Mathematics Commons^™

Deployment Of Mathematical Resources To A Philippine High School Through A Community Lte Network, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Verzosa

Mathematics Faculty Publications

In the Philippines, one challenge that continues to be faced by the Department of Education in bringing educational content in a blended learning modality is the lack of internet access of the learners. This paper discusses the distribution, through a community LTE network, of mathematical resources for Grades 7 to 10 to teachers and students of a particular high school in the Philippines. It also gives details on particular technological tools (mathematical applications) that were created to help the mathematical learning of students in a remote setting.

Sigma Chromatic Numbers Of The Middle Graph Of Some Families Of Graphs, Jay-R Manamtam, Agnes Garciano, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Let G be a nontrivial connected graph and let c : V (G) → be a vertex coloring of G, where adjacent vertices may have the same color. For a vertex υ of G, the color sum σ(υ) of υ is the sum of the colors of the vertices adjacent to υ. The coloring c is said to be a sigma coloring of G if σ(u) ≠ σ(υ) whenever u and υ are adjacent vertices in G. The minimum number of colors that can be …

Development Of An App And Videos To Support The Fraction Learning Trajectory From Grades 1-7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Juan Carlo F. Mallari, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Lack of procedural fluency in fractions impedes access to advanced mathematical courses and limits opportunities for entry into STEM-related fields. This paper describes the design and pedagogical basis of the Moving Fractions app and supplementary fraction videos for promoting fraction learning. Moving Fractions utilizes game-design factors to draw students through a trajectory of fraction learning from part-whole comparisons to a more robust understanding of the measurement concept of fractions. The supplementary video immerses students in a broad range of fraction representations. The app and video are intended to form a fraction learning package for distribution in Philippine schools. Future work …

Benchmarking Graph Neural Networks, Thomas Laurent, Vijay Prakash Dwivedi, Chaitanya K. Joshi, Anh Tuan Luu, Yoshua Bengio, Xavier Bresson

Mathematics, Statistics and Data Science Faculty Works

In the last few years, graph neural networks (GNNs) have become the standard toolkit for analyzing and learning from data on graphs. This emerging field has witnessed an extensive growth of promising techniques that have been applied with success to computer science, mathematics, biology, physics and chemistry. But for any successful field to become mainstream and reliable, benchmarks must be developed to quantify progress. This led us in March 2020 to release a benchmark framework that i) comprises of a diverse collection of mathematical and real-world graphs, ii) enables fair model comparison with the same parameter budget to identify key …

Online Algorithms With Advice For The 𝒌-Search Problem, Jhoirene B. Clemente, Henry N. Adorna, Proceso L. Fernandez Jr

Department of Information Systems & Computer Science Faculty Publications

In the online search problem, a seller seeks to find the maximum price from a sequence of prices p1, p2,…, pn that is revealed in a piece-wise manner. The bound for all prices is well known in advance with m ≤ pί ≤ M. In the online k-search problem, the seller seeks to find the k maximum out of the n prices. In this paper, we present a tight bound of [Formula Presented] on the advice complexity of optimal online algorithms for online k-search. We also provide online algorithms with advice that use less than the required number of bits …

An Introduction To Pascal’S Triangle, Daniel Chenoweth

Masters Essays

No abstract provided.

Exploration Of Triangles In Euclidean, Spherical, And Hyperbolic Spaces For The High School Geometry Classroom, John Rowell

Masters Essays

No abstract provided.

A Comparison Of Stacking Methods To Estimate Survival Using Residual Lifetime Data From Prevalent Cohort Studies, Zhaoheng Li

Mathematics, Statistics, and Computer Science Honors Projects

Prevalent cohort studies are widely used for their cost-efficiency and convenience. However, in such studies, only the residual lifetime can be observed. Traditionally, researchers rely on self-reported onset times to infer the underlying survival distribution, which may introduce additional bias that confounds downstream analysis. This study compares two stacking procedures and one mixture model approach that uses only residual lifetime data while leveraging the strengths of different estimators. Our simulation results show that the two stacked estimators outperform the nonparametric maximum likelihood estimator (NPMLE) and the mixture model, allowing robust and accurate estimations for underlying survival distributions.

The Octagon At Large M, Riccardo Argurio, Matteo Bertolini, Sebastían Franco, Eduardo García-Valdecasas, Shani Meynet, Antoine Pasternak, Valdo Tatitscheff

Publications and Research

Recently, the first instance of a model of D-branes at Calabi-Yau singularities where supersymmetry is broken dynamically into stable vacua has been proposed. This construction was based on a system of N regular and M = 1 fractional branes placed at the tip of the so-called (orientifolded) Octagon singularity. In this paper we show that this model admits a large M generalization, having the same low energy effective dynamics. This opens up the possibility that the effect on geometry is smooth, and amenable to describing the gauge theory all along the RG flow, including the deep IR, in terms of …

Cycle Decomposition For Integral Current Homology, Kristin Julia Duling

Graduate Theses, Dissertations, and Problem Reports (ETD)

A standard graph theoretical result states that every element of the cycle space of a graph has a cycle decomposition. Georgakopoulos expands this result to a primitive decomposition and minimal representation of each element in a modified 1-dimensional singular homology. We modify the m-dimensional integral current homology in order to ensure a primitive decomposition for each element.

Inverse Boundary Value Problems For Polyharmonic Operators With Non-Smooth Coefficients, Landon Gauthier

Theses and Dissertations--Mathematics

We consider inverse boundary problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.

