Physical Sciences and Mathematics Commons^™

Maximizing Productivity And Quality In Senior Thesis Writing With Artificial Intelligence And Natural Language Processing Driven Tools, Lauren Leadbetter

CMC Senior Theses

This project is a Python program designed to generate a senior thesis on a user-
inputted topic using natural language processing techniques. The program takes in a
topic from the user and then uses OpenAI API to deploy text models for text genera-
tion and evaluation, such as GPT-3 and Davinci-003. The resulting output is in .tex
format and includes a first-draft outline and paper, followed by self-generated assessment, with scoring, revisions, and feedback comments instructing manual revisions.

This submission is a sample using one available model of the project, meant to
demonstrate it’s functionality and limitations. Further model versions …

Generalized Far-Difference Representations, Prakod Ngamlamai

HMC Senior Theses

Integers are often represented as a base-$b$ representation by the sum $\sum c_ib^i$. Lekkerkerker and Zeckendorf later provided the rules for representing integers as the sum of Fibonacci numbers. Hannah Alpert then introduced the far-difference representation by providing rules for writing an integer with both positive and negative multiples of Fibonacci numbers. Our work aims to generalize her work to a broader family of linear recurrences. To do so, we describe desired properties of the representations, such as lexicographic ordering, and provide a family of algorithms for each linear recurrence that generate unique representations for any integer. We then prove …

Beginner's Analysis Of Financial Stochastic Process Models, David Garcia

HMC Senior Theses

This thesis explores the use of geometric Brownian motion (GBM) as a financial model for predicting stock prices. The model is first introduced and its assumptions and limitations are discussed. Then, it is shown how to simulate GBM in order to predict stock price values. The performance of the GBM model is then evaluated in two different periods of time to determine whether it's accuracy has changed before and after March 23, 2020.

Permutations, Representations, And Partition Algebras: A Random Walk Through Algebraic Statistics, Ian Shors

HMC Senior Theses

My thesis examines a class of functions on the symmetric group called permutation statistics using tools from representation theory. In 2014, Axel Hultman gave formulas for computing expected values of permutation statistics sampled via random walks. I present analogous formulas for computing variances of these statistics involving Kronecker coefficients – certain numbers that arise in the representation theory of the symmetric group. I also explore deep connections between the study of moments of permutation statistics and the representation theory of the partition algebras, a family of algebras introduced by Paul Martin in 1991. By harnessing these partition algebras, I derive …

Clusters, Curves, And Centroids: Stellar Flare Morphology In The Ultraviolet, Vera Berger

Pomona Senior Theses

With a novel sample of 495 high-cadence light curves for stellar flares in the near-ultraviolet, I explore similarity measures, clustering algorithms, averaging methods, and curve fitting techniques for time series. This work seeks to provide insight into whether stellar flares are similar across stars, if we can identify physically meaningful patterns in their light curves, and how to construct a comprehensive model for flares. I construct the first empirical template for flare light curves in the ultraviolet, and compute ``average elements" of flares displaying complex features such as quasi-periodic oscillations and multipeak structures. Developing accurate models for flares in the …

The Eu's Capacity To Lead The Transatlantic Alliance In Ai Regulation, Varun Roy, Vignesh Sreedhar

Claremont-UC Undergraduate Research Conference on the European Union

In the face of Chinese advances in AI in terms of technological prowess and influence, there has been a call for collaboration between the EU and the US to create a foundation for AI governance based on shared democratic beliefs. This paper maps out the EU, US, and Chinese approaches to AI development and regulation as we analyze the capacity of the US and EU to establish international standards for AI regulation through channels such as the TTC. As the EU rolled out a proportionate and risk-based approach to ensure stricter regulation for high-risk AI technologies, it laid the foundation …

A Generalized Method Of Undetermined Coefficients, James S. Cook, William J. Cook

