Mathematics Commons^™

Refracting Ufos: Solutions For Fermi Questions, May 2024, John Adam

Mathematics & Statistics Faculty Publications

This article, titled "Refracting UFOs: Solutions for Fermi Questions, May 2024," recounts the author's personal experience as a teenager observing a UFO sighting near their home in England. The author used their telescope to observe the object, which turned out to be lights from a distant airplane flying in a circular holding pattern. The article then presents two questions related to the observed phenomenon, including estimating the diameter of the aircraft's path and the banking angle of the aircraft at its speed. The article concludes with a solution to estimating the distance to the aircraft. The information is presented objectively …

Refracting Ufos, John Adam

Mathematics & Statistics Faculty Publications

Question 2: Assuming θ ≈ 2° = π/90 rad, estimate the distance R to the aircraft. Assume that R ≫ d. Question 1: Suppose that the observed “period of oscillation” is 1 min, and the speed of the aircraft is 200 km/h. Estimate the diameter d of the aircraft path (assuming that it is circular). Estimate the banking angle of the aircraft at this speed. While still a teenager (and aspiring astronomer), I became interested in the subject of UFOs (more appropriately named UAPs—see Ref. 1). The region in which I lived (50 km west of London) was in the …

Sky Smiley Face: Solutions For Fermi Questions, November 2024, John Adam

Mathematics & Statistics Faculty Publications

Question 2(a): By rotating Fig. 2 counterclockwise by 90°, explain why circumhorizontal arcs (CHAs) [Figs. 1(b) and (c)] form (under favorable conditions) only when the solar altitude exceeds 58° of arc. (In this case, the incoming ray enters a vertical face of an ice crystal and exits via the lower horizontal face.)Question 2(b): By considering the tilt of Earth’s imaginary N–S axis toward the plane of its orbit around the Sun (∼23.5°), explain why in the northern hemisphere CHAs cannot be seen above about latitude 56° N.

The History And Basics Of Fourier Series And Applications, Syafino Yunalfian

A with Honors Projects

This research paper discusses the basics of the Fourier series, how to construct the series, and a brief explanation of Fourier Transform.

Exploring Sigmoidal Bounded Confidence Models With Mean Field Methods, Tian Dong

HMC Senior Theses

Mathematicians use models of opinion dynamics to describe how opinions in a group of people change over time, which can yield insight into mechanisms behind phenomena like polarization and consensus. In these models, mathematicians represent the community as a graph, where nodes represent agents and edges represent possible interactions. Opinion updates are modeled with a system of differential equations (ODEs). Our work focuses on the sigmoidal bounded confidence model (SBCM), where agents update their opinion toward a weighted average of their neighbors' opinions by weighting similar opinions more heavily. Using tools developed in physics (mean-field theory), we derive a continuity …

On Weyl Representations Of Gl(N), Amairani Hernandez Garcia

Mathematics Dissertations - Archive

This thesis studies generalized Laurent polynomial representations of the general linear Lie algebra. These representations arise naturally as representations over the Weyl algebra consisting of differential operators on $\mathbb{C}^n$. Our main result is an explicit description of the socle filtration of $P_{\mu} = \Span \{x^{\bf m} \: | \: {\bf m} \in \mathbb Z^{n}, \: | \bf{m} | \: = \mu \}$ for $\mu \in \mathbb{Z}$.

A Study On The Correlation Between A Star's Rayleigh-Taylor Characteristic Timescale And Stellar Wind Activity, Fiona Klett

Undergraduate Journal of Mathematical Modeling: One + Two

In this paper, we investigate the correlations between a star's internal dynamics due to the Rayleigh-Taylor instability and episodes of stellar wind activity, using both a theoretical model and observational data from the NOAA.% \cite{NOAA}. Besides its relevance as an astrophysics problem, this study is also informative for models of climate change which include secular perturbations in the Sun's internal dynamics, as a potential source of solar activity variability.

Manifold Learning In Robotics: A Tutorial And Survey, Marcus Hawkins

Computer Science and Engineering Theses - Archive

In this article, we hope to represent the current state of the art of manifold learning in an understandable and approachable way. The authors will present a general overview core algorithms associated with linear and nonlinear dimensionality reduction techniques, give rudimentary definitions from differential geometry, and tenets of robotic perception, manipulation and path planning. Some of the historical applications of these algorithms will be presented, as well as conjectures about future uses, through examples from peer-reviewed journals.

