Digital Commons Network^™

Math 614-002: Numerical Methods I, X. Zhao

Mathematical Sciences Syllabi

No abstract provided.

Math 660-102: Intro To Stat Comp W/ Sas &R, C. Jin

Mathematical Sciences Syllabi

No abstract provided.

Math 661-104: Applied Statistics, T. Falconer

Mathematical Sciences Syllabi

No abstract provided.

Math 664-102: Methods For Stat Consult, J. Loh

Mathematical Sciences Syllabi

No abstract provided.

Math 678-102: Stat Methods In Data Science, A. Wang

Mathematical Sciences Syllabi

No abstract provided.

Math 707: St: Numerical Linear Algebra, K. Wicke

Mathematical Sciences Syllabi

No abstract provided.

Math 713-002: Advanced Scientific Computing, M. Siegel

Mathematical Sciences Syllabi

No abstract provided.

Representation Theory, Geometry And Combinatorics Associated To Springer Fibers, Do Kien Hoang

Yale Graduate School of Arts and Sciences Dissertations

This dissertation explores various aspects of Springer fibers and their deep connections to geometric and combinatorial representation theory. It combines the works of [H24a], [H24b], and [H24c] by the author during his PhD. Throughout these works, we explain sophisticated roles of Springer fibers in modern topics like modular representation theory and symplectic duality. Additionally, we resolve several classical questions concerning the Springer correspondence and the cohomology of Springer fibers.

The first project centers around a discretization of a Springer fiber Be. This discretization is a finite set Ye that has appeared in various contexts in representation theory. …

Construction Techniques For Linear Realizations Of Multisets With Small Support, M. A. Ollis

Emerson Authors, Researchers, & Creators

The Buratti-Horak Rosa Conjecture is a problem in graph theory asking when we can find a Hamiltonian path in the complete graph that has various properties to do with edge lengths. In this paper, we use constructive methods to show that the conjecture is true for various parameter sets where it was previously unknown.

Pairwise Comparison Method Toolkit. A Toolkit For Countries To Measure Global Learning Outcomes., United Nations Educational, Scientific And Cultural Organization (Unesco), Australian Council For Educational Research (Acer)

Global education monitoring

This toolkit has been co-authored by the Global Education Monitoring (GEM) Centre at the Australian Council for Education Research (ACER) and the United Nations Educational, Scientific and Cultural Organization (UNESCO) Institute for Statistics (UIS). ACER provides technical support to the UIS, which has been mandated to monitor the progress of countries towards achieving Sustainable Development Goal 4 (SDG 4) in education to “ensure inclusive and equitable quality education and to promote lifelong learning opportunities for all” (United Nations, 2021). The GEM Centre sponsors and contributes to public goods and activities that facilitate education systems reporting against SDG 4 in a …

Growth Indicators And Conformal Measures For Transverse Groups And Ergodic Dichotomy For Subspace Flows In Higher Rank, Yahui Wang

Yale Graduate School of Arts and Sciences Dissertations

Let G be a connected semisimple real algebraic group. The class of transverse subgroups of G includes all discrete subgroups of rank one Lie groups and any subgroups of Anosov or relatively Anosov subgroups. Given a transverse subgroup Gamma, we show that the Gamma-action on the Weyl chamber flow space determined by its limit set is properly discontinuous. This allows us to consider the quotient space and define Bowen-Margulis-Sullivan measures. We then study the ergodicity of a one-parameter diagonalizable subgroup of G acting on the aforementioned quotient space, equipped with a Bowen-Margulis-Sullivan measure. We obtain an ergodicity criterion similar to …

3. Checkit Oer Assessment Generator, Steven Clontz, Sharona Krinsky, Drew Lewis

Open Educational Resources For and As Assessment

The CheckIt framework is an open educational technology for authoring randomized exercises, banks, and assessments for mathematics. Technological means facilitate the easy sharing and modification of open-source templates and generators authored in the framework to be used both in classrooms as well as to support educational research; case studies in this paper illustrate its use in both contexts, and describe its use in both small and large classrooms.