CODEE Journal

The method of undetermined coefficients is used to solve constant coefficient nonhomogeneous differential equations whose forcing function is itself the solution of a homogeneous constant coefficient differential equation. In this paper, we show that the classical methods for tackling constant coefficient equations, including the method of undetermined coefficients, generalize to much wider class linear differential equations which, for example, include Cauchy-Euler type equations. This general method includes an explicit construction of the fundamental solution sets of such equations. We also briefly consider where this method can be applied by producing the most general second and third order differential equations that …

Mathematical Constants Beyond The Half-Circle: An Open Call For Poetry, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics invites submissions of mathematical poetry for an upcoming poetry folder tentatively titled Mathematical Constants Beyond the Half-Circle. Please send your submissions via email to the editors by November 1, 2022. Publication decisions will be made by December 31, 2022. The folder is expected to appear in January 2023.

Squate, Tom Blackford

Journal of Humanistic Mathematics

This is the story of a middle school student who befriends an irrational number, the square root of eight.

Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts), Vijay Fafat

Journal of Humanistic Mathematics

What if all of our Reality is a simulation? What, perhaps, are the unintended artifacts if we are an "approximate" simulation because God could not muster sufficient computational power for the Equations capturing the ultimate Theory of Everything? Are life and Sentience something She intended, a problem with the simulation's code, or an irreducible, teleological inevitability in Creation?

A Topologist’S Broken Heart, Josh Hiller

Journal of Humanistic Mathematics

A poem about a topologist's broken heart.

Spurious Correlation Sestina, Jules Nyquist

Journal of Humanistic Mathematics

This is a sestina poem about Spurious Correlations with a magical realism angle for beginning students learning statistics for the first time during the COVID pandemic.

Doughnut At The End Of Space, Deborah Coy

Journal of Humanistic Mathematics

No abstract provided.

Scientists Confirm Euler's Identity Is Math's Most Beautiful Expression, John F. Donoghue

Journal of Humanistic Mathematics

The poem is an exploration of the natures of mathematical and artistic beauty.

Ode To Delta, Evandro Il Cinico

Journal of Humanistic Mathematics

No abstract provided.

Circular Meditations, Kevin Farey

Journal of Humanistic Mathematics

Circular Meditations is a sequence of seventeen interconnected poems pertaining to mathematics, science, history, politics, religion, and spirituality.

Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos

Journal of Humanistic Mathematics

We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempowerment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in …

Ramanujan Cab Numbers: A Recreational Mathematics Activity, Soumya Banerjee

Journal of Humanistic Mathematics

In this paper, I introduce teaching activities about Ramanujan’s cab numbers and related software that can inspire people and help them enjoy these beautiful mathematical creations.

Academic Hats And Ice Cream: Two Optimization Problems, Valery F. Ochkov, Yulia V. Chudova

Journal of Humanistic Mathematics

This article describes the use of computer software to optimize the design of an academic hat and an ice cream cone!

Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram

Journal of Humanistic Mathematics

Soma cubes are an example of a dissection puzzle, where an object is broken down into pieces, which must then be reassembled to form either the original shape or some new design. In this paper, we present some interesting discoveries regarding the Soma Cube. Equivalence classes form aesthetically pleasing shapes in the solution set of the puzzle. These gems are identified by subgraph isomorphisms using SNAP!/Edgy, a simple block-based computer programming language. Our preliminary findings offer several opportunities for researchers from middle school to undergraduate to utilize graphs, group theory, topology, and computer science to discover connections between computation and …

Creative Writing That Combines Mathematics And Literature, Hsueh-Chen Lee

Journal of Humanistic Mathematics

In early 2015, the Mathematics-Literature Creativity Award was offered through competition for technological and vocational college students in Taiwan. This paper focuses on the two winning works, the poem Parabola and the flash-fiction, Love Letters of a Science Student, by analyzing the mathematical notions involved and their uses to enhance literary expression. The introduction surveys briefly the various ways of combining mathematics and literature in a piece of creative writing that enriches and supports communication in both disciplines.

