Mathematics Commons^™

Differentiated Teaching Module Using Problem Solving Model: Numerical Ability Of Elementary School Students, Risa Alifatin, Agus Sutono, Ida Dwijayanti

Jurnal Pendidikan Sains

This study aims to develop a differentiated teaching module using the problem-solving model that is valid, practical, and effective to improve students' numerical abilities. This study uses the ADDIE Model research and development approach. The sample in this study was class III of elementary school Tenggulangharjo as an experimental class totaling 22 students and class III of elementary school Karangtengah as a control class totaling 19 students. Data analysis used the t-test and N-Gain test. The study found that (1) the average validity score of the three parts of the Differentiated Teaching Module was 3.74, which is 93.62%, placing it …

Ethnoscience-Based Science Learning Through Composite Board Making Utilizing Eggshell Waste And Water Hyacinth Fiber (Eichornia Crassipes), Asep Khaidir Arpan, Yulia Sukmawardani, Pina Pitriana, Ade Yeti Nuryantini

Jurnal Pendidikan Sains

The demand for boards continues to increase every year, while overexploitation of wood leads to environmental degradation and forest loss. On the other hand, eggshell and water hyacinth waste continues to grow without optimal utilization. This research aims to make composite boards based on eggshell waste and water hyacinth fibers and analyze the potential of ethnoscience in science learning. This research used a qualitative descriptive method with a literature and documentation study approach. The materials used in this experiment are eggshell waste, water hyacinth fiber, and polyester resin. The composite board was made by mixing water hyacinth fiber and eggshell …

Analysis Of Students' Creative Thinking Skills In Learning Hydrocarbons By Using Daily Life-Based Practicum Method, Yenni Kurniawati, Laras Dyaz Handayani, Dea Ramadani, Nurhikmah Sari

Jurnal Pendidikan Sains

Creative thinking skill is a competence of the 21st century that is needed very much and needs to be increased by utilizing chemistry in life. This research aimed at analyzing student creative thinking skills in experimental and control groups and finding out the effect of the daily life-based practical work learning method on student creative thinking skills. This research was conducted in the eleventh grade at High School 1 Pekanbaru on the hydrocarbon lesson. The quasi-experimental method was used in this research with pretest-posttest and non-equivalent control group designs. The instruments used in this research were essay tests, observation, and …

Exploring Students’ Perceptions Of Science Laboratory Practices: A Comparative Study Between Rural And Urban Schools, Safrida Dwiningsih, Ina Lestari, Roma Ismi, Sri Wahyu Rahmadina, Masdalena Sinaga, M. Rahmad

Jurnal Pendidikan Sains

This study aims to analyze students' perceptions of the implementation of science laboratory practicums at public middle school 020 Pekanbaru and public middle school 7 Pangkalan Kuras, Riau Province. Using a quantitative survey method, this study involved 75 student respondents. The instrument used was a questionnaire consisting of 26 statements, analyzed descriptively. The results show that students' perceptions of the preparation, implementation, and conclusion stages of the practicum fall into the "good" category, with urban schools having a higher percentage. In conclusion, the implementation of practicums in urban schools is better than in rural schools, bringing attention to the need …

Digital Comic Learning Media (E-Comic) To Increase Student Learning Interest In Reaction Rate Material At High School, Berliana Afsohin Nabila, Achmad Lutfi

Jurnal Pendidikan Sains

This study aims to develop digital comic learning media that is effective in increasing students' interest in learning about reaction rate material, focusing on the media's validity, practicality, and overall effectiveness. This research utilizes the research and development method with the ADDIE model. Research instruments were used, including validity sheets to assess the media's validity, student activity observations, and student response questionnaires to evaluate the media's practicality, as well as student interest questionnaires and learning outcomes to measure the effectiveness of the learning media. The findings show that validity results showed a mode score of 4, indicating a very valid …

Teaching Materials Containing Kse To Support Character Education In Mathematics Subjects In Elementary Schools, Kunaenah Kunaenah, Rasiman Rasiman, Bagus Ardi Saputro

Jurnal Pendidikan Sains

The purpose of the study was to determine the validity, practicality, and effectiveness of teaching materials containing KSE to support character education in mathematics lesson content. This study employs a development research approach based on Borg and Gall's research design. The subjects of the study were in class V at public elementary school Kaliboyo. The data collection instruments used were validity sheets, response questionnaires, validation sheets, and observation sheets. The findings show that experts carried out the validity test, achieving a value of 93.30% in the very valid category. The practicality test results were derived from various sources: students' questionnaires, …

Development Of Differentiated Teaching Modules With A Scientific Approach To Improve Elementary School Students’ Science Literacy, Supriyanto Supriyanto, Joko Sulianto, Achmad Buchori

