Talks

Student Mini-Conference

9:00

PB 191

Jasmine Perez - Impossible Corner Rotations on Variants of the Rubik's Cube

Abstract: It is well-known in the Rubik’s cube community that a classical 3x3x3 cube cannot be fully solved with the exception of one corner rotated. This can be proved using invariants and modulo arithmetic. In some variants of Rubik’s cubes, such as the Ivy Leaf, it is possible to rotate one corner and have the rest of the cube solved due its unique structure. However, in several other variants---for example, the Skewb, Megaminx, and Octahedron---it is impossible to reach such a configuration. To prove this, we will adapt the 3x3x3 argument to each specific cube.

PB 192

Alan R Barrios - Infinitesimals Resurrected

Abstract: Infinitesimals played a crucial role in the development of calculus, which was independently developed by the well-known mathematicians Isaac Newton and Leibniz in the late 1600s. It was later abolished and replaced by the concept of a limit, which did not require the use of infinitesimals. However, it was later shown that infinitesimals do in fact exist and can be formalized - by extending the real number system to include infinitively small numbers. Since then, infinitesimal calculus resurrected as a new way of doing calculus without the use of epsilons and deltas. In my presentation, we will construct the necessary concepts that will allow us to use infinitesimals to prove the Riemann Integrable Theorem.

PB 138

Raul Reynoso - Using Recommender Systems in Genomic Mutation Data

Abstract: This project analyzes a mathematical model representing the fraction of right-handed Bradybaena similaris snails over multiple generations. By examining a discrete model, we explore how variations in initial population proportions and growth rates affect long-term outcomes, specifically focusing on the convergence of the population towards an equilibrium state. Through simulations, we demonstrate that slight deviations from an even distribution can significantly influence the stability of genetic traits within the population. Additionally, we investigate how modifying growth rates impacts the rate of convergence to equilibrium, revealing that while the final population ratio remains consistent, the speed of reaching that ratio varies. Finally, we enhance the model by incorporating real-world biological factors, such as predation, allowing for a more realistic simulation of evolutionary dynamics and providing insights into the complexities of natural selection and genetic diversity.

9:15

PB 191

Daniel Hieng - Permutations on Rubik's Cubes

Abstract: This presentation will be about my Math 198 project. I will be primarily talking about the classical Rubik's cube. There have been many studies done on the 3x3x3 Rubik's cube; in particular, it is well-known that some configurations of this cube are impossible. I will be using the ideas of these studies and apply them to larger Rubik's cubes, such as the 4x4x4 Rubik's cube. Another part of my project is about the Ivy Leaf cube and its connection to the group A_6.

PB 192

Ryan Perry - Fibonacci Polynomials and their Generalization

Abstract: It is known that the zeros of the Fibonacci polynomials lie on the purely imaginary interval I = (−2i, 2i). In this paper we generalize this famous sequence of polynomials by varying the initial condition. We show that the zeros of the general Fibonacci polynomials do not necessarily lie on I but rather approach this interval and a finite set of points which is a subset of the set of zeros of an explicit polynomial formed by the initial condition.

PB 138

Logan Carter - Linking Environmental Factors to Chronic Diseases in California

Abstract: California Office of Environmental Health Hazard Assessment combines the scores of the various pollution factors and population characteristics to determine a census tract's CalEnviroScreen 4.0 score. In an effort to determine a potential relationship between chronic diseases and pollution factors/population characteristics, we analyzed and compared rates of different diseases to CalEnviroScreen 4.0 score within California by census tract. During this presentation, we present results on asthma as example disease. Through linear regression models, we found that asthma rates in California were significantly associated with various pollution factors and population characteristics.

9:30

PB 191

Alyssa Zamora-Rai - Playing Grim on K-Cubes

Abstract: In this presentation, we will discuss how the game of Grim is played on k-cubes. We will prove that Player 2 will always win the game.

PB 192

Ashish Goswami - A Class of Polynomials from Enumerating Queen Paths

Abstract: We study a class polynomials obtained from an enumeration of the number of queen paths. In particular, we find the generating function for the diagonal sequence of this table and the zero distribution of a sequence of related polynomials.

PB 138

Cody Heinks - Deriving the Finite Element Method

Abstract: In this presentation I will discuss the theory and derivation of the finite element method (FEM). Starting from a given boundary value problem, I will derive the associated weak formulation, explain their equivalency, and discuss the effect of boundary conditions. From there I will present the FEM as a particular example of the Galerkin method, which is a means of approximating solutions to weak formulations. Lastly, I will discuss a time-dependent problem and show how to apply the FEM.

9:45

PB 191

Malee Her - Taking a Spin at Quantum Mechanics

Abstract: Motivated by the strange results of the Gerlach experiment, the framework of quantum mechanics was constructed a variety of mathematics to describe its structure, such as Pauli matrices, complex numbers, probability. With a focus on quantum spin, we will explore the mathematical structures of quantum mechanics.