Mumford Relations And The Cohomology Of Le Potier Moduli Spaces, Weite Pi

Yale Graduate School of Arts and Sciences Dissertations

The goal of this thesis is to study the cohomological aspect of Le Potier’s moduli space of 1-dimensional sheaves on the projective plane. Our main technical tools are Mumford-type geometric relations, formulated originally over moduli of bundles on curves and generalized to sheaves over del Pezzo surfaces in this thesis. We prove that these relations can be obtained effectively from certain primitive ones via the Virasoro operators. As applications, we prove a minimal generation result, a cohomological χ-dependence result, and fully compute the cohomology rings in low degrees. Finally, we propose a “Perverse = Chern” conjecture relating two filtrations …

Random Matrices And Statistical Inference With Correlated Structures, Haoyu Wang

Yale Graduate School of Arts and Sciences Dissertations

Random matrices play a central role in modern probability theory and high-dimensionalstatistics, both as fundamental mathematical objects and as powerful tools for inference. This dissertation presents several works on random matrix theory and its connections to statistical inference with correlated structures in high dimensions. On the random matrix side, we investigate the spectral properties of sample covariancematrices. Our approach is built upon the resolvent method, and we utilize local laws for various spectral analyses. Specifically, our contributions are three-fold: (1) we attain the first explicit rate of convergence for the largest eigenvalue of sample covariance matrices; (2) we derive the …

A Study Of Math 1 Students At Two Eastern High Schools In North Carolina, Employing An Explanatory Design, Anthony Mark Tracey

Doctor of Education Dissertations

This study examined the instructional experiences of Math 1 students in the Green Valley (pseudonym) County School District during the 2022-2023 academic year. Using an explanatory sequential mixed methods approach grounded in constructivism (Bruner, 1960; Vygotsky, 1978), behaviorism (Skinner, 1938), universal design for learning (CAST, 2021; Meyer et al., 2014), multiple intelligences (Gardner, 1983), and Piaget's (1954) stages of development, this study explored how students' lived instructional experiences impact academic outcomes. Data, analyzed descriptively and thematically in Qualtrics, revealed a widespread dissatisfaction among students regarding engagement, instructional pace, preparation, and classroom disruptions. Qualitative insights particularly underscore issues with a passive, …

Using Children's Picture Books To Teach Mathematical And Numeracy Concepts: An Exploration Of The Aesthetic Value Of Mathematics For Preservice Teachers’ Dispositions, Mellie Green, Lorraine Gaunt, Georgina M. Barton

Australian Journal of Teacher Education

Evidence suggests that preservice teachers tend to have negative dispositions towards the teaching of mathematics and/or numeracy. In response, this paper describes the work of three experienced teacher educators using high-quality children’s picture books to teach mathematical and/or numeracy concepts as well as foregrounding the aesthetic value of mathematics. The purpose of this type of reading is to support and improve preservice teacher dispositions towards mathematics and/or numeracy with children’s picture books. Using metalogue as methodology, the researchers discussed mathematical and/or numeracy concepts and explored the aesthetic value of mathematics within selected picture books. They used the Australian Curriculum’s General …

A Spoonful Of Sugar: A Mathematics Board And Card Games Intervention For Kindergarten Students At Risk For Mathematics Disabilities, Leah Kai Tiisler

Electronic Theses and Dissertations

Early mathematics knowledge in kindergarten students can predict their later success in school and in life, while difficulties with mathematics early on can derail a child’s future unless they are provided with effective interventions. Ideally, interventions should be developmentally appropriate, playful, low in stress, and easy to implement. Board games and card games can be integrated into math interventions and easily adapted to include early arithmetic elements. This dissertation investigates the impact of a mathematics board and card game intervention on kindergarten students at risk for mathematics disabilities. The study employed a single-subject research design to assess the effectiveness of …

Artificial Intelligence In Science And Society: The Vision Of Usern, Tommaso Dorigo, Gary D. Brown, Carlo Casonato, Artemi Cerda, Joseph Ciarrochi, Mauro Da Lio, Nicole D'Souza, Nicolas R. Gauger, Steven C. Hayes, Stefan G. Hofmann, Robert Johansson, Marcus Liwicki, Fabien Lotte, Juan J. Nieto, Giulia Olivato, Peter Parnes, George Perry, Alice Plebe, Idupulapati M. Rao, Nima Rezaei, Fredrik Sandin, Andrey Ustyuzhanin, Giorgio Vallortigara, Pietro Vischia, Niloufar Yazdanpanah