Exploring The Role Of Undergraduate And Graduate Real Analysis Experiences In The Mathematical Trajectories Of Women Mathematicians From Historically Disenfranchised Groups, Te'a Riley

Mathematics Dissertations - Archive

This phenomenological study examines the role of undergraduate and graduate Real Analysis courses in shaping the mathematical trajectories of seven women Ph.D. mathematicians from groups historically disenfranchised in mathematics.Qualitative analysis of interviews explores various aspects of their development as mathematicians with a focus on their experiences in Real Analysis. This study applies Ryan & Deci’s (1985) Self-Determination Theory's Basic Psychological Need Theory and Critical Race Theory to analyze the trajectories of the participants. The research explores how the fulfillment of basic psychological needs in their Real Analysis courses may have influenced their academic and professional journeys. The basic psychological need …

Calculus Students’ Problem-Solving Strategies On Related Rates Of Change Problems Appearing In Online Versus Paper-And-Pencil Format, Tyson Bailey

Mathematics Dissertations - Archive

This study explores first-semester calculus students’ use of mathematical problem-solving strategies while working related rates of change problems in both an online homework format and a traditional pencil-paper format. We address two research questions: (1) How do students’ mathematical problem-solving strategies when working online homework on related rates of change problems compare with their problem-solving strategies when working paper-and-pencil homework related rates of change problems? (2) What influence does the ‘view an example’ feature in online homework have on a student’s problem-solving strategies when working an online RRC homework problem? Using scores on free-response midterm exam problems on related rates …

Quantifying Non-Primary Dna Formations Through Mechanical And Geometric Models, Sonia E. Teodorescu

Undergraduate Journal of Mathematical Modeling: One + Two

In this article, mechanical and geometric models for DNA strains (regarded as a helical structure in 3 dimensions, embedded into surfaces of various shapes (straight or curved cylinders, spheres, or projected into planes), are analyzed in order to obtain parameter estimates for DNA characteristics which can be used to detect the formation of secondary and tertiary formations in the presence of disorder. The models allow for the explicit representation of the DNA shape on constrained geometries and can therefore be implemented directly into {\it{ab initio}} or synthetic simulation studies.

Meromorphic Continuations Of Euler Products With Polynomial Growth Coefficients, Kledis Ahmetaj

Senior Honors Theses and Projects

In this paper, we investigate the meromorphic continuation of Euler products, with a particular focus on those with polynomial growth coefficients. Building upon the classical example of the Riemann zeta function, we derive conditions under which Euler products can be extended beyond their regions of convergence to broader domains of the complex plane, revealing singularities and deepening our understanding of their analytic properties. We begin by establishing a framework for meromorphic continuation and then introduce a general theorem that applies to Euler products of the form

where the coefficients and exponents satisfy specific constraints. We prove that such Euler products …

Computational Methods For Oi-Modules, Michael Morrow

Theses and Dissertations--Mathematics

Computational commutative algebra has become an increasingly popular area of research. Central to the theory is the notion of a Gröbner basis, which may be thought of as a nonlinear generalization of Gaussian elimination. In 2019, Nagel and Römer introduced FI- and OI-modules over FI- and OI-algebras, which provide a framework for studying sequences of related modules defined over sequences of related polynomial rings. In particular, they laid the foundations of a theory of Gröbner bases for certain classes of OI-modules. In this dissertation we develop an OI-analog of Buchberger's algorithm in order to compute such Gröbner bases, as well …

Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron

Honors College Theses

The properties of n-color compositions have been studied parallel to those of regular compositions. The conjugate of a composition as defined by MacMahon, however, does not translate well to n-color compositions, and there is currently no established analogous concept. We propose a conjugation rule for cyclic n-color compositions. We also count the number of self-conjugates under these rules and establish a couple of connections between these and regular compositions.

First-Order Geometric Integer-Valued Autoregressive Model With Covariates, Adisak Seedamad

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we propose two integer-valued time series consisting of (1) the single parameter first-order geometric integer-valued autoregressive (SGINAR(1)) model with covariates and (2) the first-order geometric integer-valued autoregressive GINAR(1) model with covariates. In our study, we obtain the innovation distribution using stationary properties and obtain moment properties of two models. In addition, we obtain parameter estimation by using the conditional least squares (CLS) method and the penalized conditional least squares (PCLS) method. Finally, we conduct simulation studies and apply to real data.