PB 192

Riley White - Sums of Gegenbauer Polynomials

Abstract: The Gegenbauer Polynomials are a sequence of polynomials which generalize the Chebyshev polynomials of the second kind. In my research, I am studying the zeroes of the sequence of polynomials which are given by the sum of the first n Gegenbauer Polynomials. My goal is to show that these zeroes are all real and lie on the interval (-1,1) under certain conditions.

PB 138

Ryan Her - GCDs, from integers to polynomials in Q[x] and Z_p[x] using C++

Abstract: Finding the GCD of two integers using the Euclidean Algorithm is well known, and often a quick exercise for introductory computer science students to replicate. The question arises then if the code for GCD of polynomials, such as Q[x] (polynomials with rational coefficients) or Zp[x] (polynomials with coefficients in Zp), is just as trivial. This talk then shows demo code for the GCD for Q[x], Zp[x], and explores the use of “templates” in C++ to generalize for any class/ring where Euclidean’s Algorithm can be used.

10:00

PB 191

Olivia Soghomonian - The Cantor Set: A Fixed Point of an Iterative Function System

Abstract: This talk explores the Cantor Set through the lens of iterative function systems. We use the Banach Fixed Point Theorem and the properties of Hausdorff metrics to establish the Cantor set as a fixed point of an iterative function system, thereby allowing us to conclude that the Cantor set can be viewed as a limit point of an iterative process.

PB 192

Aya Elhabashy - Multiplier Sequences

Abstract: This talk is an introduction to our work on polynomially interpolated multiplier sequences in orthogonal bases. After briefly motivating the study of polynomial roots in physical systems, we introduce the notion of a multiplier sequence. We explore key examples and discuss recent works involving diagonal differential operators. In the second half of the talk, we outline our current research and how we aim to resolve an open problem posed by R. Bates in 2014.

PB 138

Logan Smith - Implementing Symbolic Polynomial Computation in R

Abstract: Overview of the process to implement symbolic polynomial representation and key operations (addition, subtraction, multiplication, division) into the R programming language. Details programming concepts and practices used for code optimization. Fully mathematically clear to students who completed or are taking abstract algebra, but is accessible to anyone with programming experience.

10:15

PB 191

PB 192

Cesar Gonzalez Luna - P-adics: Where Divergent Sums Find a Home

Abstract: This a brief introduction to 𝑝-adic numbers, a number system (field) where distances are measured in a completely different way using something called 𝑝-adic valuation. This leads to surprising results, such as the convergence of the infinite sum ∑𝑝^𝑘 for any fixed prime 𝑝 -- something that we don't have over the real numbers!

PB 138

Joseph Thiers - Bookdown: Flexible Document Creation in RStudio

Abstract: This talk introduces Bookdown, a powerful yet user-friendly documentation tool within RStudio, tailored for math students of all levels. In mathematics we tackle complex topics, so effectively documenting analyses and findings is essential for disseminating information, and Bookdown offers streamlined methods to enhance this process. Attendees will explore Bookdown’s key features, including embedding mathematical equations, integrating visualizations, organizing complex data analyses, and outputting your work in multiple formats. With a focus on simplicity, this session will show how Bookdown supports clear, professional, and engaging documentation for a range of mathematical and statistical projects.

10:30

PB 191

Victoria Wiest - An extension of the sl(n) polynomial to knotted 4-valent graphs

Abstract: The emergence of knot theory as a distinct mathematical discipline can be traced to January 1867, originating from William Thomson's, or Lord Kelvin, hypothesis about atomic structure through vortex rings in the ether. This presentation examines how Peter Guthrie Tait's subsequent work in categorizing knots, initially inspired by Kelvin's atomic theory, led to the development of a systematic mathematical framework that persisted even after the underlying physical theory was disproved. We explore the evolution of knot theory from its theoretical foundations through contributions of notable mathematicians like James Clerk Maxwell, the development of key concepts such as knot invariants and Reidemeister moves, and will culminate with an analysis of modern achievements and contemporary applications. Particularly, Jean-Pierre Sauvage's groundbreaking work in synthesizing knotted molecules, which demonstrates knot theory's potential impact on material science and molecular chemistry. This historical trajectory illustrates how a mathematical field that emerged from a defunct physical theory has evolved into a robust discipline with significant practical applications in modern science.

PB 192

Isaac Ramos - A Quick Guide to the Construction of a Mathematical Model

Abstract: We will go over the key steps used in the construction of a mathematical model. We will do this by looking at an example that aims to model the population of a species of endangered turtles.

PB 138

Bianca Hinojosa - How can low-code tools make Data Science accessible?

