Other Mathematics Commons^™

Rockin’ Rover On The Rainbow Road, Michael Kolta, Lawrence Burgee, Ying Yuan

Transformations

This paper presents a progressive series of age-appropriate lesson plans for grades K-12 that all use the same interdisciplinary activity to educate students about Science, Technology, Engineering, Art, and Mathematics (STEAM) simultaneously. Technology from Texas Instruments (TI) was employed including a TI Nspire graphing calculator that can run Python programs, a TI Innovator Hub, and a TI Rover. The TI Rover is a small, robotic car that has sensors and is controlled by the calculator via the Hub hardware interface. A Python program was developed that uses the color sensor in the Rover to detect the color on colored paper …

Machine Learning For Predictive Energy And Emissions Modeling Of Vehicles And Power Grids In The United States, S M Tanvir Faysal Alam Chowdhoury

Dissertations

The environmental benefits of electric vehicle (EV) adoption depend on more than replacing internal combustion engine vehicles with electric powertrains. EV adoption reshapes electricity demand, interacts with regional generation mixes, and influences travel behavior and congestion, creating a coupled transportation-energy system in which vehicle and power-plant emissions must be evaluated together. This dissertation develops machine-learning frameworks for predicting energy consumption and emissions from vehicles and power grids under rising EV adoption. The first component forecasts grid emissions from EV charging. Using simulation data from NREL's Cambium database, a Prophet-based time-series framework predicts carbon dioxide, nitrous oxide, and methane emission rates …

Comparing 3-Connectedness And Roundness In Matroid Theory, Blanca Delia Larios

Electronic Theses, Projects, and Dissertations

A matroid is a discrete mathematical object that abstracts and connects the various notions of independence found throughout mathematics. Such notions of independence include linear independence, algebraic independence, as well as notions of independence that arise in graph theory. There are many broad classes of matroids. Important examples include binary matroids, graphic matroids, regular matroids, uniform matroids, and various levels of connected matroids. Some of the most important problems in matroid theory involve characterizing classes of matroids so that such characterizations can be used to prove results concerning these matroid classes. This thesis is a study of two important classes …

Advantages Of Dynamic Representation For Related Rates Problems In Calculus, Eri Osuna

Electronic Theses, Projects, and Dissertations

Related-rates problems are a standard yet persistently difficult topic in first-semester calculus. Research increasingly recommends dynamic visualization tools such as GeoGebra, but direct comparisons of static and dynamic representations in related-rates settings remain scarce. This qualitative study examines how representation type shapes the quality of students' reasoning and their perceived experience during related-rates problem solving. Six mathematics students who had completed Calculus —a group of four undergraduates and a pair of graduate students—completed a static sliding-ladder task and a dynamic airplane-and-camera task supported by an interactive GeoGebra applet, followed by an interview. Findings indicate that the two representations supported reasoning …

Waiting For The Magic: A Historical And Mathematical Study Of Queues In Disney Theme Parks, Nina E. Becket

Journal of Humanistic Mathematics

This paper, written as part of an honors research project in high school, provides an introduction to the line and queuing systems at Disney theme parks. We begin with a brief history of Disney World and its creators. We then introduce the basics of queuing theory and queuing notation. Finally, we examine modern line systems at Disney (as of 2023) and the future of its different queue systems.

Math 141 Calculus I (Queens College), Anisha Clarke

Open Educational Resources

This syllabus provides the outline for a calculus one course using OpenStax Calculus Volume I and no graphing calculator.

Math 119: Math For Elementary School Teachers Syllabus, Seth Lehman

Open Educational Resources

OER course syllabus for Math 119, Math for Elementary School Teachers, at Queens College

Math 119: Math For Elementary School Teachers Instructor Guide, Seth Lehman

Open Educational Resources

OER instructor guide for Math 119: Math for Elementary School Teachers at Queens College

A Stochastic Maximum Principle For Singular Mean-Field Regime-Switching Optimal Control, Maalvladedon Ganet Some, Edward Korveh

Journal of Stochastic Analysis

In this paper, we investigate a mean-field singular stochastic optimal control problem for systems governed by mean-field regime-switching singular stochastic differential equations. The state process is assumed to depend on both a regular and a singular control, and the coefficient associated with the singular component is allowed to be regime dependent. We derive both necessary and sufficient singular stochastic maximum principles. Because the regular control domain is not assumed to be convex, we employ the spike variation technique and obtain the necessary maximum principle by introducing a second-order adjoint process. As an application, we use the main theoretical results to …

Generalized Delayed Black–Scholes Formula, Bi Gole Hubert Le, Auguste Aman

Journal of Stochastic Analysis

The aim of this paper is to derive an explicit pricing formula for European options when the underlying asset follows a linear generalized delay differential equation in two distinct financial markets. The pricing methodology is based on the construction of an equivalent martingale measure using Girsanov’s theorem. Our models preserve both the no-arbitrage condition and market completeness. As such, this work extends the framework previously developed by Arriojas et al. in [16], providing a broader class of delay-based option pricing models.

Robust Optimal Consumption, Investment And Reinsurance For Recursive Preferences, Elizabeth Dadzie, Wilfried Kuissi Kamdem, Marcel Ndengo

Journal of Stochastic Analysis

This paper investigates a robust optimal consumption, investment, and reinsurance problem for an insurer with Epstein-Zin recursive preferences operating under model uncertainty. The insurer’s surplus follows the diffusion approximation of the Cramér-Lundberg model, and the insurer can purchase proportional reinsurance. Model ambiguity is characterised by a class of equivalent probability measures, and the insurer, being ambiguity-averse, aims to maximise utility under the worst-case scenario. By solving the associated coupled forward-backward stochastic differential equation (FBSDE), we derive closed-form solutions for the optimal strategies and the value function. Our analysis reveals how ambiguity aversion, risk aversion, and the elasticity of intertemporal substitution …

An Itô Integral For A Two-Sided Lévy Process, Raluca Balan, Jaime Garza

Journal of Stochastic Analysis

In this article, we construct an Itô integral with respect to a two-sided finite-variance Lévy process {L(x)}x∈R, without a Gaussian component. Using Rosenthal inequality for discrete-time martingales, we give an estimate for the p-th moment of this integral, for any even integer p ≥ 2. Then, using Poisson-Malliavin calculus, we show that the Itô integral is an extension of the Hitsuda-Skorokhod integral with respect to the compensated Poisson random measure associated to the Lévy process.

