Sociomathematical Norms And Automated Proof Checking In Mathematical Education: Reflections And Experiences,
2024
Europa-Universität Flensburg
Sociomathematical Norms And Automated Proof Checking In Mathematical Education: Reflections And Experiences, Merlin Carl
Journal of Humanistic Mathematics
According to a widely held view, mathematical proofs are essentially (indications of) formal derivations, and thus in principle mechanically checkable (this view is defended, for example, by Azzouni [3]). This should in particular hold for the kind of simple proof exercises typically given to students of mathematics learning to write proofs. If that is so, then automated proof checking should be an attractive option for math education at the undergraduate level. An opposing view would be that mathematical proofs are social objects and that what constitutes a mathematical proof can thus not be separated from the social context in which …
My Own Private World Of Non-Ordinary Associative Arithmetics,
2024
Drexel University
My Own Private World Of Non-Ordinary Associative Arithmetics, Marion D. Cohen
Journal of Humanistic Mathematics
A binary operation # on Z+ is said to be an associative arithmetic if both # and its iteration — the binary operation ∗ defined recursively by: x∗1 = x and x∗y = [x ∗ (y − 1)]#x — are associative. E. Rosinger [6] showed that under reasonable conditions an associative arithmetic must be ordinary addition. However, in the general case, there are associative arithmetics that are not ordinary addition. This paper gives examples of these as well as results towards a structure theorem for associative arithmetics. The paper also describes the role that this particular math problem has played …
Picturing Mathematics (Education) In New Ways,
2024
Claremont McKenna College
Picturing Mathematics (Education) In New Ways, Mark Huber, Gizem Karaali
Journal of Humanistic Mathematics
No abstract provided.
Front Matter,
2024
Claremont Colleges
Nilpotent Global Centers Of Generalized Polynomial Kukles System With Degree Three,
2024
The University of Texas Rio Grande Valley
Nilpotent Global Centers Of Generalized Polynomial Kukles System With Degree Three, Hebai Chen, Zhaosheng Feng, Rui Zahg
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we study and characterize the nilpotent global centers of a generalized polynomial Kukles system with degree three. A sufficient and necessary condition of global centers is established under certain parametric conditions.
Visualization Of Species Tree Likelihood Under The Multispecies Coalescent Model,
2024
University of New Mexico
Visualization Of Species Tree Likelihood Under The Multispecies Coalescent Model, Jaimasan Sutton
Mathematics & Statistics ETDs
A commonly used tool for evolutionary biologists is a phylogenetic tree that represents the ancestry of a set of species and the evolution of traits. Statistical models can be used to predict the probabilities of gene trees which represent ancestral relationships of genes sampled from species. Because of this, we are able to represent the likelihood of a species tree, which represents the evolutionary history of a set of species, as a function of the counts of gene tree topologies, where each gene tree represents the ancestry of a specific genetic locus for multiple species. Because we can represent these …
Short-Time Fourier Transform And Superoscillations,
2024
Chapman University
Short-Time Fourier Transform And Superoscillations, Daniel Alpay, Antonino De Martino, Kamal Diki, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we investigate new results on the theory of superoscillations using time-frequency analysis tools and techniques such as the short-time Fourier transform (STFT) and the Zak transform. We start by studying how the short-time Fourier transform acts on superoscillation sequences. We then apply the supershift property to prove that the short-time Fourier transform preserves the superoscillatory behavior by taking the limit. It turns out that these computations lead to interesting connections with various features of time-frequency analysis such as Gabor spaces, Gabor kernels, Gabor frames, 2D-complex Hermite polynomials, and polyanalytic functions. We treat different cases depending on the …
Quantitative Reasoning: What’S Math Got To Do With It?,
2024
Just Equations
Quantitative Reasoning: What’S Math Got To Do With It?, Pamela Burdman
Numeracy
This keynote address explores the history and role of college math requirements with a focus on ensuring math courses serve to expand students’ horizons, rather than serve as gatekeepers. It discusses the advent of general education math courses, which brought more students into math departments, which ultimately contributed to broadening the scope of the courses to align with more students’ interests and majors, since their purpose was to advance quantitative reasoning, not mathematics skill per se. It also examines several practices to address calculus’ gatekeeping role: revising placement practices and prerequisites, redesigning courses, and updating instruction and assessment practices. Lastly, …
Stochastic Solutions For Hyperbolic Pde,
2024
Queen's University - Kingston, Ontario
Stochastic Solutions For Hyperbolic Pde, Abdol-Reza Mansouri, Zachary Selk
Journal of Stochastic Analysis
No abstract provided.
