, the reader must engage more deeply with the paradoxes than he or she would in a static work of fiction. …

What Gets Checked At The Door? Embracing Students' Complex Mathematical Identities, Jennifer L. Ruef

Journal of Humanistic Mathematics

Identity formation is complex, ongoing, and context specific. To be successful in mathematics classes, students must negotiate and navigate the normative identity of the class--what counts as being "good at math" (Cobb, Gresalfi & Hodge, 2009). Within the constraints of normative identity, students must also negotiate a personal doer-of-math identity: who they are within the context of this particular mathematics class. When students are compelled to suppress key aspects of their identity in order to accommodate the normative identity of the class cognitive bandwidth for learning may be impeded (Steele, 1997). Conversely, when students are guided in braiding individual identity …

John Cheever's Story "The Geometry Of Love", Robert Haas

Journal of Humanistic Mathematics

Though John Cheever was a leading writer of short fiction, his story “The Geometry of Love” has received little prior literary or mathematical comment. In this essay it is read, against the background of Cheever’s own troubled life and marriage, as a Don Quixote – like search, explicitly following the model of Euclidean geometry, and at times wildly funny, for an ideal world of truth and happiness.

Starting Our Decennial, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Intercropping For Water Conservation: Environmental And Economic Implications Of A Sustainable Farming Practice In California's Central Valley, Sophie Baker

Scripps Senior Theses

California’s agricultural sector is the biggest water consumer in the state and faces intense pressure to reduce its overall water usage. Industrialized monoculture systems dominate the industry and often disregard long-term environmental and economic externalities for short-term profit maximization. To maintain longstanding food security and economic stability as well as protect the state’s water supply, it is critical that these systems transition to more sustainable and resilient production mechanisms. As an alternative to monoculture, intercropping affords greater potential to conserve water, protect soil quality, and increase crop yields, among other metrics of sustainability. However, there has been much controversy over …

Synthesis And Reactivity Of A New Platinum(Ii) Complex, Maria Lew

Scripps Senior Theses

Alkanes are some of the most abundant organic molecules, yet currently there are no efficient ways of directly converting them to more functional molecules. One viable method of direct functionalization is C–H bond activation by transition metal catalysts. The focus of this research has been the synthesis of a new Pt(II) pincer complex to be used in mechanistic investigations of C–H activation, as well as the beginnings of those investigations. The complex [NN^ON]PtMe was successfully synthesized. Reactions with various acids indicated that [NN^ON]PtMe is capable of reductively eliminating methane after addition of two equivalents of acid. …

Shrimp Farming In Thailand: A Pathway To Sustainability, Warinyupa Phornprapha

Pomona Senior Theses

Throughout this thesis I have laid out several factors that have contributed to the sustainability of shrimp farming in Thailand, and if sustainability whilst maintaining production can ever be achieved. To find out the current situation of shrimp farming in Thailand, the history of global and Thai shrimp farming is described. The social and environmental problems of the unsustainable history of shrimp farming in Thailand is then considered. Solutions to these effects conclude that it is up to the consumer to demand for better regulations from the government and the shrimp companies to ensure a sustainable future for shrimp farming …

Electrodynamics Modeling Of Plasmonic-Organic Hybrid Waveguides, Marcus Michel

Pomona Senior Theses

Optical fibers have multiple advantages over conventional electrical connections, such as lower energy losses and higher bandwidth. To use optics for chip-to-chip communication, electro-optic (EO) modulators need to be scaled down to be incorporated on integrated circuits. This size reduction has been accomplished using plasmonic-organic hybrid (POH) waveguides, which make use of nonlinear organic EO materials and surface plasmon polaritons to achieve light modulation in devices with lengths on the micron scale. As these devices are just starting to be developed, there are many avenues for their potential optimization. In order to streamline and reduce the cost of the optimization …

Plastics Derived From Derelict Fishing Gear In The Arctic: Looking At Sustainable Fisheries For A Strategy Of Mitigation, Remediation And Prevention In Iceland And Alaska, Natalie S. Armstrong