Jurnal Pendidikan Sains

The study aim is to determine the validity, practicality, and effectiveness of teaching materials. This type of research involves the development and creation of teaching module products. The research design used is ADDIE (Analysis, Design, Development, Implementation, Evaluation). The instruments used are validity sheets for experts and practitioners, teacher response questionnaires, teaching module validation sheets, and pretest and posttest questions. The findings show that experts conducted the validity test, achieving a score of 92.22 in the very valid category. The practicality test was obtained from the teacher questionnaire, which was stated as practical with an average value of 91.25, and …

Analysis Of Misconceptions In Learning Biology Mutation Material At High School, Fitri Hayati Kurnia, Tri Wahyu Agustina, Wahyuni Handayani

Jurnal Pendidikan Sains

This research aims to analyze student misconceptions regarding mutation material in class XII. The research method uses a descriptive approach with mixed methods, which combines qualitative and quantitative methods. Qualitative data was obtained through interviews with biology teachers, while quantitative data was obtained through questionnaires and essay tests on students. The research results indicate that the material that students like is growth and development, while the material they don't like is gene mutation and genetic material. Students' misconceptions occur due to preconception aspects, associative thinking, and a lack of understanding of genetic concepts. It was found that students' understanding of …

On Uses For And Constructions Of Differential Graded Algebras, Henry Potts-Rubin

Dissertations - ALL

This thesis is comprised of two projects (in reverse chronological order) with the unifying theme of differential graded (dg) algebras. The first is a collaborative effort with Hugh Geller and Desiree Martin, in which we completely classify the trees and cycles whose edge ideals are minimally resolved by dg algebras. To do this, we pull from discrete Morse theory and homological algebra to give descriptions of the dg algebra structures at play. We also use a "pruning" technique due to Boocher to give a combinatorial obstruction to the existence of dg algebra structure on minimal free resolutions of edge ideals …

Applications Of Contracting Self-Similar Groups To Cryptography And Scale Groups, Arsalan Akram Malik

USF Tampa Graduate Theses and Dissertations

Given their peculiar properties, self-similar groups are of great interest both from applications and theoretical standpoints. In this work we study the scope of their applications in post-quantum cryptography and in constructing scale groups via lifting maps.

We propose self-similar contracting groups as a platform for cryptographic schemes based on simultaneous conjugacy search problem (SCSP). This class of groups admits fast polynomial-time algorithms for the word problem and element multiplication that can be used for effective encryption and decryption of messages. It contains extraordinary examples like the Grigorchuk group, which is known to be non-linear, thus making some of existing …

On Some Hypergraph Coloring Algorithms, Boyoon Lee

USF Tampa Graduate Theses and Dissertations

Of a given bipartite graph G = (V, E), it is elementary to construct a bipartition in timeO(|V |+|E|). For a given k-graph H = H(k) with k ≥ 3 fixed, Lovász proved that deciding whether H is bipartite is NP-complete. In this thesis, we consider the average running time of this problem. For that, let B_n = (B^(k))_n be the collection (family) of all bipartite k-graphs H on the fixed vertex set [n] = {1, ...., n}. We construct, of a given H ∈ B_n, a bipartition in time averaging O(n^k) over the class B_n. We provide two proofs …

The Only Constant Is Change: The Role Of Genetic Diversification In Cancer And Beyond, Malgorzata Tyczynska Weh

USF Tampa Graduate Theses and Dissertations

Genetic diversification, the process by which genetic variation arises in a population, is fundamental to evolution by natural selection. Mutation, a central diversification process, fuels adaptation across species, including in cancer. Yet most new mutations are neutral or deleterious on cell fitness, raising the question of how mutation-driven adaptation persists. To explore this paradox, I developed a spatial agent-based model (ABM) in which population fitness emerges from individual cells acquiring mutations at varied rates and with diverse fitness effects. I evaluated model behavior across adaptive states, mutation rates, and distributions of fitness effects. The results show that high mutation rates …

Probabilities With Values In Scaled Hyperbolic Numbers, Daniel Alpay, Ilwoo Choo

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper, we introduce a notion of a probabilistic measure which takes values in t-scaled hyperbolic numbers for t ∈ R, with a system of axioms generalizing directly Kolmogorov’s axioms. i.e., we establish a suitable measure theory in the set Dt of all t-scaled hyperbolic numbers for arbitrarily fixed t ∈ R.

Machine Learning: Neural Networking With Relu And Optimization, Aidan Redmond Brownell

Undergraduate Theses, Capstones, and Recitals

At its core, learning is an algorithmic process: it begins with input data, undergoes a series of transformations or computations, and yields an output intended to solve a specific task. This output is then compared against a target or desired result, and the internal mechanisms are updated based on how well the output aligns with expectations. While this feedback-driven process occurs almost effortlessly in humans, it is a far more structured, deliberate, and computationally intensive undertaking for machines.

