Mathematics Commons^™

From Textbook To Classroom: Gaps In Mathematical Representation And Translation In Nepali Education, Deepak Basyal

Mathematics and Statistics

Translating real-world problem contexts into mathematical symbols is a key skill in curricula worldwide. This study examines Nepali students’ abilities to translate words into symbols and how Nepali textbooks from earlier grades support the development of these skills. To investigate this phenomenon, a sequential explanatory study was conducted with a test for 10th graders and an analysis of Grades 6—9 textbooks. Results show that students struggle to convert real-world contexts into mathematical symbols, while textbooks provide limited opportunities for practice. In particular, students have difficulty translating symbols back into real-world situations, suggesting a link between textbook opportunities and achievement. These …

Orbital Stability Of Solitary Wave Solutions Of The Generalized Benjamin Equation, Leijin Cao, Binhua Feng, Zhaosheng Feng, Yichun Mo

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study the existence and stability of solitary wave solutions for the generalized Benjamin equation in both the L2-critical and L2-supercritical cases by applying the variational methods and the non-homogeneous Gagliardo–Nirenberg inequality. Our main results generalize and complement the existing results in the literature.

Degeneracies In A Weighted Sum Of Two Squares, Ishan V. Ramesh

Rose-Hulman Undergraduate Mathematics Journal

This work is an attempt to classify and quantify instances when a weighted sum of two squares of positive integers, 3n2 1 +n2 2, can be realized in more than one way. Our project was inspired by a particular study of two-dimensional quantum billiards [S. G. Jackson, H. Perrin, G. E. Astrakharchik, and M. Olshanii, SciPost Phys. Core 7, 062 (2024)] where the weighted sums of interest represents an energy level with the two integers being the billiard’s quantum numbers; there, the 3-fold degeneracies seem to dominate the energy spectrum. Interestingly, contrary to the conventional paradigm, these degeneracies are not …

Math Meets Climate: The Energy Balance Model, Maria I. Sanchez Muniz

Open Educational Resources

This assignment introduces students to the mathematics of Earth’s climate through the classical energy balance model. Students analyze how incoming solar radiation, outgoing thermal radiation, and temperature-dependent albedo interact to determine Earth’s equilibrium temperature. Using analytical calculations and computational tools, students identify equilibrium states, assess their stability, and interpret the results through the lens of dynamical systems and bifurcation theory. The activity builds conceptual understanding of climate feedbacks, greenhouse effects, and tipping behavior using a transparent, one-variable model. Designed for applied mathematics and interdisciplinary STEM courses, this assignment emphasizes computation, physical interpretation, and real-world relevance. It is released as a …

Collaborative Research: Cif: Medium: Foundations Of Robust Deep Learning Via Data Geometry And Dyadic Structure, Kevin Moon

Funded Research Records

No abstract provided.

Representation Theory In Unoriented And Non-Semisimple Physics, Matthew Bruce Young

Funded Research Records

No abstract provided.

Understanding Enso Through Mathematical Models, Maria I. Sanchez Muniz

Open Educational Resources

This assignment introduces students to conceptual models of the El Niño–Southern Oscillation (ENSO) and guides them through a structured investigation of their physical and mathematical foundations. Students analyze the recharge–oscillator and delayed–oscillator frameworks, explore how differential equations capture ocean–atmosphere interactions, and evaluate parameter-driven changes in oscillatory behavior. A key component of the work is the guided use of generative AI as a research tool: students employ AI models to locate peer-reviewed literature, interrogate model extensions, and refine their understanding of complex mechanisms, while synthesizing all final explanations in their own words. By blending classical climate modeling with modern AI-supported inquiry, …

Systematics And Systems Theory: Reconstructability Analysis Of The Tetrad, Martin Zwick

Complex Systems Faculty Publications and Presentations

This talk discusses the relationship between systems theory, specifically Reconstructability Analysis, and Systematics, a systems theory-like framework of number symbolism developed by John G. Bennett, which he presented in his four-volume magnum opus, The Dramatic Universe. The talk, given to a community of people interested in Bennett's ideas, focuses on Martin Zwick's paper "Ideas and Graphs: the Tetrad of Activity" archived at https://archives.pdx.edu/ds/psu/36249.