Pitzer Senior Theses

Marine plastics are not just a problem, they are a silent, sinister epidemic. Marine plastics are the largest economic and ecological threat to our marine ecosystems, particularly marine plastics derived from lost and or discarded fishing gear, which affects sensitive marine communities, the chemical composition of the ocean water, and the physical makeup of the seafloor. With 6.4 million tons of marine debris entering our oceans annually, a third of which is lost fishing gear, it is estimated that, by weight, in 2050 there will be an accumulation of more plastic than fish in the ocean (Heath, 2018; Wilcox, 2015). …

Complex Ciliary Flows Around Stentor Polymorphus In Solutions Of 2% Buttermilk And Chlamydomonas Reinhardtii, Eliana B. Smithstein

Scripps Senior Theses

Stentor are large, unicellular ciliates of the Heterotricha order. They live in both freshwater and marine habitats and are mostly found in ponds. I studied Stentor polymorphus, which is a species of Stentor only recently discovered to be lab culturable. They range from 0.5-1.5mm in length and are unusual because they live with endosymbiotic algae and are much more likely than other, more widely studied, species of Stentor to form aggregates while they are eating. There are three main components to this thesis: First, I established protocols for keeping a viable S. polymorphus culture, since no protocols had been …

Stationary Distribution Of Recombination On 4x4 Grid Graph As It Relates To Gerrymandering, Camryn Hollarsmith

Scripps Senior Theses

A gerrymandered political districting plan is used to benefit a group seeking to elect more of their own officials into office. This practice happens at the city, county and state level. A gerrymandered plan can be strategically designed based on partisanship, race, and other factors. Gerrymandering poses a contradiction to the idea of “one person, one vote” ruled by the United States Supreme Court case Reynolds v. Sims (1964) because it values one demographic’s votes more than another’s, thus creating an unfair advantage and compromising American democracy. To prevent the practice of gerrymandering, we must know how to detect a …

Decay And Dissipation: Finding Energy Level Jumps In A Harmonic Oscillator System Using Fortran And Fourier Analysis, Clara Chilton

Scripps Senior Theses

In this paper, I will look at a mass-spring system that can be described by a Hamiltonian. In most systems described by a Hamiltonian, the energy levels will be quantized, and the system will be able to jump between them. However, many methods of finding these jumps aren’t well-suited to numerical analysis. I’ll use a Markovian approximation (The Liouville von Neuman Equation), which allows me to use only the last time step to find the current one. Using this, I will analyze the system to find the time evolution of the probability density matrix – whose diagonal shows the probability …

Characterizing Solar Cells, Katheryn R. Kornegay

Pomona Senior Theses

Perovskite solar cells and organic photovoltaics are both attractive because of their potential flexibility, tunable material properties, and low cost. Though perovskite solar cells have reached efficiencies comparable to conventional silicon solar cells, these have only occurred with lab-scale devices. Organic photovoltaics have much lower operating efficiencies than both perovskite and silicon solar cells, often due to non-uniformities and defects. In this thesis, we use two different techniques to better characterize these two types of solar cells. For perovskite solar cells, we use a drift-diffusion model, to characterize the transition between different doped states in its hole-transport layer, Spiro-OMeTAD, and …

Contaminants Of Emerging Concern: Reconsidering Our Paradigm Of Water Pollution, Jonathan Gunasti

Pomona Senior Theses

In this senior thesis, I explore contaminants of emerging concern (CECs) and endocrine disrupting compounds (EDCs) and discuss the ways in which these novel contaminants defy traditional notions of pollution. I discuss the history and “emergence” of CECs and EDCs in scientific and public spheres and outline ongoing challenges to recognizing, prioritizing, and understanding the action of these contaminants. I position EDCs within the framework of environmental injustice and health disparities and suggest that these compounds could reinforce multigenerational health inequities. Finally, I perform a pilot analysis of the EDC bisphenol A (BPA) in Mt. Baldy Creek, the Los Angeles …

Use Of Kalman Filtering In State And Parameter Estimation Of Diabetes Models, Cassidy Le

