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Articles 31 - 60 of 1916

Full-Text Articles in Other Mathematics

Primitive Pythagorean Triples In Lean And Reduction Modulo Odd Prime Powers, Luke Biddle May 2026

Primitive Pythagorean Triples In Lean And Reduction Modulo Odd Prime Powers, Luke Biddle

Mathematical Sciences Undergraduate Honors Theses

Primitive Pythagorean triples (PPTs) are (a,b,c) triples that satisfy the Pythagorean theorem and share no other common factors outside of 1. This project examines these PPTs reduction modulo odd prime powers by combining proof writing and number-theoretical analysis with the process of verification and formalization in the Lean proof coding language. Using the parameterization of PPTs generated by using the unit circle with additional conditions, we investigate how these triples behave modulo  for odd primes , with emphasis on counting the number of elements in the set of PPTs (a,b,c) modulo pn . By using cases based on initial …

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A New Approach To Generate Combinatorial Patterns In Logical Analysis Of Data And Its Application To Predict College Retention, Salihah Ahmed E. Jaafari May 2026

A New Approach To Generate Combinatorial Patterns In Logical Analysis Of Data And Its Application To Predict College Retention, Salihah Ahmed E. Jaafari

Theses and Dissertations

Student retention and degree completion remain central challenges for higher-education institutions, with significant implications for student success, institutional effectiveness, and public accountability. While advances in predictive analytics have enabled earlier identification of students at risk of withdrawal, many commonly used machine learning approaches suffer from limited interpretability, constraining their practical usefulness for advising, intervention, and policy decision making. This dissertation addresses the problem of predicting student persistence by developing and evaluating optimization based, interpretable classification models within the Logical Analysis of Data (LAD) framework. Building on existing LAD formulations, this research introduces two novel pattern generation models, the Best Term …

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Examining Student Practices In A Technology-Mediated Math Classroom, Bradley T. Dodd May 2026

Examining Student Practices In A Technology-Mediated Math Classroom, Bradley T. Dodd

Electronic Theses, Projects, and Dissertations

It is important for math educators to make sense of student thinking in the classroom. Without opportunities to practice this skill math educators struggle to improve, particularly when students are engaging in mathematics using technology. As such, there is a need for video artifacts of students engaging with mathematics using technology for use in professional development activities (Lovett 2020). In accordance with Lovett et al.'s (2020) design principles for examining student practices in a technology-mediated environment, I carried out a study to determine whether these artifacts of student work could be created working with college undergraduates as participants. Students engaged …

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Decision Making For Large-Scale Problems Under Uncertainty And Conflict, Benjamin J. Hamlin May 2026

Decision Making For Large-Scale Problems Under Uncertainty And Conflict, Benjamin J. Hamlin

All Dissertations

Large-scale decision-making problems appear in many areas including long-range forecasting such as energy generation forecasting. Many such problems are subject to conflicting objectives and uncertain data, and can be modeled as linear optimization problems. We study novel theoretical results and algorithms for large-scale linear decision problems under conflict and uncertainty. First, we propose a parametric Benders decomposition algorithm for solving large-scale linear optimization problems with multiple objectives or deterministically uncertain objectives. Second, we extend the parametric Benders decomposition to a multi-stage setting, developing a parametric stochastic dual dynamic programming algorithm, which enables decision-making when conflicts and uncertainty have planning impacts …

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Fractsynth: Exploring Glitch Timbres With Chaos Theory, Aidan Roach Apr 2026

Fractsynth: Exploring Glitch Timbres With Chaos Theory, Aidan Roach

The Transdisciplinary STEAM+ Journal

In this paper, I explore how chaos theory can be used to design a new kind of synthesizer with the primary focus of producing glitchy, unpredictable sounds. Glitch music embraces abstract sound design, malfunctioning electronics, and randomness as the main compositional elements. However, most synthesizers rely on stable, repetitive oscillators that often sound too controlled. To challenge this, I developed FractSynth, a real-time synthesizer that uses chaotic attractors–including the Logistic Map, Henon Map, and Lorenz System–as modulation sources for frequency, amplitude, and tone. The software also features real-time Lyapunov Exponent Tracking, which gives users a direct visual of how …