A (Mini) Mathematics Research Experience In A Math Teachers’ Circle Session, Michelle Manes, Linda Venenciano, Seanyelle Yagi

Journal of Math Circles

We describe a single Math Teachers’ Circle session during which a group of teachers collectively engaged in a “mini mathematics research experience.” This provides a model for providing research experiences for mathematics teachers through content-based professional development programs. We conjecture that these experiences will have many of the same benefits as research experiences for teachers in lab sciences.

Timss 2023 – Infographic: Future Pd Needs Of Maths Teachers, Jo Earp

Teacher infographics

The IEA’s Trends in International Mathematics and Science Study (TIMSS) is a global assessment measuring student achievement in years 4 and 8. Teachers from participating schools also complete a questionnaire. Today’s infographic looks at the topics that mathematics teachers reported needing professional development on in the future.

(R2127) On 2-Absorbing Hesitant Primary Fuzzy Ideals Of Rings, B. Anitha, M. Vidhya

Applications and Applied Mathematics: An International Journal (AAM)

By presenting 2-absorbing hesitant primary fuzzy ideals, we begin the investigation of a generalisation of hesitant primary fuzzy ideals (HPRFI) in rings in this research. The concepts of a weakly completely 2-absorbing hesitant primary fuzzy ideal (WC2-AHPRFI) and a Weakly completely 2-absorbing hesitant fuzzy ideal (WC2-AHFI) are developed, and their structural features and attributes are examined. We introduce the idea of a 2-absorbing hesitant K-fuzzy ideal (2-AHK-FI), 2-absorbing hesitant K-primary fuzzy ideal (2-AHK-PRFI) and examine a few of its characteristics.

(R2122) Analysis Of Halo Orbits In The Elliptical R3bp With Mass Variation, Majhar Ali, Abdullah .

Applications and Applied Mathematics: An International Journal (AAM)

The elliptic restricted three-body problem investigates the motion behaviour of the variable mass infinitesimal body under the gravitational forces of the radiated oblate primary and dipole secondary. The equations of motion of the infinitesimal body are determined using Jeans law and Meshcherskii space time transformations. Using the Lindstedt-Poincaré method, we perform the solutions of the equations of motion. With the use of these solutions and the equations of motion, we numerically illustrate the time series, phase spaces, projections and the Halo orbits.

(R2094) On Mds Bisymmetric Rhotrices Using Self-Dual Bases And Conjugate Elements Of Finite Fields, Shalini Gupta, Ruchi Narang, Manpreet Singh

Applications and Applied Mathematics: An International Journal (AAM)

Bisymmetric matrices have wide range of applications in statistics, engineering problems, information theory and computer science including coding theory and cryptography. In cryptography, a rhotrix being a couple matrix doubles the security of the cryptosystem. Here, we construct maximum distance separable (MDS) bisymmetric rhotrices using self-dual bases and conjugate elements of finite fields. MDS rhotrices are very crucial for the designing of block ciphers and hash functions in cryptography.

Error Reduction Methodology And Data Simulation For Interval Data, Ranik Christopher Jelinek

Undergraduate Honors Capstone Projects

Chronic kidney disease (CKD) is a progressive condition affecting hundreds of millions of individuals worldwide. However, clinical datasets often record continuous laboratory measurements as categorical intervals rather than precise numerical values. This interval-censored structure presents methodological challenges for standard regression-based classifiers. This study compares three strategies for handling interval-valued predictors prior to fitting a logistic LASSO model: (1) midpoint imputation, which replaces each interval with its arithmetic center; (2) ordinal encoding, which maps intervals to integer ranks; and (3) a Monte Carlo simulation approach, which repeatedly samples uniformly from each observed interval and averages predictions across replications. Using a 10-fold …

A Persistent Homology Framework For Scrna-Seq: Assessing Clustering Robustness And Quantifying Preprocessing And Integration Effects On Topological Features., Jonah Daneshmand