Developing Machine Learning And Time-Series Analysis Methods With Applications In Diverse Fields, Muhammed Aljifri

Theses and Dissertations

This dissertation introduces methodologies that combine machine learning models with time-series analysis to tackle data analysis challenges in varied fields. The first study enhances the traditional cumulative sum control charts with machine learning models to leverage their predictive power for better detection of process shifts, applying this advanced control chart to monitor hospital readmission rates. The second project develops multi-layer models for predicting chemical concentrations from ultraviolet-visible spectroscopy data, specifically addressing the challenge of analyzing chemicals with a wide range of concentrations. The third study presents a new method for detecting multiple changepoints in autocorrelated ordinal time series, using the …

Bayesian Analyses For Time-Varying Data And Opinion Dynamics, Torin Quinlivan

Graduate Research Theses & Dissertations

We consider Bayesian analyses for time-varying data from the opinion dynamics in social networks and the processes of sensorimotor learning. Firstly, understanding the underlying opinions of social media users is a difficult process, as they must be understood filtered through the messages sent. To understand how to best estimate the latent opinions, we use a Bayesian approach to estimate various characteristics of the users and the network. We present a model for using Bayesian methods for this problem, along with a simulation study to demonstrate effectiveness. Secondly, incentivization with punishments or rewards may affect human skill learning. To investigate the …

Volume 15, Connor Thompson, Emily Steffenhagen, Emily Robertson, Luis Fernando Dos Reis, Emily Farmer, Samuel Villa, Robert Allison, Zachary Chessor, Megan Borden, Austin Burnett, Larry W. Grant Jr., Tristan Marowski, Emma Moore, Pearl Siff

Incite: The Journal of Undergraduate Scholarship

Introduction Dr. Amorette Barber, Director, Office of Student Research

From the Editor Dr. Hannah Dudley-Shotwell

Artist’s Statement Connor Thompson

On Mentorship Dr. John Miller

The Meat of the Matter: Alien, Human, and Animal in Terry Bisson’s “They’re Made Out of Meat” by Emily Steffenhagen

“Please REBLOG!”: An Ethical Analysis of Doxxing, Internet Vigilantism and Racists Getting Fired by Emily Robertson

Journaling: Paper Has More Patience Than People by Luis Fernando Dos Reis

The Effects of Climate Change on the Archaeological World by Emily Farmer

Lowered Seat Height Does Not Impair Wingate Performance in Untrained Cyclists by Samuel Villa, Robert Allison, …

Prospective Teachers' Conceptions Of Area, Betsy Mcneal, Sayonita Ghosh Hajra, Michael Battista, Ayse Ozturk

Teaching & Learning Faculty Publications

This study explored 10 prospective teachers’ (PTs’) understanding of the area of a rectangular region using square and non-square rectangular area-units. In an hour-long interview, each PT was first asked to explain how they would find the area of a given rectangular region in terms of a non-square notecard. For several PTs, this task prompted discussion of a square unit defined by the edge of the notecard. In a second task, PTs were presented with a rectangular array of squares and were asked to explain to a fictional child why multiplying length times width does not count the top left …

Rado Numbers For Two Systems Of Linear Equations, Anthony Glackin

Electronic Theses and Dissertations

For any positive integer n and any equation E of either the form x1+x2+· · ·+xn = x0 or x1 + x2 + n = x0, the two-color Rado number R2(E) is the least integer such that any 2-coloring of the natural numbers 1 through R2(E) will contain a monochromatic solution to E. Let Ek be a system of k equations of the aforementioned form, where Ei represents the ith equation in Ek and the set I = {1, 2, . . . , k} is the set of indices of these equations. This thesis shows that the two-color Rado …

Principal Component Analysis With Application To Credit Card Data, Elenor Cain

Schultz-Werth Award Papers

Principal Component Analysis (PCA) is a type of dimension reduction technique used in data analysis to process the data before making a model. In general, dimension reduction allows analysts to make conclusions about large data sets by reducing the number of variables while retaining as much information as possible. Using the numerical variables from a data set, PCA aims to compute a smaller set of uncorrelated variables, called principal components, that account for a majority of the variability from the data. The purpose of this paper is to understand PCA and determine which principal components should be kept from a …

College Algebra, Leslie Bain

ATU Faculty OER Book Reviews

Review of OER College Algebra textbook by Carl Stitz, available at https://open.umn.edu/opentextbooks/textbooks/college-algebra

The Independence Polynomial Of A Graph At −1, Phoebe Rose Zielonka

Theses, Dissertations and Culminating Projects

No abstract provided.