All Peer-Reviewed Publications

The recent rise in relevance and diffusion of Artificial Intelligence (AI)-based systems and the increasing number and power of applications of AI methods invites a profound reflection on the impact of these innovative systems on scientific research and society at large. The Universal Scientific Education and Research Network (USERN), an organization that promotes initiatives to support interdisciplinary science and education across borders and actively works to improve science policy, collects here the vision of its Advisory Board members, together with a selection of AI experts, to summarize how we see developments in this exciting technology impacting science and society in …

Spectral Theory And The Gelfand Transform, Brenden Schlader

All Graduate Theses, Dissertations, and Other Capstone Projects

The overall goal of this thesis is to study spectral and Gelfand theory as it relates to unital Banach and C∗-algebras. In the first part, we develop the necessary algebraic, analytic, and topological background relevant to the content of this work. We also discuss concrete examples of algebras frequently used in the subsequent sections. In the second part of this thesis, we develop spectral theory by first defining the spectrum of an algebra through the characterization of the invertible and noninvertible elements. In particular, we establish properties of the commutative unital Banach algebra ℓ1(Z). We also establish fundamental results such …

Integrating Sentiment Analysis In Predictive Models: A Comparative Study On Game Popularity On Steam, Khaleefa Alhemeiri

CMC Senior Theses

Over the past decades, the gaming industry has managed to evolve into a multi-billion-dollar enterprise. Gaming platforms such as Steam foster unprecedented amounts of engagement among players worldwide daily. In this thesis, we investigate the effect of incorporating sentiment-driven metrics, specifically YouTube view counts and positive reviews, into predictive models for game popularity. In addition, by comparing our linear regression sentiment-based approach to the Bayesian hierarchical folded normal model used by De Luisa et al. (2021), we can understand the many differences, strengths, and limitations of each methodology. In our thesis, we focus on three games. Each is of varying …

Guessing Games To Determine 1 Of Several Secret Numbers, Kyle Mckee, Julia Osmun, Dori Schlutt

Mathematics Undergraduate Research

A guessing game is a two-player game between a Responder and a Questioner. In a guessing game, the Responder is thinking of x ≥ 1 secret numbers in a set S of size n. The Questioner is tasked with asking questions of the form: “How many numbers are in Q ⊆ S?” until the Questioner knows at least 1 of the Responder’s secret numbers. We find a game-winning strategy for the Questioner with minimal possible questions for games with x = 2. We also find lower-bounds for x = 2 and x = 3.

Offline Guessing Games With Two Numbers, Justin Sciullo, Lisa Shen, Sarah Zaske

Mathematics Undergraduate Research

In an offline guessing game, there is a player called the Questioner and a player called the Responder. The Responder first picks two distinct numbers from the set {1, 2, 3, . . . , n}. The Questioner then creates a set of questions of the form “How many of your numbers are in the set q_i ⊆ {1, 2, 3, . . . , n}?” and sends them to the Responder who answers them. The Questioner wins if they can guess the Responder’s numbers no matter which numbers the Responder chose. The Responder wins otherwise. We …

Voltage-Dependent Anion-Selective Channels 1 And 2 Wild Type And Mutant Bh3-Like Domain Peptides: Analysis Of Secondary Structure And Binding Stoichiometry To Recombinant Bax, Geanell C. Adams

Electronic Theses and Dissertations

Despite national efforts to increase female participation in science, technology, engineering, and mathematics (STEM), women remain significantly underrepresented in collegiate STEM programs. This pilot study sought to identify pre-collegiate factors that influence female students’ decisions to enroll and persist in STEM collegiate programs at the University of Mississippi, a predominantly white R1 research institution using qualitative methods. Grounded in Bandura’s Social Learning Theory, the research examined the environmental, behavioral, and personal determinants that shape academic pathways for women in STEM.