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Interactions Of Dance And Mathematics: A Closer Look At Mathematical Sequences As Scores For Choreography From A Choreographic Lens, Caroline Wolfe Apr 2026

Interactions Of Dance And Mathematics: A Closer Look At Mathematical Sequences As Scores For Choreography From A Choreographic Lens, Caroline Wolfe

The Transdisciplinary STEAM+ Journal

This paper investigates the embodiment of infinite mathematical sequences through concert contemporary dance, examining how choreography can serve both as an artistic and analytical tool for exploring numerical patterns. Grounded in interdisciplinary literature on mathematical visualization in choreography, the study centers on two original choreographic works presented and performed at Missouri State University: Golden Ratio Sequence (Spring 2025), which maps the Fibonacci sequence and the natural applications of the Golden Ratio onto a spiral floor pattern, and Tetrahedral Numbers (Fall 2024), which employs an accumulation score to embody three-dimensional number growth through layered movement motifs and body created tetrahedra. The …

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Unique Combinations Of Packing Integer Squares, Keith M. Dreiling, Austin Leanna, William Mooney Apr 2026

Unique Combinations Of Packing Integer Squares, Keith M. Dreiling, Austin Leanna, William Mooney

SACAD: Scholarly Activities

This research investigates a function, informally named WAK(x), that describes the number of ways to divide an integer square into integer subsquares counting only the list of parts. Previous research has shown values up to 28, though finding these values is computationally complex and requires a long runtime using computer algorithms. We attempt to find patterns in the values and many aspects of the values, hoping to find a general solution. We are unsure if a solution exists, but we have ideas for how to move forward in finding a solution.

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Counting Hamiltonian Cycles In Quartic Circulant Graphs, Allison Hilliard Apr 2026

Counting Hamiltonian Cycles In Quartic Circulant Graphs, Allison Hilliard

Seaver College Research And Scholarly Achievement Symposium

We consider the problem of counting Hamiltonian cycles in circulant graphs $C^K_n$ where $n$ is the number of vertices and $K$ is a set containing elements that correspond to the allowed edges in the circulant graphs. After sorting the cycles by a topological invariant called the winding number, we use a modified transfer matrix method to convert local data into global structures. The result is a generating function that counts the number of Hamiltonian cycles in a circulant graph with $n$ vertices. The results for $K=\{1,2\}$ and $K=\{1,3\}$ have been found by previous authors. We focus on the case where …

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On Links Between A Theorem Of Schoenberg, Rohlin Decompositions Of Measures, The Bochner-Minlos Theorem And The Fock Space, Daniel Alpay, Paula Cerejeiras, Palle Jorgensen, Uwe Kaehler Mar 2026

On Links Between A Theorem Of Schoenberg, Rohlin Decompositions Of Measures, The Bochner-Minlos Theorem And The Fock Space, Daniel Alpay, Paula Cerejeiras, Palle Jorgensen, Uwe Kaehler

Mathematics, Physics, and Computer Science Faculty Articles and Research

The main goal of this paper is to gain new results in stochastics by drawing on, and combining, different areas that are normally not considered to be related. Thus, in this paper we extend the previous class of Gaussian-like functions ML which will allow for future generalized stochastic processes in infinite dimensional analysis. We show that an approach similar to the one by the classical Bochner-Minlos theorem for the white-noise case can be achieved by using Gaussian-like functions belonging to a large family -the MLr classes (0 < r ≤∞). We show how Schoenberg’s theorem for positive definite functions on a Hilbert space allows to go beyond the classical setting of Bochner-Milnos theorem. Furthermore, we show that the application of the Rohlin’s disintegration theorem allows for a decomposition of the associated probability measures , see Theorems 3.2 and 4.3. We end this paper with several important examples of functions in these classes MLr and provide some interesting counterexamples, e.g. Theorem 7.4, to get a …

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Automating Cardiff Model Data Capture In Emergency Departments: Ambient Nlp Integration With Oracle-Cerner Fhir Systems, Simi Augustine, Marco A. Lopez, Jacquelyn Cheun, Chris Papesh Mar 2026