Implementation Of 1/2-Approximation Path Cover Algorithm And Its Empirical Analysis, Junyuan Lin, Guangpen Ren

Mathematics, Statistics and Data Science Faculty Works

In this paper, we demonstrate a deterministic algorithm that approximates the optimal path cover on various graphs and networks derived from a wide range of real world problems. Based on the 1-Approximation Path Cover Algorithm by Moran et al., we first organize the original algorithm into two versions - one with redundant edge removal and one without. To compare the two versions of algorithms, we prove the number of redundant edges for any general graphs to analyze the effects of edge removal. We also analyze theoretical guarantees of the two algorithms. To test the time complexity and performance, we conduct …

Experiencing Tensions Of Nepantla With Inner-Departmental Change Groups, Rachel Tremaine, Jess Ellis Hagman, Matthew Voigt, Amy Been Bennett, Fanatasi Nicole, Margaret Ann Bolick, Leilani Pai, Nancy Kress, Kelsey Quaisley, Rachel Funk, Patricia Wonch Hill, Wendy M. Smith

Mathematics, Statistics and Data Science Faculty Works

This study explores the experiences of three Networked Improvement Communities (NICs) within mathematics departments as they work to critically transform their introductory mathematics programs. Drawing on the framework of dominant and critical axes of equity, we identify three key tensions experienced by the NICs: identity neutrality versus identity centrality, power over versus power with, and students as novices versus students as experts. These tensions are framed as productive enactments of working to change systems from within, highlighting the challenges and opportunities inherent in navigating the liminal space of nepantla. We argue that engaging with these tensions is crucial for fostering …

Machine Learning Approaches For Cyberbullying Detection, Roland Fiagbe

Data Science and Data Mining

Cyberbullying refers to the act of bullying using electronic means and the internet. In recent years, this act has been identifed to be a major problem among young people and even adults. It can negatively impact one’s emotions and lead to adverse outcomes like depression, anxiety, harassment, and suicide, among others. This has led to the need to employ machine learning techniques to automatically detect cyberbullying and prevent them on various social media platforms. In this study, we want to analyze the combination of some Natural Language Processing (NLP) algorithms (such as Bag-of-Words and TFIDF) with some popular machine learning …

Exploring Loss Functions In Machine Learning, Yujie Wang

CGU Theses & Dissertations

The loss function plays a critical role in machine learning. It is fundamental in training, evaluating, and optimizing machine learning models, directly impacting their effectiveness and efficiency in solving specific tasks. We explore three new loss functions and their applications. Softmax Cross-Entropy Loss, stands as a prevalent choice in neural network classification tasks. It treats all misclassifications uniformly. However, multi-class classification problems often have many semantically similar classes. We should expect that these semantically similar classes will have similar parameter vectors. We introduce a weighted loss function, the tree loss as a drop-in replacement for the cross entropy loss. The …

Σ-Ary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Enumeration Of Increasing Trees, Garrett M. Southwood

Honors College Theses

We consider the generating function for increasingly labelled trees. By generalizing the proof through symbolic method, we are able to study various statistics regarding binary increasing trees with respect to height restrictions. We then apply our approach to special colorings of increasing trees in order to obtain their generating functions and, from there, derive the counting sequence for (ak+a)-colored recursive trees. We also present some interesting bijections between colored and non-colored increasing trees.

Accessing And Assessing Components Of Elementary And Middle School Students’ Mathematical Disposition Through Metaphors, Emily Deal, Edward Mooney, Amanda Cullen, Neet Priya Bajwa, Allison M. Kroesch, Julien Corven, Beth Macdonald

Faculty Publications – Mathematics

This study examined student-generated metaphors comparing food to math as a means of accessing and assessing components of prekindergarten through Grade 8 students’ (N = 306) mathematical disposition. Previous research provided insight into predominantly affective components of older students’ mathematical disposition (i.e. Grade 4 through college). However, we extend these findings to include nonaffective components and younger students. Our study highlights the value in conceptualizing mathematical disposition as the sum of three mental functions, namely cognitive (e.g., mental processes such as reasoning), affective (e.g., attitudes, feelings, beliefs about mathematics or oneself as a learner), and conative (e.g., effort, grit, …