Unitary Rational Functions: The Scaled Quaternion Case,
2026
Chapman University
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 …
Let's Play Uno! Training Mathematical Thinking With An Inclusive Card Game,
2026
University of Luxembourg, Luxembourg
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 …
Arbitrage-Free Pricing With Diffusion-Dependent Jumps,
2026
Dept of Math., Hofstra University, Hempstead, NY 11549, USA
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.
Evaluating Lunch Plan Data In The St. Charles School District (Scsd),
2026
Lindenwood University
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 …
Teaching Numeracy For Social Justice: Educational Equity,
2026
Lehman College and the Graduate Center of the City University of New York (CUNY)
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 …
The Sunday Math Circle,
2026
Amherst College
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.
When The Gorenstein Projective Modules Are Precovering: A Survey On The Existence Of The Gorenstein Projective Precovers,
2026
Georgia Southern University
When The Gorenstein Projective Modules Are Precovering: A Survey On The Existence Of The Gorenstein Projective Precovers, Alexis L. Mcburney
College of Graduate Studies: Theses & Dissertations
This thesis surveys known results on the existence of Gorenstein projective precovers and studies conditions under which the class of Gorenstein projective modules is precovering. In classical homological algebra, projective resolutions are used to study modules, while relative homological algebra replaces projective modules with a different class that must be precovering for resolutions to exist. Gorenstein homological algebra extends these ideas using Gorenstein projective modules. We review key developments by Jorgensen, Murfet and Salarian, Estrada, Iacob, and Yeomans, and Cortés and Saroch. We discuss the strongest known existence result, showing that Gorenstein projective precovers exist under suitable conditions; in particular, …
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 …
Mat 1500 Calculus I Syllabus,
2026
CUNY Kingsborough Community College
Mat 1500 Calculus I Syllabus, Tian Cai
Open Educational Resources
No abstract provided.
Mat 1600 Syllabus Ii Syllabus,
2026
CUNY Kingsborough Community College
Mat 1600 Syllabus Ii Syllabus, Tian Cai
Open Educational Resources
No abstract provided.
Balanced Multi-Party Tournament Designs,
2026
Wayne State University
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, …
Understanding Möbius Inversion As Composite Of Dual Pairs,
2026
University of Kentucky
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.
Education And The Maternal Childcare Gap: Evidence From The Uk Covid-19 Pandemic,
2026
University of Richmond
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 …
Spillover Effects Of Medicare Advantage On Fee-For-Service Post-Acute Care Spending,
2026
University of Richmond
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 …
Arrangements Of N Planes Resulting In One Bounded Tetrahedral Chamber,
2026
The University of Akron
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 …
Catalan And Hyper-Catalan Numbers: Combinatorial Applications To Polynomial Equations,
2026
The University of Akron
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 …
Fostering A Growth Mindset In Mathematics: Faculty And Student Experiences,
2026
Illinois State University
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 …
Student Conceptions Of Summation And Limits In The Definite Integral Following Quantitatively Focused Instruction,
2026
West Virginia University Institute of Technology
Student Conceptions Of Summation And Limits In The Definite Integral Following Quantitatively Focused Instruction, Caleb Daniel Holloway
2026 Scholarly Teaching Conference: Concurrent Session Papers
Recent studies have examined how students form productive conceptions of the definite integral and discussed techniques for promoting such conceptions. In this paper I present findings from interviews held with six students enrolled in second-semester calculus, four of whom had received quantitatively focused instruction on the definite integral. All six were chosen for their observed use of summation conceptions on definite integral problems, and here their conceptions are explored further. Additionally, we gain insight on their thinking regarding limits as related to the definite integral. The findings presented here add to our understanding of student thinking regarding the integral and …
Exploring The Metric Dimension Of The Graph Representing A Four-Ring Polycyclic Aromatic Hydrocarbon: Interstellar 1-Cyanopyrene,
2025
Statefields School, Incorporated
Exploring The Metric Dimension Of The Graph Representing A Four-Ring Polycyclic Aromatic Hydrocarbon: Interstellar 1-Cyanopyrene, Andrei Matthew V. Robino, Sebastian Alex C. Traviña, Karl Benedict P. Narag, Mark Anthony B. Casao, Helix Raven C. Llanes, Azriel C. Alejo, Jonel C. Celamor
Sinaya: A Philippine Journal for Senior High School Teachers and Students
A graph's metric dimension is a parameter that denotes the minimum possible number of vertices in a subset that gives each vertex in the graph a unique representation. Despite extensive research on the metric dimension of polycyclic aromatic hydrocarbons (PAHs), there is currently no focused analysis on the metric basis and metric dimension of 1-cyanopyrene. In chemistry, graphs can be used to depict molecular structures. In this study, graph theory, specifically the concept of metric dimensions, is applied to the molecular structure of 1-cyanopyrene, which was detected in space for the first time in 2024. 1-cyanopyrene is a molecule made …
Locally Integral Involutive Po-Semigroups,
2025
Chapman University
Locally Integral Involutive Po-Semigroups, José Gil-Férez, Peter Jipsen, Melissa Sugimoto
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show that every locally integral involutive partially ordered semigroup (ipo-semigroup) A=(A,≤,⋅,∼,−), and in particular every locally integral involutive semiring, decomposes in a unique way into a family {Ap:p∈A+} of integral ipo-monoids, which we call its integral components. In the semiring case, the integral components are unital semirings. Moreover, we show that there is a family of monoid homomorphisms Φ={φpq:Ap→Aq:p≤q}, indexed over the positive cone (A+,≤), so that the structure of A can be recovered as a glueing ∫ΦAp of its integral components along Φ. Reciprocally, we give necessary and sufficient conditions so that the Płonka sum of any family …
