Mathematics Commons^™

Ai Beliefs And Practices In Community College Classrooms, Julie Eng, Heather Umphlett, Jocelyn Gilchrist, Alicia Howell, Mary Ann Howell, Wendy Miller-Edwards, Laurel Pope

Inquiry: The Journal of the Virginia Community Colleges

The country, the Commonwealth of Virginia, and Virginia Community College System initiatives all promote generative AI within education. It is a topic of great concern and interest for higher education instructors, yet at the same time many faculty members feel uncertain about effectively integrating it into class material. To further add pressure to the AI explosion, community colleges particularly face a responsibility to prepare their students for success in this new AI-focused environment. In this article, seven faculty members from Camp Community College discuss the implications of generative AI programs, including subscriptions and chatbots, within their particular courses and how …

Evaluating The Performance Of Bayesian Removal Models For Estimating Population Density And Detecting Trends With Variable Detection Probability, David R. Stewart

Mathematics & Statistics ETDs

Removal models have long been used to estimate population abundance by progressively capturing and removing individuals from a closed population. These models provide a valuable tool for ecological monitoring, but their accuracy depends heavily on assumptions about detection probability, which may decline over successive sampling passes. Traditional removal models assume constant detection probabilities, an assumption that is often violated in real-world applications. This thesis aims to advance hierarchical Bayesian models by accounting for variable detection probabilities, improving the reliability of abundance estimates and trend detection. By integrating simulation-based analyses with empirical data from Lahontan Cutthroat Trout (Oncorhynchus clarkia henshawi …

32 - Nested Two Level Decomposition For Quantum Computing, Andrew Maciejunes, John Stenger, Dan Gunlycke, Nikos Chrisochoides

Undergraduate Research Symposium

Abstract—We present a two-level decomposition strategy for solving the Vehicle Routing Problem (VRP) using the Quantum Approximate Optimization Algorithm (QAOA). A Problem-Level Decomposition (PLD) partitions a 9-node (72-qubit) VRP into smaller Traveling Salesman Problem (TSP) instances. Each TSP is then further simplified via Circuit-Level Decomposition (CLD), enabling execution on near-term quantum devices. Our approach achieves up to 90% reductions in circuit depth and qubit count. These results demonstrate the feasibility of solving VRPs previously too complex for quantum simulators and provide early evidence of potential quantum utility.

My Tunisia Encounters: Inspiration For Some Mathematical Ideas, Hui-Hsiung Kuo

Journal of Stochastic Analysis

No abstract provided.

Perencanaan Bauran Pembangkit Listrik Energi Terbarukan Di Indonesia: Pendekatan Optimasi Program Linier Berbasis Wilayah, Annisa Garmaisa, Uka Wikarya

Jurnal Kebijakan Ekonomi

Indonesia has renewable energy potential spread across various islands. However, limited interconnection between regions is an obstacle to energy distribution. The purpose of this study is to analyze the planning of renewable energy (RE) power plants covering eight types: Geothermal Power Plants (PLTP), Solar Power Plants (PLTS), Wind Power Plants (PLTB), Biomass Power Plants (PLTBm), Biogas Power Plants (PLTBg), and Waste Power Plants (PLTSa). The analysis was conducted in four main system regions in Indonesia, namely Java-Bali, Sumatra, Kalimantan, and Sulawesi, which are currently not interconnected. The study is based on the availability of renewable energy potential, production forecasts, and …

Robust Multifidelity Operator Learning For Partial Differential Equations, Jacob Hauck, Yanzhi Zhang

Miners Solving for Tomorrow Research Conference

No abstract provided.

Coupled Time-Dependent Stokes - Darcy Model With Beavers–Joseph–Saffman–Jones Interface Boundary Condition, Yafang Hei, Xiaoming He

Miners Solving for Tomorrow Research Conference

No abstract provided.

The Importance Of Motivation And Self-Concept For Predicting Performance In Service Mathematics Modules: Replicating And Extending Previous Findings, Catherine Palmer, Maryna Lishchynska, Declan O’Connor, Seán Lacey

Department of Mathematics Publications

Students’ difficulties and lower-than-desired mathematics performance in higher education have been the focus of educational research and practice for a period of time. In a recent study by Lishchynska et al. (2023), learners’ motivation, dispositions towards mathematics and learning strategies were examined as factors potentially affecting performance in service mathematics modules. The main objectives of this study were to replicate the findings of Lishchynska et al. (2023) with a new student cohort; determine if self-concept is a significant contributortomathematicsperformance;andexploreifmathematicalbackgroundremainsan important predictor of mathematics performance for students as they migrate from first year to final year of study. A survey of …

Unraveling The Impact Of Curricular Complexity On Graduation Time: A Causal Analysis In Higher Education, Ameer Slim

Mathematics & Statistics ETDs

This study examines the causal relationship between program complexity and graduation time at UNM. While program complexity is recognized as a factor influencing student outcomes, its precise impact on graduation timelines remains underexplored. Using comprehensive cohort data, this study employs causal inference methods, including generalized propensity scores, to estimate the effect of complexity on time-to-degree. Findings reveal that higher program complexity extends graduation timelines, even after controlling for demographics and academic preparedness. Socioeconomic factors also play a role. Specifically, programs with more Pell Grant recipients and lower median high school GPAs tend to have lower complexity levels. These results provide …

A Study Of The Sum Of Divisors, Henry M. Willie

Miners Solving for Tomorrow Research Conference

No abstract provided.