Automating Cardiff Model Data Capture In Emergency Departments: Ambient Nlp Integration With Oracle-Cerner Fhir Systems, Simi Augustine, Marco A. Lopez, Jacquelyn Cheun, Chris Papesh

SMU Data Science Review

Violence and overdose events in Las Vegas occur at rates above the national average, with fewer than half of violent injuries reported to law enforcement [2,7]. The Cardiff Model offers a proven framework for standardized data collection and sharing between hospitals and public safety partners, yet many implementations still rely on manual entry. We propose an ambient triage pipeline integrated with Oracle-Cerner electronic health record systems to listen to nurse–patient dialogue, convert speech to text, extract Cardiff fields, and write standards-based FHIR Bundles for analytics. Using SMART on FHIR standards and Cerner Millennium APIs, the study evaluates whether ambient capture …

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Numerals And Other Means Of Expressing Plurality In Language And Thought: A Developmental Perspective Across Cultures., Giovanni Giuseppe G.G. Nicosia Prof. Mar 2026

Numerals And Other Means Of Expressing Plurality In Language And Thought: A Developmental Perspective Across Cultures., Giovanni Giuseppe G.G. Nicosia Prof.

Numeracy

Several ancient languages use linguistic structures to differentiate between singular, dual, and plural forms that are used when one, two, or many objects are referenced. (Some languages go further, adding a trial form to differentiate two from three.) In many modern languages, numerals are used to convey precise number. After reviewing a range of ways languages express number (including the interesting case of Pirahã which does not express precise number), the paper concludes with a proposed developmental path for the expression of quantity in languages.

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Minimal Supersolution Of Bsdes Driven By Continuous Martingales In A General Filtration, Badr Elmansouri, Mohamed El Otmani Feb 2026

Minimal Supersolution Of Bsdes Driven By Continuous Martingales In A General Filtration, Badr Elmansouri, Mohamed El Otmani

Journal of Stochastic Analysis

In this paper, we study minimal supersolutions of backward stochastic differential equations (BSDEs) driven by a continuous local martingale in a general filtration. We establish existence, uniqueness, and stability results under various mild conditions on the terminal value and the generator. Additionally, we explore the connection between the concept of non-linear expectation and minimal supersolutions, emphasizing the specific properties that are relevant to our framework. We also prove a general monotonic limit theorem and apply this result to determine the smallest constrained supersolution of a BSDE with a possibly non-convex constraint.

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A Virtual Community Math Circle, Skona Brittain, Sayonita Ghosh Hajra, Steve Heller, Daniel Hodgins, Peter Petto, Gabriella Pinter, Lauren Rose, A. Gwinn Royal, Asmita Sodhi Feb 2026

A Virtual Community Math Circle, Skona Brittain, Sayonita Ghosh Hajra, Steve Heller, Daniel Hodgins, Peter Petto, Gabriella Pinter, Lauren Rose, A. Gwinn Royal, Asmita Sodhi

Journal of Math Circles

The Julia Robinson Mathematics Festival (JRMF) Community Math Circle is free, volunteer-run, and online. We collaborate with JRMF and use their activities in our events. Started during the pandemic, the Community Math Circle continues to thrive. We have about 40 participants attending every month, typically kids aged 6 to 13, teachers, facilitators, and other adults. This article describes how our event is organized, planned, and executed, and how we train facilitators. We will also offer reflections on our successes and challenges.

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Effective Wordle Heuristics, Ronald I. Greenberg Feb 2026

Effective Wordle Heuristics, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

While previous researchers have performed an exhaustive search to determine an optimal Wordle strategy, that computation is very time consuming and produced a strategy using words that are unfamiliar to most people. With Wordle solutions being gradually eliminated (with a new puzzle each day and no reuse), an improved strategy could be generated each day, but the computation time makes a daily exhaustive search impractical. This paper shows that simple heuristics allow for fast generation of effective strategies and that little is lost by guessing only words that are possible solution words rather than more obscure words.