The Arbitrariness Of Symmetry In Mathematical Proofs,
2024
The University of Texas Rio Grande Valley
The Arbitrariness Of Symmetry In Mathematical Proofs, Melisa Vivanco
Philosophy Faculty Publications
Symmetry is not an inherent characteristic of mathematical proofs; instead, it is a property that arbitrarily manifests in different modes of presentation. This arbitrariness leads to the conclusion that symmetry cannot be part of the defining or essential properties that characterize proofs. Consequently, contrary to some authors’ claims, symmetry does not significantly contribute to the validity, accuracy, or soundness of mathematical proofs. What is more, it does not even play any critical role in heuristic aspects such as explanatory power. The examples developed in this paper constitute compelling evidence supporting these claims.
Uniformly Distributing Points On A Sphere,
2024
Institute of Analysis and Number Theory
Uniformly Distributing Points On A Sphere, Flavio Arrigoni
Rose-Hulman Undergraduate Mathematics Journal
In this paper, we are going to present and discuss different procedures for distributing points on a sphere's surface. Furthermore, we will assess their quality with three different distribution tests. The MATHEMATICA package that we created for testing and plotting the points is publicly available.
Modeling Virus Diffusion On Social Media Networks With The Smirq Model,
2024
University of North Texas
Modeling Virus Diffusion On Social Media Networks With The Smirq Model, Justin Browning, Arnav Mazumder, Gowri Nanda
Rose-Hulman Undergraduate Mathematics Journal
As social networking services become more complex and widespread, users become increasingly susceptible to becoming infected with malware and risk their data being compromised. In the United States, it costs the government billions of dollars annually to handle malware attacks. Additionally, computer viruses can be spread through schools, businesses, and individuals’ personal devices and accounts. Malware affecting larger groups of people causes problems with privacy, personal files, and financial security. Thus, we developed the probabilistic SMIRQ (pSMIRQ) model that shows how a virus spreads through a generated network as a way to track and prevent future viruses. Our model is …
Resonant Solutions Of The Non-Linear Schrödinger Equation With Periodic Potential,
2024
College of Saint Benedict/Saint John's University
Resonant Solutions Of The Non-Linear Schrödinger Equation With Periodic Potential, Arein Duaibes, Yulia Karpeshina
Mathematics Faculty Publications
The goal is construction of stationary solutions close to non-trivial combinations of two plane waves at high energies for a periodic non-linear Schrödinger Equation in dimension two. The corresponding isoenergetic surface is described for any sufficiently large energy k2. It is shown that the isoenergetic surface corresponding to k2 is essentially different from that for the zero potential even for small potentials. We use a combination of the perturbative results obtained earlier for the linear case and a method of successive approximation.
Longitudinal Investigation Of Early Mathematical Achievement And Classroom Strategic Diversity: A Replication And Extension Study,
2024
University of Denver
Longitudinal Investigation Of Early Mathematical Achievement And Classroom Strategic Diversity: A Replication And Extension Study, Douglas H. Clements, Yixiao Dong, Crystal A. Day-Hess, Julie Sarama
Early Childhood Special Education: Faculty Scholarship
Developing solution strategies, effortful procedures that students employ to solve a specific problem, is an important mathematical goal. Studies have documented intraindividual strategy variability and its significance for learning, but only some have addressed the interindividual strategic diversity across students within a classroom. This study analyzed classroom strategy diversity using assessments of 527 kindergartens to 2nd-grade students. Latent growth modeling analysis revealed that the best fit was a spline model featuring two phases of linear growth with different growth rates (i.e., one in Kindergarten, the other from Kindergarten spring to second grade). A growth mixture modeling analysis demonstrated that only …
On The Asymptotics Of Cubic Fields Ordered By General Invariants,
2024
University of South Carolina
On The Asymptotics Of Cubic Fields Ordered By General Invariants, Arul Shankar, Frank Thorne
Faculty Publications
In this article, we introduce a class of invariants of cubic fields termed “generalized discriminants”. We then obtain asymptotics for the families of cubic fields ordered by these invariants. In addition, we determine which of these families satisfy the Malle–Bhargava heuristic.