Abstract: From health and financial data, to environmental and economic data, engaging with today's world requires familiarity with data analysis and statistics. Data literacy unlocks new lenses through which we can engage with the world, empowering individuals to exercise more agency in their daily lives. How can students outside of STEM disciplines learn data analysis and statistics concepts in an accessible way? This talk will explore how the Process-Oriented Guided Inquiry Learning framework can be used to guide non-STEM students through the analysis of geographically relevant data using the low-code user-friendly software tool CODAP. The goal of this exploration is to broaden participation across the disciplines in Data Science and increase data literacy.

10:45

PB 191

Elizabeth Lemus - Knot Theory and the Braid Group

Abstract: The braid group $B_n$ is the group of equivalence classes of braids on $n$ strands with respect to a certain equivalence relation. Any braid can be represented as the product of generators $\sigma_i$ and their inverses, where $\sigma_i$ represents a crossing of the $i$-th strand passing over the $(i + 1 )$-th strand. We will observe the group structure of $B_n$ and draw connections to knot theory.

PB 192

Rafael Lopez - Rumor Spreading

Abstract: To understand how rumors would be spread throughout a population, a logistic equation DN/dt = k*N*(P-N) was utilized. We found the equilibrium solution, general solution, and applied multiple variables to understand the rate at which rumors spread throughout a population. We were able to graph multiple models that represent this problem well on Maple. We found it interesting that the rate was so fast at spreading throughout the population and we would've never expected the results we got. This is relevant in showcasing how fast things spread throughout a population.

PB 138

Christy Nakad - Recovering Seismic Sources via Inversion and Iterative Techniques

Abstract: In exploration seismology, seismic data plays a vital role in understanding Earth's subsurface and locating resources. Seismic sources are often estimated through inverting wave equations modeling the seismic waves. Upon recovering seismic sources, medium parameters may then be additionally recovered. Although both the seismic source and medium parameters are not specified in practice, it is first essential to correctly recover the source parameter through inversion. In this presentation, we model seismic waves with the acoustic equations, given medium parameters, and invert to solve for the seismic source.

11:00

PB 191

Grace Burton - The Tied Braid Monoid

Abstract: A monoid is a set together with an operation, such that the set is closed under the operation, it has an identity element and the operation is associative. The tied braid monoid, TB_n, is the monoid whose elements are tied braids on n strands. Such a braid can be drawn as n vertical strings, where strings can go one over another or have a tie between two strings. We draw a tie as a spring between two strands of the braid. In this talk, we will provide a presentation of the tied braid monoid, TB_n, via generators and relations, provide diagrammatic explanations of the monoid relations, and a motivation for studying this algebraic structure.

PB 192

Manjot Dhanda - Right-Handed Snails

PB 138

Ignite Talks

Isaac Ramos - A Glimpse of Math Club

A quick view into Fresno State's very own Math Club. Learn about our officers, club advisor, activities held during the semester, and opportunities to get involved within the Mathematics Department.

Catie Corchado - YeS I AM talking about SIAM!

Looking for programming tutorials, student internship presentations, craft making, auctions, and great snacks? Get a glimpse of all the great benefits of joining the Society for Industrial and Applied Mathematics chapter at Fresno State. You may even see yourself or a classmate/friend make a guest appearance!

Jocelyn Hernandez and Itzel Michel-Carrillo (w/ Dr. Rajee Amarasinghe) - Our Experience of Study Abroad to Sri Lanka 2024

In the summer of 2024, twenty-one students, primarily mathematics majors, participated in a week-long study abroad program titled Exploring K-16 STEM Education in Sri Lanka. This presentation aims to share our experiences and inspire other mathematics majors to consider participating in similar study-abroad programs. The program included visits to universities, teacher training institutions, and a high school, where we engaged with local students and educators. Additionally, we explored cultural landmarks, offering a rich blend of academic and cultural immersion. During this presentation, we will showcase pictures and videos from our journey and reflect on the insights we gained through this transformative experience.

Dr. Yaomingxin Lu - The Power of Algebra Tiles: Enhancing Algebraic Understanding

Algebra tiles are a hands-on tool that help students bridge the gap between concrete and abstract mathematical concepts. This talk explores how algebra tiles can enhance understanding of operations with polynomials, factoring, and solving equations. By providing a visual and tactile representation of algebraic expressions, algebra tiles make abstract ideas more accessible and promote deeper conceptual understanding. Practical examples will demonstrate how this tool supports active learning, differentiation, and student engagement in the classroom.

Dr. Michael Bishop - The Wyatt Earp Effect

Whenever we model a phenomenon using probability, we learn a lot about the 'average' or 'expected' outcomes. But what about exception outcomes and outliers? One outlier was Wyatt Earp: a lawman from the Wild West who survived and won many gunfights without being grazed by a bullet. Was he an amazing gunfighter or simply lucky? In this Ignite talk, we will discuss the probability of outliers.