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Unitary Rational Functions: The Scaled Quaternion Case, Daniel Alpay, Ilwoo Choo, Mihaela Vajiac Feb 2026

Unitary Rational Functions: The Scaled Quaternion Case, Daniel Alpay, Ilwoo Choo, Mihaela Vajiac

Mathematics, Physics, and Computer Science Faculty Articles and Research

We develop the theory of minimal realizations and factorizations of rational functions where the coefficient space is a ring of the type introduced in our previous work, the scaled quaternions, which includes as special cases the quaternions and the split quaternions. The methods involved are not a direct generalization of the complex or quaternionic settings, and in particular, the adjoint is not the classical adjoint and we use properties of real Hilbert spaces. This adjoint allows to define the counterpart of unitarity for matrix-rational functions, and we develop the corresponding theories of realizations and unitary factorizations. We also begin a …

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Let's Play Uno! Training Mathematical Thinking With An Inclusive Card Game, Thierry Meyrath, Clara-Ioana Mincu, Antonella Perucca Jan 2026

Let's Play Uno! Training Mathematical Thinking With An Inclusive Card Game, Thierry Meyrath, Clara-Ioana Mincu, Antonella Perucca

Journal of Humanistic Mathematics

We explore probability exercises based on the game UNO. Excluding the Wild cards, the deck contains precisely 100 cards, which makes it convenient to express probabilities as percentages. We discuss the mathematical relation between cards that can be played after other cards. We also propose an algebraic exercise that relates several quantities, such as the number of cards left in the losing player’s hand. Finally, we argue that UNO is a very inclusive game: it is logistically easy to play, allows for players of different skill levels, and can be adapted to meet special needs. Beyond being playful exercises, our …

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Arbitrage-Free Pricing With Diffusion-Dependent Jumps, Hamza A. Virk, Yihren Wu, Majnu John Jan 2026

Arbitrage-Free Pricing With Diffusion-Dependent Jumps, Hamza A. Virk, Yihren Wu, Majnu John

Journal of Stochastic Analysis

Standard jump-diffusion models assume independence between jumps and diffusion components. We develop a multi-type jump-diffusion model where jump occurrence and magnitude depend on contemporaneous diffusion movements. Unlike previous one-sided models that create arbitrage opportunities, our framework includes upward and downward jumps triggered by both large upward and large downward diffusion increments. We derive the explicit no-arbitrage condition linking the physical drift to model pa- rameters and market risk premia by constructing an Equivalent Martingale Measure using Girsanov’s theorem and a normalized Esscher transform. This condition provides a rigorous foundation for arbitrage-free pricing in models with diffusion-dependent jumps.

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Evaluating Lunch Plan Data In The St. Charles School District (Scsd), Maddy Alexander, Guillermo Bilbao Olarreaga, Duncan Krige, Alyssa Schreiber, Nick Wintz, Wojciech Golik Jan 2026

Evaluating Lunch Plan Data In The St. Charles School District (Scsd), Maddy Alexander, Guillermo Bilbao Olarreaga, Duncan Krige, Alyssa Schreiber, Nick Wintz, Wojciech Golik

The Confluence

The SCSD is a public school district in St. Charles, with, on average, 4500 students a year. The SCSD is subdivided into an early childhood center, six elementary schools, two intermediate (5-6,7-8) schools, and two high schools. Vocational schools are also within this district but were not included in this report. The SCSD is concerned with the impact of the Covid-19 pandemic on their district’s population and on the number of students that needed assistance with lunch. They have asked Lindenwood’s 2024-25 PIC Math group to analyze their data from the years 2020-25 and identify any trends. Identifying these trends …

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Teaching Numeracy For Social Justice: Educational Equity, Esther Isabelle Wilder, Crystal C. Rodriguez, Caterina Shost, Eduardo Vianna, Frank Wang Jan 2026

Teaching Numeracy For Social Justice: Educational Equity, Esther Isabelle Wilder, Crystal C. Rodriguez, Caterina Shost, Eduardo Vianna, Frank Wang