An Integrated Computational Pipeline To Construct Patient-Specific Cancer Models, Daniel Plaugher

Theses and Dissertations--Mathematics

Precision oncology largely involves tumor genomics to guide therapy protocols. Yet, it is well known that many commonly mutated genes cannot be easily targeted. Even when genes can be targeted, resistance to therapy is quite common. A rising field with promising results is that of mathematical biology, where in silico models are often used for the discovery of general principles and novel hypotheses that can guide the development of new treatments. A major goal is that eventually in silico models will accurately predict clinically relevant endpoints and find optimal control interventions to stop (or reverse) disease progression. Thus, it is …

Improving College Students’ Views And Beliefs Relative To Mathematics: A Systematic Literature Review Followed By A Multiple Case Mixed Methods Exploration Of The Experiences That Underpin Community College Students’ Attitudes, Self-Efficacy, And Values In Mathematics, Marquita H. Sea

Theses and Dissertations

Mathematics is particularly important due to its relevance in our daily lives. It is a general requirement throughout schooling. Unfortunately, many students openly declare negative views/beliefs regarding math in their personal and academic lives. These in turn, negatively influence students’ achievement related behaviors and outcomes. First, a systematic literature review was conducted to determine what types of studies/initiatives have aimed to enhance students’ views/beliefs relative to mathematics, including domain general and specific perceptions of math as well as their judgements of who is successful in mathematics and if they themselves can be successful. Specifically, the review centered on the components …

Estimating The Statistics Of Operational Loss Through The Analyzation Of A Time Series, Maurice L. Brown

Theses and Dissertations

In the world of finance, appropriately understanding risk is key to success or failure because it is a fundamental driver for institutional behavior. Here we focus on risk as it relates to the operations of financial institutions, namely operational risk. Quantifying operational risk begins with data in the form of a time series of realized losses, which can occur for a number of reasons, can vary over different time intervals, and can pose a challenge that is exacerbated by having to account for both frequency and severity of losses. We introduce a stochastic point process model for the frequency distribution …

Mathematical Reasoning: Writing And Proof (Pretext Edition), Ted Sundstrom

Open Textbooks

Mathematical Reasoning: Writing and Proof is a text for the first college mathematics course that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics.

Mathematical Reasoning: Writing and Proof (PreTeXt Edition) was developed as part of the Accelerating Open Educational Resources Initiative at Grand Valley State University, with support from the University Libraries and the President's Innovation Fund.

Mathematical Reasoning: Writing and Proof was written by Ted Sundstrom, Professor Emeritus of Mathematics at Grand Valley State University. This textbook was converted into PreTeXt by Ian Curtis, Editorial Assistant for the …

Automated Conjecturing On The Independence Number And Minimum Degree Of Diameter-2-Critical Graphs, Joshua R. Forkin

Theses and Dissertations

A diameter-2-critical (D2C) graph is a graph with diameter two such that removing any edge increases the diameter or disconnects the graph. In this paper, we look at other lesser-studied properties of D2C graphs, focusing mainly on their independence number and minimum degree. We show that there exist D2C graphs with minimum degree strictly larger than their independence number, and that this gap can be arbitrarily large. We also exhibit D2C graphs with maximum number of common neighbors strictly greater than their independence number, and that this gap can be arbitrarily large. Furthermore, we exhibit a D2C graph whose number …

Methods For Computing The Global Optimum Of Non-Convex Objectives, Isaac Michael Hawn

Graduate Research Theses & Dissertations

\begin{abstract}In this thesis, we concern ourselves with solving the unconstrained optimization problem % \begin{gather*} \text{Minimize}\; f(x)\\\text{subject to}\; x\in X \end{gather*} % where $f\colon\mathbb{R}^N\to \mathbb{R}$ is a non-convex function, possibly with infinitely many local minima. Solving such a problem, especially in higher dimensions often proves to be an extraordinarily difficult task, either in time complexity or in the methodology itself. Indeed, mathematicians must often resort to algorithms which make use of problem structure and which may not generalize well. In this thesis, we present two algorithms which solve this problem, albeit with their own shortcomings.

First, we present a new, $N$-dimensional …

Conductors For Maximal Orders Of Group Rings Over Local Fields, Brooke Randazzo

Graduate Research Theses & Dissertations

This dissertation examines conductors for maximal orders of group rings, $FD$, contained in integral group rings, $\mathcal{O}_F D$, where $D$ is a finite group, $F$ a local field, and $\mathcal{O}_F$ its discrete valuation ring. (Given two rings $R \subseteq S$, the conductor of $S$ in $R$, if it exists, is the largest ideal of $S$ contained in $R$.) First, we use a theorem of Jacobinski to make this conductor explicit where $F$ is a particular extension of $\mathbb{Q}_p$ of varying ramification index and $D$ is any elementary abelian $p$-group. Next, we examine this conductor problem for this same $F$ within …

Numerical Solution Of A Singularly Perturbed Fredholm Integro Differential Equation With Robin Boundary Condition, Muhammet Enes Durmaz, Gabi̇l Ami̇rali̇, Mustafa Kudu

Turkish Journal of Mathematics

In this paper, we deal with singularly perturbed Fredholm integro differential equation (SPFIDE) with mixed boundary conditions. By using interpolating quadrature rules and exponential basis function, fitted second order difference scheme has been constructed on a Shishkin mesh. The stability and convergence of the difference scheme have been analyzed in the discrete maximum norm. Some numerical examples have been solved and numerical outcomes are obtained.

Scattering Properties Of Impulsive Difference Dirac Equations, Şeyda Solmaz, Elgi̇z Bayram

Turkish Journal of Mathematics

In this paper, we explore the Jost solutions and the scattering matrix of the impulsive difference Dirac systems (IDDS) on the whole axis and study their analytic and asymptotic properties. Furthermore, characteristic properties of the scattering matrix of the IDDS have been examined.