HMC Senior Theses

Diabetes continues to affect many lives every year, putting those affected by it at higher risk of serious health issues. Despite many efforts, there currently is no cure for diabetes. Nevertheless, researchers continue to study diabetes in hopes of understanding the disease and how it affects people, creating mathematical models to simulate the onset and progression of diabetes. Recent research by David J. Albers, Matthew E. Levine, Andrew Stuart, Lena Mamykina, Bruce Gluckman, and George Hripcsak¹ has suggested that these models can be furthered through the use of Data Assimilation, a regression method that synchronizes a model with a …

On The Mysteries Of Interpolation Jack Polynomials, Havi Ellers

HMC Senior Theses

Interpolation Jack polynomials are certain symmetric polynomials in N variables with coefficients that are rational functions in another parameter k, indexed by partitions of length at most N. Introduced first in 1996 by F. Knop and S. Sahi, and later studied extensively by Sahi, Knop-Sahi, and Okounkov-Olshanski, they have interesting connections to the representation theory of Lie algebras. Given an interpolation Jack polynomial we would like to differentiate it with respect to the variable k and write the result as a linear combination of other interpolation Jack polynomials where the coefficients are again rational functions in k. In this …

Pascal's Mystic Hexagon In Tropical Geometry, Hanna Hoffman

HMC Senior Theses

Pascal's mystic hexagon is a theorem from projective geometry. Given six points in the projective plane, we can construct three points by extending opposite sides of the hexagon. These three points are collinear if and only if the six original points lie on a nondegenerate conic. We attempt to prove this theorem in the tropical plane.

A Discrete Analogue For The Poincaré-Hopf Theorem, Savana Ammons

HMC Senior Theses

In this thesis, we develop a discrete analogue to the Poincaré–Hopf Theorem. We define the notion of a vector field on a graph, and establish an index theory for such a field. Specifically, we create well-defined indices for the nodes and “cells" formed by a planar graph. Then, we show that the sum of these indices remains constant for certain types of planar graphs, regardless of the discrete vector fields they have.

Where The Wild Knots Are, Forest Kobayashi

HMC Senior Theses

The new work in this document can be broken down into two main parts. In the first, we introduce a formalism for viewing the signed Gauss code for virtual knots in terms of an action of the symmetric group on a countable set. This is achieved by creating a "standard unknot" whose diagram contains countably-many crossings, and then representing tame knots in terms of the action of permutations with finite support. We present some preliminary computational results regarding the group operation given by this encoding, but do not explore it in detail. To make the encoding above formal, we require …

An Exploration Of Combinatorial Interpretations For Fibonomial Coefficients, Richard Shapley

HMC Senior Theses

We can define Fibonomial coefficients as an analogue to binomial coefficients as F(n,k) = F_nF_n-1 … F­_n-k+1 / F­_kF_k-­1…F₁, where F_n represents the nth Fibonacci number. Like binomial coefficients, there are many identities for Fibonomial coefficients that have been proven algebraically. However, most of these identities have eluded combinatorial proofs.

Sagan and Savage (2010) first presented a combinatorial interpretation for these Fibonomial coefficients. More recently, Bennett et al. (2018) provided yet another interpretation, that is perhaps more tractable. However, there still has been little progress towards using these interpretations …

Agent-Based Modeling Of Locust Foraging And Social Behavior, Hannah Larson

HMC Senior Theses

Locust swarms contain millions of individuals and are a threat to agriculture on four continents. At low densities, locusts are solitary foragers; however, when crowded, they undergo an epigenetic phase change to a gregarious state in which they are attracted to other locusts. It is believed that this is an evolutionary adaptation that optimizes the seeking of resources. We have developed an agent-based model based on the solitary-gregarious transition and foraging behaviors due to hunger levels. A novel feature of our model is that it treats food resources as a dynamic variable in the environment. We discuss how social interaction …

A Coherent Proof Of Mac Lane's Coherence Theorem, Luke Trujillo

HMC Senior Theses

Mac Lane’s Coherence Theorem is a subtle, foundational characterization of monoidal categories, a categorical concept which is now an important and popular tool in areas of pure mathematics and theoretical physics. Mac Lane’s original proof, while extremely clever, is written somewhat confusingly. Many years later, there still does not exist a fully complete and clearly written version of Mac Lane’s proof anywhere, which is unfortunate as Mac Lane’s proof provides very deep insight into the nature of monoidal categories. In this thesis, we provide brief introductions to category theory and monoidal categories, and we offer a precise, clear development of …