Numeracy

The special collection, “Teaching Numeracy for Social Justice: Educational Equity,” focuses on how quantitative reasoning (QR) can function as a vehicle for equity, empowerment, and democratic participation. Building on a longstanding tradition that treats numeracy as inseparable from social justice, these contributions highlight how progressive pedagogies (e.g., active learning, authentic research, and equity-oriented assessment) have the potential to broaden access for students historically excluded from quantitative fields. The studies span a variety of conceptual frameworks, introductory and advanced quantitative instruction, and interdisciplinary applications, showcasing how inclusive QR practices can build confidence, agency, and real-world understanding. These articles demonstrate that when …

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The Sunday Math Circle, Nathan Pflueger Jan 2026

The Sunday Math Circle, Nathan Pflueger

Journal of Math Circles

Bob and Ellen Kaplan envisioned and organized a style of math circle centered on the idea that children of all ages can work like mathematicians do: creatively, collaboratively, and ecstatically. This article surveys four sample topics covered during a Sunday morning math circle in the Boston area, based on Bob and Ellen's invaluable guidance. I also offer some reflections on what I learned from Bob and Ellen, and how it is reflected in these math circles.

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Mathematics And Political Ideology: A Historical Argument Against The Cultural Understanding Of Mathematics As An Apolitical Field, And A Journalistic Report On The Impact Of The Trump Administration On American Mathematics In 2026, Philo Judson Jan 2026

Mathematics And Political Ideology: A Historical Argument Against The Cultural Understanding Of Mathematics As An Apolitical Field, And A Journalistic Report On The Impact Of The Trump Administration On American Mathematics In 2026, Philo Judson

Pitzer Senior Theses

The interplay between political ideology and mathematics is a recurring theme throughout the history of the academic field. Mathematics has been used as a tool of empire, while mathematicians have been elevated by states as symbols of national genius for political prestige. Political ideologies have also shaped the field from within, both through the suppression of mathematical thought and the enforcement of mathematical authority. Since 2025, the Trump administration has launched large-scale political attacks on American institutions of higher education, which include lawsuits, discrimination investigations, and the removal of federal funding from certain institutions that don’t adhere to the administration’s …

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Mat 1500 Calculus I Syllabus, Tian Cai Jan 2026

Mat 1500 Calculus I Syllabus, Tian Cai

Open Educational Resources

No abstract provided.

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Mat 1600 Syllabus Ii Syllabus, Tian Cai Jan 2026

Mat 1600 Syllabus Ii Syllabus, Tian Cai

Open Educational Resources

No abstract provided.

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Fostering A Growth Mindset In Mathematics: Faculty And Student Experiences, Yolanda G. Rush Jan 2026

Fostering A Growth Mindset In Mathematics: Faculty And Student Experiences, Yolanda G. Rush

Theses and Dissertations

According to the Center for Community College Student Engagement (2019), many students attending two-year institutions need productive persistence strategies, including the development of a growth mindset. Although some growth mindset interventions have been effective in improving academic achievement among students (Boaler, 2016; Canning et al., 2024) and persistence (Lewis, 2019) among students, especially those with developmental needs (Suh et al., 2019) and those in mathematics, little is known about the experiences of students and teachers (i.e., students’ perceptions of teachers’ intentions and implementation) as teachers work to foster a growth mindset culture (Murphy et al., 2021). In this dissertation, I …

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Balanced Multi-Party Tournament Designs, Parsa Nematollahe Jan 2026

Balanced Multi-Party Tournament Designs, Parsa Nematollahe

Honors College Theses

This paper introduces Multi-Party Tournament (MPT) designs that generalize established combinatorial structures, including Whist, Pitch, and Generalized Whist tournament designs. This work will formally define MPTs, establish the fundamental properties of resolvability, fullness, and balance, and formulate a mathematical and algorithmic foundation for multi-party tournament scheduling. The primary contributions of this research are the presentation of necessary and sufficient existence conditions for MPTs across various properties and parameters, the identification of connections between MPTs and other fields of mathematics such as combinatorial design theory, graph theory, and probability theory, and the investigation of MPT construction algorithms, including tree-search, finite-field constructions, …