Calculus Iii: Under The Influence Of Peer Instruction, Alan Von Herrmann, L. Jeneva Clark

Journal of Humanistic Mathematics

In peer Instruction, students engage with core course concepts and then explain those concepts to one another in small groups. Unlike in lecture format, peer instruction involves every student in the class. In Spring 2019, the first authot began using a modified version of peer instruction in Calculus III classes. He started each class by discussing important Calculus III concepts from three standpoints (the formula, the geometry behind the formula, and the physics behind the formula). During the last 20 minutes of each 50-minute class session, he polled the students using questions in the “Goldilocks Zone” – not too hard …

The Fractal Geometry Of Mathematics Classrooms: Navigating Classroom Environments In Factory-Model Schools, Cacey L. Wells

Journal of Humanistic Mathematics

Mathematics education has a diverse and complex history. After decades of national reform, mathematics classrooms today are still in desperate need of change. This article examines the current state of factory-model schooling through the lens of Mandelbrot's The Fractal Geometry of Nature in order to rethink pedagogic practices.

In Mathematics, As In Art, Andrew Granville

Journal of Humanistic Mathematics

The artist’s vision helps decide what should be created; the mathematician’s insight what can be created. Yet most people view art as merely decoration, or a reflection of existing reality, while they think of mathematics as just a tool for accurate scientific description. Can more people learn to value and enjoy both art and mathematics? And spend a lifetime exploring them and appreciating them for their own sakes?

Irruption Of The New: Truth, Events, History, Parallels, Fidelity, David L. Neel

Journal of Humanistic Mathematics

A historical meditation on non-Euclidean geometry, three Jesuits, a radical egalitarian mathematical philosopher, and the atom bomb, structured by word-count with attention to divisors of 441 and the Fano plane.

The Aleph Of Borges And The Paradise Of Cantor, Raffaella Mulas

Journal of Humanistic Mathematics

The mathematician Georg Cantor, the writer Jorge Luis Borges, and the protagonist of Borges' short story The Aleph, Carlos Argentino Daneri, are seen here as three pieces of a single puzzle. We put these pieces together and we look at the surprising figure that we obtain.

Mathematical Counterpoint: A Short Essay On The Point, Ruža Jeličić

Journal of Humanistic Mathematics

The dot is the simplest graphic symbol, and in the most diverse areas of human thought it signifies the original principle. At the point as a symbol lies the basis of antinomy in the corresponding areas; as the beginning of everything, the point is and is not. The dot represents emptiness, but also fullness. It is imagined on the border of being and non-being, either as a place of transition from what we consider reality in everyday life -- to its negation, or, on the contrary, as a transition from otherworldly reality to nothingness here. In any case, the point …

Higher Meanings: A Speaker Series Connecting Mathematics And Religion, Lawrence M. Lesser, Patricia S. Barrientos, Ben Zeidman

Journal of Humanistic Mathematics

An innovative grant-funded general adult audiences international speaker series on connections between mathematics and religion yielded six 2021 (now archived) presentations. We share reflections and lessons learned, informed by two sets of surveys.

Conic Diagrams, David Pierce

Journal of Humanistic Mathematics

Textbooks may say that the so-called conic sections can be obtained from cones, but this is rarely proved. However, diagrams of the proof require no intuition for solids and can be read as flat. We construct the diagrams with ruler and compass and derive from them basic properties of conic sections as established by Apollonius of Perga, though again in a way that does not require a third dimension. The construction inevitably involves choices that give play to one’s aesthetic sense.

Navigating Mathematics Teacher Preparation During A Time Of Crisis, Zareen G. Rahman, Rani Satyam, Younggon Bae

Journal of Humanistic Mathematics

In this paper we highlight the experience of a mathematics teacher educator (MTE) and their prospective teachers (PTs) in a middle school mathematics methods course during the 2020 shift to online instruction due to the COVID-19 pandemic. We believe it is valuable to report how the MTE reflected on their instructional decision-making in response to this massive transition to remote instruction. We also report that PTs needed support and guidance to employ new teaching practices they had learned in the methods course instead of reverting to familiar teaching methods.