Basic Theory And Implementations Of Quantum Error Correction, Derek Rodriguez

Undergraduate Theses, Capstones, and Recitals

The introduction of quantum computing has presented algorithmic solutions to computationally difficult challenges that are far more efficient than those of classical computers. These algorithms leverage the properties of quantum mechanics to manipulate the quantum properties of subatomic particles, requiring immense precision and stability. Current quantum hardware, however, is too noisy and introduces too many errors for these algorithms to be useful in practice, necessitating the use of error correction algorithms. This field survey seeks to introduce various principles of quantum mechanics relevant to quantum computing and quantum error correction (QEC), detail the implementation and motivations of a basic QEC …

Simplicial Decomposition And Realization, Matthew Ellison

Dartmouth College Ph.D Dissertations

In simplicial decomposition, we define two invariants --- V_Z and V_Q --- which represent notions of integral and rational volume of a certain class of simplicial complexes. We prove V_Z and V_Q are additive under disjoint union and connected sum, and investigate `integrality gaps' between the two quantities. We apply the theory to establish a conjecture of Sleator, Thurston, and Tarjan on tetrahedral fillings, and, as a corollary, obtain a new proof of Pournin's 2012 result on the diameter of the associahedron. In simplicial realization, we provide practical sufficient conditions and computer code to prove the existence of Euclidean embeddings …

Some Results In Thermodynamic Formalism, C. Evans Hedges

Electronic Theses and Dissertations

This dissertation investigates several key questions at the intersection of dynamical systems, computability theory, and thermodynamic formalism. In the symbolic setting, we establish novel results regarding the statistical properties of equilibrium states, deriving bounds on probabilities of configurations and relating these bounds to the Gibbs property through the homoclinic relation. Additionally, we examine the computability of thermodynamic quantities such as pressure, ground state energy, and residual entropy. We show that topological pressure is computable from above for general subshifts and computable for strongly irreducible shifts, with similar results extending to ground state energy and residual entropy.

Extending beyond subshifts, we …

A Study On Fuzzy Time-Series And Its Applications To Stock Price Forecasting, Takeshi Stormer

University Honors Theses

Fuzzy mathematics looks to incorporate the vagueness that exists within the real world, specifically regarding imprecise classes, or non-numerical information expressed as "linguistic" variables. Since most traditional mathematical theories do not have the ability to be applied with the exactness that is otherwise seen in mathematics. As such, there had been many applications of fuzzy mathematics throughout many different fields of mathematics, including that of forecasting. By exploring the fundamentals of fuzzy mathematics, including fuzzy sets, operations of fuzzy sets, the surface level introduction to fuzzy logic, fuzzy relations, operations of fuzzy relations, and fuzzy time-series, this work looks to …

A Spatial Modeling Framework For Identifying Multidimensional Risk Factors Of Colorectal Cancer, Johnna K. Berryhill

Student Theses and Dissertations

Colorectal cancer (CRC) is one of the most common and preventable cancers, yet significant disparities in screening, incidence, and late-stage diagnosis persist across different geographic and socioeconomic contexts. This thesis presents a spatial modeling framework for identifying multidimensional risk factors associated with CRC outcomes across various geographic scales. Using county- and census-tract-level data from national and state sources, the study integrates demographic, socioeconomic, environmental, built environment, and behavioral predictors to analyze geographic variability in CRC risk factors. Advanced spatial modeling techniques, including Geographically Weighted Regression (GWR) and Geographically Weighted Random Forest (GW-RF), are employed to capture spatial heterogeneity in these …

Notes On The Invariance Of Tautness Under Lie Sphere Transformations, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

An embedding ϕ : V → Sⁿ of a compact, connected manifold V into the unit sphere Sⁿ ⊂ Rⁿ⁺¹ is said to be taut, if every nondegenerate spherical distance function d_p, p ∈ Sⁿ, is a perfect Morse function on V , i.e., it has the minimum number of critical points on V required by the Morse inequalities. In these notes, we give an exposition of the proof of the invariance of tautness under Lie sphere transformations due to ´Alvarez Paiva. First we extend the definition of tautness of submanifolds of S …

Class Groups And Selmer Groups In Special Families, Debanjana Kundu, Abhishek _

School of Mathematical & Statistical Sciences Faculty Publications

We explore the relationship between (3-isogeny induced) Selmer group of an elliptic curve and the (3 part of) the ideal class group, over certain non-abelian number fields.

Temporal Modeling And Forecasting Of Blood Glucose Dynamics In Individuals With Diabetes Mellitus, Mj Ruff

University Honors Theses

People living with Diabetes Mellitus face significant health risks, including an increased likelihood of heart disease, stroke, and fluctuations in blood glucose levels. The unpredictable nature of glucose levels can lead to dangerous conditions such as ketoacidosis and hypoglycemia. This study employs advanced time series analysis tools to forecast the glucose levels for an individual diagnosed with Type 1 Diabetes Mellitus.