Supersymmetric Quantum Fields Via Quantum Probability, Radhakrishnan Balu

Journal of Stochastic Analysis

The super version of imprimitivity theorem is available now to describe global supersymmetry of systems using the representations of super Lie groups (SLG). This result uses the equivalence between super Harish- Chandra pairs and super Lie groups, at the categorical level, and is applicable to super Poincaré group and generalizes a smooth SI to super context. We apply the result to build supersymmetric quantum fields. Towards this end, we set up a super Fock space of a disjoint union of super Hilbert spaces which is equivalent to super tensoring of boson (even) part symmetrically and that of fermion (odd) part …

Convergence To Fractional Brownian Motion For Weighted Random Sums In Besov Space, Ibrahima Mendy

Journal of Stochastic Analysis

We consider infinite sums of weighted i.i.d. random variables, with finite variance and arbitrary distribution, and we derives conditions for the weak convergence in Besov space of normalized sums to fractional Brownian motion (fBm).

Pricing Variance Swaps Using Extended Heston Model, Semere Gebresilasie, Mulue Gebreslasie, Indranil Sengupta

Journal of Stochastic Analysis

Abstract. In this study, we introduce a variance swap for the underlying asset utilizing the Heston model, incorporating a long-term variance that is treated as a stochastic function of time. We develop a closed-form solution for the variance swap under this framework, where the log returns are driven by a compound Poisson process. Our analysis of historical data reveals that long-term variance is not constant; instead, it fluctuates over time, reflecting market dynamics more accurately. By integrating this time-varying long-term variance into the model, we achieve an improvement in prediction performance of approximately 60%. Furthermore, we perform model calibration using …

Bias, Structure, And Inference In Applied Network Analysis, Anna Vasenina

Dartmouth College Ph.D Dissertations

This dissertation develops mathematical and statistical methods for extracting reliable information from network data across biological applications, with an emphasis on understanding what observed network structure can and cannot resolve. The first study leverages protein–protein interaction network topology in the c-di-GMP signaling system of Pseudomonas fluorescens, showing that node centrality measures accurately classify protein domain types and that physical interaction structure contributes statistically significant predictive power for biofilm formation phenotypes across nearly 200 environments, while gene expression does not. The second study examines sampling bias in lemur-plant trophic interaction networks in Madagascar, demonstrating that differential detection of diurnal versus …

Quiver Of Affine Monoid Of A Vector Space Over Finite Field, James Junie Chen Cleary

Dissertations, Theses, and Capstone Projects

In this paper, we study the quiver of the complex monoid algebra CAFF(n, q). There are n + 1 maximal subgroups of AFF(n, q), each isomorphic to AGL(k, q) for some 0 ≤ k ≤ n. Every irreducible representation of CAFF(n, q) arises from a character of CAGL(k, q) for a suitable k. Thus, we study two different approaches to classifying the characters of CAGL(k, q). Next, we compute the full quiver Q(CAFF(n, q)). Finally, we show that this quiver is a disjoint union of straight-line paths and that its basic algebra has radical square zero. Hence, it has finite …

Algorithmic Problems In Automorphic Orbits Of Free Groups, Siobhan B. O'Connor

Dissertations, Theses, and Capstone Projects

One of the fundamental problems in the field of combinatorial group theory is telling when two group presentations represent isomorphic groups. Since applying a free group automorphism to the set of relators of a presentation gives an isomorphic group, we want to be able to quickly decide when looking at a relator whether a given word can be sent to it via an automorphism. We give a hands-on introduction to the automorphisms of free groups using patterns of colored beads. We show that you can make this decision correctly in constant time on average by looking for "orbit-blocking" words that …

Identifying Textual Predictors Of Early Termination In Clinical Trials In Medicine: An Explainable Machine-Learning Study, Rohan Ramnarain

Dissertations, Theses, and Capstone Projects

About one in five clinical trials in medicine ends early, wasting valuable resources and reducing the evidence available for developing life-saving medical treatments. This project uses a method called Trial2Vec, which is a self-supervised machine-learning method that converts clinical trial documents into dense numerical representations that capture their key design and clinical characteristics, to turn each proposed clinical trial’s written protocol into a compact numerical profile (a process referred to as embedding). These profiles are then paired with a predictive machine learning models to identify the words and phrases in the trial documents that can signal a higher risk of …

Comparing The Sensitivity And Degree Of Boolean Functions Via The Hypercube, Anne-Caroline Rupp

University Honors Theses

This thesis studies three complexity measures of total Boolean functions f:{0,1}ⁿ → {0,1}: maximum sensitivity s(f), polynomial degree deg(f), and spectral sensitivity λ(f), where λ(f) is defined as the spectral norm of the adjacency matrix of the sensitivity graph. Building on the results of Aaronson et al., we examine the inequality chain √s(f) ≤ λ(f) ≤ deg(f) and investigate whether all three quantities can be simultaneously equal.

The first part of the thesis reverse engineers the equality cases of the two known inequalities to isolate necessary extremal conditions on both the Fourier structure of f and the local geometry …