Data were collected through semi-structured interviews with six sophomore female STEM majors. Thematic analysis revealed that early exposure to structured …

Teachers' Perceptions Of Their Self-Regulated Learning Practices In Elementary School Classrooms, Stephanie Greenquist-Marlett, Linda Bol, Courtney Hill

STEMPS Faculty Publications

Self-regulated learning (SRL) is associated with adaptable, critical, lifelong thinking skills. Teachers are essential to promoting SRL in learners, yet infrequently teach these learning strategies in classrooms. We addressed three research questions: (1) How do K–5 teachers implement SRL in their teaching?, (2) How is the use of SRL strategies linked to their self-efficacy or confidence in teaching?, and (3) How do teachers differ in their use of SRL depending on school type (public vs. private)? Semi-structured interviews were conducted with 12 primary in-service teachers, sampled equally from one public and one private school, to explore their SRL practices. They …

Elementary School Teachers' Perceptions Of The Common Core State Standards For Mathematics, Rebecca Potts

PCOM Psychology Dissertations

This dissertation examines elementary school teachers' perceptions of the Common Core State Standards for Mathematics (CCSS-M), focusing on evaluating their views on developmental appropriateness and identifying challenges encountered during implementation. Rooted in the broader historical context of educational reforms in the U.S., the study investigates whether the adoption of CCSS-M adequately integrates research on child development, learning trajectories, and cognitive neuroscience. Using a mixed-methods design incorporating surveys and semi-structured interviews, this study gathered insights from kindergarten through fifth-grade teachers and mathematics interventionists. Findings reveal mixed perceptions among educators regarding the developmental appropriateness of the CCSS-M, highlighting concerns that some standards …

A Decision-Space Model Explains Context-Specific Decision Making, Dirk W. Beck, Cory N. Heaton, Luis D. Davila, Lara I. Rakocevic, Sabrina M. Drammis, Danil Tyulmankov, Atanu Giri, Shreeya Umashankar Beck, Qingyang Zhang, Michael Pokojovy, Kenichiro Negishi, Alexis A. Salcido, Neftali F. Reyes, Andrea Y. Macias, Serina A. Batson, Paulina Vara, Raquel J. Ibáñez Alcalá, Safa B. Hossain, Graham L. Waller, Laura E. O'Dell, Travis M. Moschak, Ki A. Goosens, Alexander Friedman

Mathematics & Statistics Faculty Publications

Optimal decision-making requires consideration of internal and external contexts. Biased decision-making is a transdiagnostic symptom of neuropsychiatric disorders. We created a computational model demonstrating how the striosome compartment of the striatum constructs a context-dependent mathematical space for decision-making computations, and how the matrix compartment uses this space to define action value. The model explains multiple experimental results and unifies other theories like reward prediction error, roles of the direct versus indirect pathways, and roles of the striosome versus matrix, under one framework. We also found, through new analyses, that striosome and matrix neurons increase their synchrony during difficult tasks, caused …

A Bridge Too Low: Solutions For Fermi Questions, May 2025, John Adam

Mathematics & Statistics Faculty Publications

The article discusses a low bridge in Keswick, England, near the River Greta, with an arch shaped like a semiellipse. It presents Fermi questions related to the bridge's dimensions, such as the maximum distance a person of a certain height can walk under it without hitting their head. The solutions involve mathematical calculations and approximations, including the use of formulas provided by the Indian mathematician Srinivasa Ramanujan.

Exploring Factors Influencing Student Growth In Mathematics: Elementary Teacher Instructional Practices, Beliefs, And Professional Development Experiences, Marni E. Driessen

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

High-quality student learning experiences in mathematics rely on effective teaching. This mixed methods study investigates how elementary teachers’ instructional practices, beliefs about mathematics teaching and learning, and professional development experiences relate to student mathematics growth in a large urban district. Quantitative survey data were analyzed to examine relationships among these factors and student growth outcomes, while qualitative data complemented and deepened the measurable findings. This study builds on prior research on instructional practices and professional development effectiveness by integrating constructs typically examined separately and identifying multiple teacher-related factors that distinguish classrooms with high student growth from those with low growth. …

Untangling The Classification Of Surfaces: An Accessibility-Centered Perspective On Topology, Charlotte N. Richards

Pitzer Senior Theses

Mathematics has clear benefits in education, from preparing students for future careers to teaching them how to problem-solve. While mathematics achievement has been falling in recent decades, students claim that the problem is not the mathematics itself, but the ‘boring’ classroom material that feels removed from real life. More advanced mathematics topics, such as topology, could offer a solution, as their applications lie in countless fields. However, topology has been restricted to upper-level mathematics, disregarding the potential benefits of making this material broadly reachable for a junior high-school audience. In this paper, we analyze five different proofs of the theorem …

Math 615-102: Approaches To Quantitative Analysis In The Life Sciences, Gareth Russell

Biology Syllabi

No abstract provided.