Electronic Theses and Dissertations

As single-cell RNA sequencing (scRNA-seq) data expands, robust methods for integrating diverse datasets are critical. This dissertation applies Persistent Homology (PH), a technique from Topological Data Analysis (TDA), to a collection of scRNA-seq datasets spanning eight tissue types to quantify how data integration affects topological features and biological interpretability. We assessed global topological structure using Betti curves, Euler characteristics, and persistence landscapes across raw, normalized, and integrated data representations. Our analysis revealed a performance inversion: while conventional methods excelled on unintegrated data, high-granularity topological methods, particularly those sensitive to global data structure, became superior after integration. This suggests a synergy …

Fast Computation Of The Friction Stir Welding Process With Model Order Reduction, Joshua Kay

All Graduate Theses and Dissertations, Fall 2023 to Present

Friction stir welding (FSW) is a manufacturing process used to join materials through intense heat and pressure. To better understand and optimize this FSW process, mathematical models incorporating non-Newtonian Navier-stokes equations for large plastic deformation and heat equation for the heat transfer are used to simulate the FSW process. However, solving these coupled and nonlinear equations with high accuracy requires significant computational power and time. This thesis has applied model order reduction, more precisely the Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM), to efficiently solve the FSW system in low-dimensional space. Slight modifications are made regarding the …

The Impact Of Transmission Thresholds Across Multiple Scales On The Spread Of Chronic Wasting Disease In Wisconsin, Jen Mcclure

All Graduate Theses and Dissertations, Fall 2023 to Present

Wildlife diseases can be difficult to control once they are established. This is especially true when they spread through contact with infectious material left in the environment. One such disease is chronic wasting disease (CWD), a fatal illness affecting deer and related species in North America and other regions. CWD is caused by prions, misfolded proteins that can remain infectious for years after shedding by infected hosts.

Recent research shows that CWD infection does not always follow from the gradual accumulation of prions through small contact events. Rather, an individual may need to encounter a certain prion dose all at …

Wacsaw: An Adaptive, Statistical Method To Classify Movement Into Sleep And Wakefulness States, Austin Vandegriffe, V. A. Samaranayake, Matthew S. Thimgan

Mathematics and Statistics Faculty Research & Creative Works

Wearable actimeters can improve our understanding of sleep in the natural environments. Current algorithms may produce inaccuracies in specific individuals and circumstances, such as quiet wakefulness. New hardware allows data collection at higher frequencies enabling sophisticated analytical methods. We have developed a novel statistical algorithm, the Wasserstein Algorithm for Classifying Sleep and Wakefulness (WACSAW), to identify behavioral states from recordings of everyday movement. WACSAW employs optimal transport techniques to identify segments with differing activity variability. Functions characterizing the segments' movement distributions were clustered into two groups using a k-nearest neighbors and labeled as sleep or wake based on their proximity …

(R2137) Smarandache Curved Ruled Surfaces And Their Characterizations According To Modified Orthogonal Frame In E^3, Gülnur Şaffak Atalay

Applications and Applied Mathematics: An International Journal (AAM)

In this study, the ruled surfaces generated by Smarandache curves are expressed according to the modified orthogonal frame defined according to both curvature and torsion of the given unit speed curve in 3-dimensional Euclidean space; some special characterizations of these surfaces such as developability, striction curves, distribution parameters are given. In addition, some examples of these surfaces are given in graphical form. We use Maple to draw the graphs of the examples.

Investigating The Efficiency Of Ingan P-N-P-N Homojunction Solar Cells, Moath Alhejji, Mohammad Alavijeh, Jacob Kupernik, Mirsaeid Sarollahi, Abbas Jammali, Seyed Taghavi, Reem Alhelais, Md Hel Uddin Maruf, Morgan Ware

Electrical Engineering and Computer Science Faculty Publications and Presentations

This research investigates the development of a novel p-n-p-n homostructure solar cell, through semiconductor simulations using the Nextnano software. InGaN was used as a model system in order to achieve a bandgap with optimized efficiency for a p-n homojunction solar cell. By increasing the uniform doping concentration from 1.5*10(16) cm(-3) to 1.5*10(17) cm(-3), the open circuit voltage (V-oc) increased while the short-circuit current density (J(sc)) decreased, as expected in simple p-n junctions. The p-n-p-n structure achieved a peak efficiency of 32.91% at a doping level of 6.5*10(16) cm(-3), a similar to 7% improvement over a conventional p-n junction's 25.31% efficiency …