Constrained Quantization For The Cantor Distribution,
2024
The University of Texas Rio Grande Valley
Constrained Quantization For The Cantor Distribution, Megha Pandey, Mrinal Kanti Roychowdhury
School of Mathematical & Statistical Sciences Faculty Publications
The theory of constrained quantization has been recently introduced by Pandey and Roychowdhury. In this paper, they have further generalized their previous definition of constrained quantization and studied the constrained quantization for the classical Cantor distribution. Toward this, they have calculated the optimal sets of n-points, nth constrained quantization errors, the constrained quantization dimensions, and the constrained quantization coefficients, taking different families of constraints for all n∈N. The results in this paper show that both the constrained quantization dimension and the constrained quantization coefficient for the Cantor distribution depend on the underlying constraints. It also shows that the constrained quantization …
Diving Deeper Into Supercuspidal Representations,
2024
Louisiana State University and Agricultural and Mechanical College
Diving Deeper Into Supercuspidal Representations, Prerna Agarwal
LSU Doctoral Dissertations
In 2013, Reeder and Yu introduced certain low positive depth supercuspidal representations of $p$-adic groups called \textit{epipelagic} representations. These representations generalize the simple supercuspidal representations of Gross and Reeder, which have the lowest possible depth. Epipelagic representations also arise in recent work on the Langlands correspondence; for example, simple supercuspidals appear in the automorphic data corresponding to the Kloosterman $l$-adic sheaf. In this thesis, we take a first step towards the construction of ``\textit{mesopelagic} representation (of Iwahori type)'' which are the higher depth analogues of simple supercuspidal representations. We see that these constructions can be done in a similar way …
Designing Learning Trajectory To Support Preservice Mathematics Teachers' Skills In Creating And Implementing Realistic Mathematics Tasks,
2024
Sanata Dharma University
Designing Learning Trajectory To Support Preservice Mathematics Teachers' Skills In Creating And Implementing Realistic Mathematics Tasks, Veronika Fitri Rianasari, Angela Fatima H. Guzon
Mathematics Faculty Publications
In mathematics teaching and learning, mathematics tasks embedded in realistic contexts are crucial for developing mathematical concepts, procedures, and the application of mathematical knowledge. Despite this, mathematics teachers often encounter challenges in designing and implementing such realistic mathematics tasks. Therefore, this study aims to construct a learning trajectory to enhance preservice mathematics teachers' abilities to create and implement Realistic Mathematics Tasks (RMTs). Employing a design research methodology, the study comprises three phases: preliminary design, teaching experiment, and retrospective analysis. The data presented in this article are from the first cycle, encompassing all three phases. The research involved four fourth-year preservice …
Multi-Symplectic Method For The Two-Component Camassa–Holm (2ch) System,
2024
The University of Texas Rio Grande Valley
Multi-Symplectic Method For The Two-Component Camassa–Holm (2ch) System, Xiaojian Xi, Weipeng Hu, Bo Tang, Pingwei Deng, Zhijun Qiao
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, the multi-symplectic formulations of the two-component Camassa–Holm system are presented. Both the multi-symplectic structure and two local conservation laws of the generalized two-component Camassa–Holm model are proposed for its first-order canonical form. Then, combining the Fourier pseudo-spectral method in the spatial domain with the midpoint method in the time dimension, the multi-symplectic Fourier pseudo-spectral scheme is constructed for the first-order canonical form. Meanwhile, the discrete scheme of the residuals of the multi-symplectic structure and two local conservation laws are also provided. By using the multi-symplectic Fourier pseudo-spectral scheme, the evolution of one- and two-soliton solutions for the …
Limit Theorems For Increments Of Branching Particle Systems With Linear Rates And Poisson Initial Condition,
2024
University of Toronto, Toronto, Canada
Limit Theorems For Increments Of Branching Particle Systems With Linear Rates And Poisson Initial Condition, Alexander Kreinin, Vladimir V. Vinogradov
Journal of Stochastic Analysis
No abstract provided.