A Proposal To Explore Geometry With Geogebra: Graphical Exploration And Formal Demonstration Of The Collinearity Of The Barycenters Of A Polygon, Saulo Mosquera Lopez, Marlio Paredes, Walter Castro

School of Mathematical & Statistical Sciences Faculty Publications

This paper illustrates an example of a mathematical activity that teachers and students can replicate to create an experience that resembles professional mathematical activity. We extend the property “Consider a triangle ABC, any straight line and let A’, B’, C’ be the reflections of the points A, B, C on the straight line then the barycenters of the triangles ABC, A’BC, AB’C and ABC’ are collinear and the line of collinearity is perpendicular to the straight line” for any quadrilateral. It is proved that there are four additional triangles, for a total of eight, whose barycenters are collinear and that …

On Excursions Associated With A Certain Local Time Of Simple Symmetric Random Walks, With Applications, Takahiko Fujita, Naohiro Yoshida

Journal of Stochastic Analysis

In this note, some applications of excursions associated with a certain local time of simple symmetric random walks are presented. Specifically, the excursions are applied to calculate some probability distributions of interest regarding the random walks. Furthermore, a solution of the Skorokhod embedding problem for random walks is obtained through the excursions.

Forecasting Influenza Rates Using Machine Learning: A Study Of Chatgpt's Predictive Accuracy, Sara Saleh

University Honors Theses

This study evaluates ChatGPT's ability to forecast influenza rates, such as the number of flu cases, hospitalizations, and death during peak season periods using CDC data, and comparing forecasts against actual results to calculate statistical accuracy and consistency. Influenza forecasting is essential for public health planning, but traditional methods may not always provide timely or accurate predictions. In this research study, ChatGPT was utilized to predict the influenza rates for the following week based on the previous week's data obtained from the FluView surveillance system. The predicted rates were compared to the actual influenza rates to assess the model's overall …

Tilings In The 3 Dimensional Lattice With L-Tetrominoes, Ian N. Bridges

Rose-Hulman Undergraduate Mathematics Journal

We consider three dimensional L-tetrominoes. We show that there exists at least one way to tile every three dimensional rectangle whose side lengths are at least $3$ and area is congruent to $1 \pmod 4$ such that one square goes untiled. In addition, we show that every three dimensional rectangle is tileable provided one side has length at least $2$ and the other is a multiple of $4$.

The Other Side Of The Equation: De-Simplification, A Prerequisite For Calculus, Stephen L. Brown

ACMS Conference Proceedings 2005

No abstract provided.

Ceno: Non-Uniform, Segment And Parallel Zero-Knowledge Virtual Machine, Tianyi Liu, Zhenfei Zhang, Yuncong Zhang, Wenqing Hu, Ye Zhang

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we explore a novel Zero-knowledge Virtual Machine (zkVM) framework leveraging succinct, non-interactive zero-knowledge proofs for verifiable computation over any code. Our approach divides the proof of program execution into two stages. In the first stage, the process breaks down program execution into segments, identifying and grouping identical sections. These segments are then proved through data-parallel circuits that allow for varying amounts of duplication. In the subsequent stage, the verifier examines these segment proofs, reconstructing the program's control and data flow based on the segments' duplication number and the original program. The second stage can be further attested …

A Bayesian Approach To Grappa Parallel Fmri Image Reconstruction Increases Snr And Power Of Task Detection, Chase J. Sakitis, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

In fMRI, capturing brain activation during a task is dependent on how quickly k-space arrays are obtained. Acquiring full k-space arrays, which are reconstructed into images using the inverse Fourier transform (IFT), that make up volume images can take a considerable amount of scan time. Undersampling k-space reduces the acquisition time but results in aliased, or “folded,” images. GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA) is a parallel imaging technique that yields full images from subsampled arrays of k-space. GRAPPA uses localized interpolation weights, which are estimated prescan and fixed over time, to fill in the missing …

High Moment And Pathwise Error Estimates For Fully Discrete Mixed Finite Element Approximations Of The Stochastic Stokes Equations With Multiplicative Noise, Liet Vo

School of Mathematical & Statistical Sciences Faculty Publications

This paper is concerned with high moment and pathwise error estimates for both velocity and pressure approximations of the Euler–Maruyama scheme for time discretization and its fully discrete mixed finite element discretization. Optimal rates of convergence are established for all pth moment errors for p ≥ 2 using a novel doubling of moments technique. The almost optimal rates of convergence are then obtained using Kolmogorov’s theorem based on the high moment error estimates. Unlike for the velocity error estimate, the high moment and pathwise error estimates for the pressure approximation are proved in a time-averaged norm. In addition, the …