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Understanding Möbius Inversion As Composite Of Dual Pairs, Isaac B. Kochmaan Jan 2026

Understanding Möbius Inversion As Composite Of Dual Pairs, Isaac B. Kochmaan

Theses and Dissertations--Mathematics

Möbius inversion is a well-studied computational tool in number theory and combinatorics, but it exhibits a pattern which may be familiar to those who study categorical traces. In 2016, Kate Ponto and Michael Shulman characterized duality and traces in the bicategory of profunctors for a particularly nice class of one-cells. We extend these results. Consequently, we construct, for a given poset, a profunctor whose Euler characteristic is the Möbius function of said poset. In light of this, we propose a categorical notion of Möbius inversion.

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Education And The Maternal Childcare Gap: Evidence From The Uk Covid-19 Pandemic, Lara Bakhaya Jan 2026

Education And The Maternal Childcare Gap: Evidence From The Uk Covid-19 Pandemic, Lara Bakhaya

Honors Theses

This paper examines whether college education shapes working mothers’ access to remote work, flexible working, and childcare hours in the United Kingdom, and whether COVID-19 school closures amplified these inequalities. Using data from the UK Time Use Survey (2016–2021), a repeated cross-sectional diary dataset spanning the pre-pandemic period and five COVID-19 waves, this paper estimates weighted logistic and ordinary least squares regressions on a sample of married or cohabiting, employed mothers. School closures serve as a natural experiment, providing an exogenous shock to caregiving demands that affected all mothers simultaneously regardless of education level. College education significantly predicted working from …

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Spillover Effects Of Medicare Advantage On Fee-For-Service Post-Acute Care Spending, Nyel Bangash Jan 2026

Spillover Effects Of Medicare Advantage On Fee-For-Service Post-Acute Care Spending, Nyel Bangash

Honors Theses

Does the growth of Medicare Advantage reduce fee-for-service post-acute care spending through practice-pattern spillovers, or do observed spending differences primarily reflect favorable selection? Using a county-level panel of roughly 2,700 counties (2014–2023) and a two-way fixed effects specification, I find that a one percentage-point increase in MA penetration is associated with $9.54 less per-capita standardized FFS spending. Spending per episode falls while participation rates remain stable, consistent with practice-pattern spillovers rather than compositional changes from selection. Welfare indicators from County Health Rankings, CDC PLACES, and CMS Care Compare show no evidence that spending reductions harm health or care quality. The …

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Arrangements Of N Planes Resulting In One Bounded Tetrahedral Chamber, Ava Knight Jan 2026

Arrangements Of N Planes Resulting In One Bounded Tetrahedral Chamber, Ava Knight

Williams Honors College, Honors Research Projects

This paper investigates the combinatorial geometry of plane arrangements in three-dimensional space, focusing on configurations that produce exactly one bounded tetrahedral chamber. We define T(n) as the number of face-combinatorial equivalence classes of arrangements of n planes in ℝ³ containing exactly one bounded tetrahedral chamber. Known values — T(3) = 0, T(4) = 1, and T(5) = 2 — are established through direct construction, while T(6) remains an open problem. This paper contributes experimental evidence toward resolving T(6) by systematically extending the two valid 5-plane arrangements and verifying, through a plane removal argument, that each yields a valid plane configuration …

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Catalan And Hyper-Catalan Numbers: Combinatorial Applications To Polynomial Equations, Leilani Natale Jan 2026

Catalan And Hyper-Catalan Numbers: Combinatorial Applications To Polynomial Equations, Leilani Natale

Williams Honors College, Honors Research Projects

In this paper, we study Catalan numbers and their generalization, hyper-Catalan numbers, and explore how these sequences arise naturally in the context of solving polynomial equations using infinite power series. We begin by introducing the Catalan numbers through their combinatorial interpretation as triangulations of convex polygons. Using this geometric definition, we derive a relation whose recursive structure leads to a quadratic functional equation. Interpreting this relation as a formal power series equation allows us to express solutions to quadratic equations as infinite power series whose coefficients are given by the Catalan numbers. This framework is then extended by allowing polygon …

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