Mathematics Commons^™

The Effort To Improve Students’ Problem-Solving Ability: Physics E-Modules For High School Students, Hidayatullah Hana Putra, Edi Supriana, Nasikhuddin Nasikhuddin, Annisa U. Yana, Suhailee Sohnui

Jurnal Pendidikan Sains

Physics teachers in Indonesia still face obstacles during learning, such as students who are less active and have difficulty in solving physics problems. The physics learning media used are also still not very interesting and are not based on authentic problem solving. Therefore, this study focuses on the development of PBL-based e-modules on work and energy to improve the physics problem-solving abilities of high school students. This research and development used the ADDIE design and was tested on 90 high school students in High School 1 Sumber Pucung Malang in the 2022/2023 academic year. The questionnaire instrument was used in …

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 …

Contextual Approach To Improve Problem Solving Skills In Ipas Subject At Elementary School: A Study Development Of Teaching Materials, Nur Hidayah, Sumarno Sumarno, Joko Siswanto

Jurnal Pendidikan Sains

The objective of this study is to assess the validity, practicality, and efficacy of instructional materials. We refer to this research as research and development, with a focus on the creation of teaching materials. The research design proposed by Borg and Gall consists of six steps: identification of potential and difficulties, data collecting, product design, design validation, design revision, and product trial. The utilized instruments comprise expert and practitioner validity sheets, teacher and student response surveys, and validation sheets for teaching materials and modules, as well as pretest and posttest questions. Experts performed the validity assessment, attaining a score of …

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 …

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 …

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 …

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 …

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 …

Geometric Algebra For Field Theory In Curved Spacetime, Kevin Rhine

All Graduate Reports and Creative Projects, Fall 2023 to Present

Physics seeks to understand the universe by uncovering the fundamental laws that govern matter, energy, space, and time. At its heart lies the challenge of unification: finding a mathematical framework that consistently describes these interactions across all scales, from the subatomic to the cosmological.

This thesis explores geometric algebra, a mathematical language that unifies algebra and geometry, as a tool for advancing this understanding. By extending this framework to curved spacetimes, where gravity influences the structure of space and time, we investigate its ability to describe physical phenomena such as electromagnetism and general relativity. A notable contribution includes the geometric …

An Analysis On The Time Effectiveness Of Speeding While Driving A Vehicle, Joy Skaggs

ATU Scholars Symposium

Speeding is responsible for roughly a third of all crashes, often coming at a deadly cost. The National Highway Traffic Safety Administration reports many negative consequences, such as a greater likelihood of loss of vehicle control, reduced protection equipment effectiveness, increased stopping distance, crash severity, and fuel consumption (National Highway Traffic Safety Administration, n.d.). Yet despite these costs, drivers continue to speed. In fact, in our fast paced world, speeding is so normalized that it’s uncommon to encounter a driver following the speed limit. Hawaiian psychology professor Leon James explains it best: people have twisted their definitions of speeding to …

Volume 16, Maggie Duncan, Madeline Little, Alicia Hoffman, Megan Livesay, Gabrielle Quaresma, Serenity Allen, Laina Pfountz, Ainslie Allred, Sabrina Robles, Nicholas J. Duellman, Trinity L. Deguzman, Melissa H. Savage, Margaret Dudley, Jocelyn Escobar, Olivia Hildreth, Olivia Hopkins, Benjamin Gettier, Lee Kassay, Jade Riddle, Ashley Seiders

Incite: The Journal of Undergraduate Scholarship

Introduction Dr. Amorette Barber, Director, Office of Student Research

From the Editor Dr. Hannah Dudley-Shotwell

Artist’s Statement Maggie Duncan

On Mentoring Dr. Lee Millar Bidwell

The Hujum Campaign in Uzbekistan and its Consequences by Madeline Little

Wet Cupping Compared to Dry Needling for Treatment of Patients with Low Back Pain: A Critically Appraised Topic by Alicia Hoffman and Megan Livesay

Optimization of eDNA Air Sampling Via 3D Printed Fan by Gabrielle Quaresma

Beyond the Classroom: A Qualitative Study of Teacher Attrition and Retention by Serenity Allen and Laina Pfountz

The Treatment of Subacromial Impingement Syndrome with Platelet-Rich plasma Injections Verses …