How Machine Learning And Probability Concepts Can Improve Nba Player Evaluation, Harrison Miller

CMC Senior Theses

In this paper I will be breaking down a scholarly article, written by Sameer K. Deshpande and Shane T. Jensen, that proposed a new method to evaluate NBA players. The NBA is the highest level professional basketball league in America and stands for the National Basketball Association. They proposed to build a model that would result in how NBA players impact their teams chances of winning a game, using machine learning and probability concepts. I preface that by diving into these concepts and their mathematical backgrounds. These concepts include building a linear model using ordinary least squares method, the bias …

Gravity-Drawing Flexible Silicone Filaments As Fiber Optics And Model Foldamers, Katherine Snell

CMC Senior Theses

Here, we present a method of gravity-drawing polydimethylsiloxane (PDMS) silicone fibers with application as fiber optics and as model foldamers. Beginning as a viscous liquid, PDMS is cured using heat until its measured viscosity reaches 4000 mPa•s. The semi-cured elastomer is then extruded through a tube furnace to produce thin (diameters on the order of hundred micrometers) filaments with scalable lengths. PDMS is biocompatible, gas-permeable, flexible, and hydrophobic. Additionally, the PDMS surface hydrophobicity can be modified via UV exposure, O2 plasma, and corona discharge. We demonstrate the patternibility (i.e patterns of hydrophobicity) of PDMS fibers, adding complexity to potential foldamer …

An Exploration Of 5g Wireless Network Attenuation Using Finite Element Analysis In Comsol Multiphysics, Matthew Johnson

CMC Senior Theses

5G, ultra-high frequency wireless networks face numerous hurdles due to significant signal attenuation in materials and large path loss. Empirical research on signal attenuation has been limited to low frequencies or very select high frequencies. This paper utilizes Finite Element Analysis in COMSOL Multiphysics to analyze signal attenuation in materials over a range of the frequency spectrum, from 100Mhz to 40Ghz, which is inclusive of 5G wireless frequencies. The focus of this paper is on glass and dry wood, as well as wet wood (representative of trees), as these materials are some of the most likely to stand in the …

Optimal Execution In Cryptocurrency Markets, Ethan Kurz

CMC Senior Theses

The purpose of this paper is to study the Almgren and Chriss model on the optimal execution of large block orders both on the NYSE and in cryptocurrency exchanges. Their model minimizes execution costs, which include linear temporary and permanent price impacts. We focus on how the stock market microstructure differs from a cryptocurrency exchange microstructure and what that means for how the model functions. Once the model and microstructures are explained, we examine how the Almgren-Chriss model functions with stocks from the NYSE, looking at specifically selling a large number of shares. We then investigate how a large "wholesale" …

K-Means Stock Clustering Analysis Based On Historical Price Movements And Financial Ratios, Shu Bin

CMC Senior Theses

The 2015 article Creating Diversified Portfolios Using Cluster Analysis proposes an algorithm that uses the Sharpe ratio and results from K-means clustering conducted on companies' historical financial ratios to generate stock market portfolios. This project seeks to evaluate the performance of the portfolio-building algorithm during the beginning period of the COVID-19 recession. S&P 500 companies' historical stock price movement and their historical return on assets and asset turnover ratios are used as dissimilarity metrics for K-means clustering. After clustering, stock with the highest Sharpe ratio from each cluster is picked to become a part of the portfolio. The economic and …

Discrete Geometry And Covering Problems, Alexander Hsu

CMC Senior Theses

This thesis explores several problems in discrete geometry, focusing on covering problems. We first go over some well known results, explaining Keith Ball's solution to the symmetric Tarski plank problem, as well as results of Alon and F\"uredi on covering all but vertices of a cube with hyperplanes. The former extensively utilizes techniques from matrix analysis, and the latter applies polynomial method. We state and explore the related problem, asking for the number of parallel hyperplanes required to cover a given discrete set of points in $\mathbb{Z}^{d}$ whose entries are bounded, and prove that there exist sets which are ``difficult'' …