Chain Theorems For Different Classes Of 3-Connected Graphs, Avin Sunuwar

LSU Doctoral Dissertations

This dissertation explores the structural properties of graphs by extending the classical result of Tutte's Wheel Theorem. In particular, we develop an improved version of Tutte's Wheel Theorem along with new chain theorems for subclasses of 3-connected graphs. These chain theorems provide a systematic approach to characterizing graphs that exclude certain minors, leading to significantly shorter proofs of established results.

In Chapter 5, we present a generalization of the block-tree theorem for connected graphs, which removes the restriction on cut vertices and allows greater flexibility in separator sizes. By integrating the results from Chapters 3, 4, and 5, we …

Gaussian Quantum Markov Semigroups In The Fock-Anti-Fock Representation Of Weyl Algebra, A Dhahri, Franco Fagnola, D Poletti, Hyun Jae Yoo

Journal of Stochastic Analysis

No abstract provided.

7 Plus Minus 2 Law Revisited: Alternative Geometric Explanation, Mayan Arithmetic, And Using 9- And 18-Based Numbers In Jewish Tradition, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A recent paper showed that to make sure that the movements in the crowd are not chaotic, the directions of all the motions should deviate from some fixed direction by no more than 13 degrees. We show that this results provides a new geometric explanation for the seven plus minus two law in psychology, according to which we can keep in mind no more than 7 plus minus 2 items. We also show that all this is related to the somewhat mysterious appearance of 9- and 18-based number systems in Jewish and Mayan traditions.

Why Um And U*Log(U) Are The Most Effective Nonlinear Functions In Fuzzy Clustering: Theoretical Explanation Of The Empirical Fact, Olga Kosheleva, Vladik Kreinovich, Yuchi Kanzawa

Departmental Technical Reports (CS)

In fuzzy clustering, we need to have non-linear functions of the membership degrees. Different nonlinear functions have been tried. Empirical evidence shows that for fuzzy clustering, the most effective nonlinear functions are um and u*log(u). In this paper, we provide a theoretical explanation for this empirical fact.

Egyptian Triangle And Geometry Of Airplane Wings: A Simplified Explanation, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In historically first planes, wings were orthogonal to the fuselage. However, later it turned out that from the aerodynamic viewpoint, it is most efficient to place the wings at about 37 degrees from this orthogonal direction -- and this is where wings are placed in most modern planes. There exist theoretical explanations for this optimality -- explanations based on solving the equations of aerodynamics. In such situations when only a complex not-very-intuitive explanation exists, it is desirable to come up with a simpler more intuitive explanation. For the wing angles, such an explanation is provided in this paper. Namely, we …

"At Least K Out Of N" Under Fuzzy Uncertainty: Efficient Algorithm For General "And"-Operations, Olga Kosheleva, Vladik Kreinovich, Klaus-Peter Adlassnig

Departmental Technical Reports (CS)

In medicine, many diagnoses are made when, for some value k, at least k of n possible symptoms are present. Many of such symptoms -- such as fever -- are, in reality, fuzzy. For example, it makes no sense that say that 38.0 is fever while 37.9 is not a fever, both are fever to some degree. Once such degrees are given, we need to use them to estimate the degree to which the patient has the corresponding disease. For this problem, the usual fuzzy techniques require exponentially many computational steps -- so it is desirable to have a more …

Why Interval-Valued (And Type-2) Fuzzy Methods Are Often More Effective, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Interval-valued and type-2 fuzzy techniques were designed to provide a more adequate representation of expert knowledge than the traditional (type-1) fuzzy techniques. Somewhat unexpectedly, they also often turn out to be more effective even when there is no expert knowledge at all -- when we are simply using fuzzy rules to fit experimental data. In precise terms, for the same number of parameters, interval-valued and type-2 systems often provide a better fit for the data and/or better quality control than traditional (type-1) fuzzy techniques. In this paper, we provide a theoretical explanation for this surprising phenomenon.

Why Convex Combinations Of Interval Endpoints: Related Explanations For Cases Of Data Processing And Decision Making, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

There are two cases in which it has been empirically shown that a convex combination of the interval's endpoints works better than any other combination: processing interval data and dealing with situations in which we know both approximate probability and possibility and we need to make a decision. In this paper, we provide an explanation of both phenomena.

Number Talks To Promote Discourse In The Algebra 1 Classroom: A Number Talk Curriculum Development For A Unit On Quadratic Expressions, Lindsay C. Borger

Masters Theses/Capstone Projects

This project sought to develop a curriculum of Number Talks for use at the secondary level, specifically in an Algebra 1 class as a supplement to a unit on quadratic expressions. The project begins with a look at existing research on constructivism and social constructionism as well as the reforms in mathematics education informed by those learning theories. It then looks at calls for more discourse in the mathematics classroom as a part of these reform efforts, and the part Number Talks play in fostering discourse and mathematical thinking for students. The Number Talk curriculum includes a guide for implementing …

Quarterback Statistics Vs. Season Success, Brendan Woods

Mathematics Senior Capstone Papers

The purpose of this research is to determine which quarterback statistic most significantly impacts team success in the National Football League. By analyzing data from quarterbacks with at least 100 pass attempts per season from 2006 to 2023, we examine the relationship between quarterback rating, passer rating, completion percentage, and TD-INT ratio with end-of-season power rankings. We ran the data through multiple linear regression models to identify which statistic has the strongest correlation with team performance. Our model considers variations across different seasons and accounts for statistical trends over time. With over 17 seasons of data analyzed, further exploration could …