Analyticity And Supershift With Regular Sampling, Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa, Alain Yger

Mathematics, Physics, and Computer Science Faculty Articles and Research

The notion of supershift (in itself a generalization of the notion of superoscillation arising in quantum mechanics) expresses the fact that the sampling of a function in an interval allows to compute the values of the function far from the interval. In this paper, we study the relation between supershift and real analyticity. We use a classical result due to Serge Bernstein to show that real analyticity for a complex-valued function implies a strong form of supershift. On the other hand, we use a parametric version of a result by Leonid Kantorovitch to show that the converse is not true. …

Fiber Bundles Of The Complex Projective Space And Their Relation To Quantum Physics, Emily Wessman

Student Research Symposium

The complex projective space CPⁿ is the space of lines through the origin in Cⁿ⁺¹ with an equivalence relation defined by Z ~ λZ' for λ ∈ C*. We define the points under the equivalence relation as homogeneous coordinates, represented by [Z₀ : Z₁ : ... Z_n]. Since all Z,sub>i cannot equal zero, we can find a unique set of n coordinates (z₁,...,z_n) such that [Z₀ : Z₁ : ... : Z_n] ~ [1 : z₁ : ... : z_n] where z …

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.

Transient Thermal Energy Harvesting At A Single Temperature Using Nonlinearity, Tamzeed B. Amin, James M. Mangum, Md R. Kabir, Syed M. Rahman, Pradeep Ashaduzzaman, Pradeep Kumar, Luis L. Bonilla, Paul M. Thibado

Physics Faculty Publications and Presentations

The authors present an in-depth theoretical study of two nonlinear circuits capable of transient thermal energy harvesting at one temperature. The first circuit has a storage capacitor and diode connected in series. The second circuit has three storage capacitors, and two diodes arranged for full wave rectification. The authors solve both Ito-Langevin and Fokker-Planck equations for both circuits using a large parameter space including capacitance values and diode quality. Surprisingly, using diodes one can harvest thermal energy at a single temperature by charging capacitors. However, this is a transient phenomenon. In equilibrium, the capacitor charge is zero, and this solution …

Robust Spacecraft Autonomy For Deep Space Exploration In Special Euclidean Group Se(3), Matthew Wittal

Doctoral Dissertations and Master's Theses

Over the past half-century, humanity has gained extensive experience conducting manned spaceflight near Earth. Arguably, "near Earth" could even include the Moon — the most distant destination humans have reached. However, "near" in this work primarily refers low Earth orbit (LEO). One could argue that we have not truly left Earth since the Apollo, as spacecraft in some LEOs remain subject to atmospheric drag thus emphasizing their continued connection to Earth's immediate environment. Reflecting on this, it becomes clear that humanity has largely remained bound to Earth’s immediate vicinity since the Apollo missions reached the Moon. However, that is set …

Optimal Control And Structurally-Informed Gradient Optimization Of A Custom 4-Dof Rigid-Body, Brock Marcinczyk, Logan E. Beaver

Mechanical & Aerospace Engineering Faculty Publications

This work develops a control-centric framework for a custom 4-DOF rigid-body manipulator by coupling a reduced-order Pontryagin’s Maximum Principle (PMP) controller with a physics-informed Gradient Descent stage. The reduced PMP model provides a closed-form optimal control law for the joint accelerations, while the Gradient Descent module determines the corresponding time horizons by minimizing a cost functional built directly from the full Rigid-Body Dynamics. Structural-mechanics reaction analysis is used only to initialize feasible joint velocities—most critically the azimuthal component—ensuring that the optimizer begins in a physically admissible region. The resulting kinematic trajectories and dynamically consistent time horizons are then supplied to …

Developments On Quantum Phase Space Dynamics And Foundations, Gabriel Nowaskie

Mahurin Honors College Capstone Experience/Thesis Projects

This work explores the development and unification of quantum theory within phase space, with a particular focus on new mathematical structures and solution techniques that extend the standard quantum formalism. Building upon the Quantum Phase Space Representation (QPSR) introduced by Torres-Vega and Frederick, we present several advancements that address longstanding gaps in the formulation and solvability of quantum systems in this framework. We introduce the Half-Transform Ansatz, a novel method for solving the Time-Independent Schrodinger Equation by recasting it into a hypergeometric form, enabling the application of the Nikiforov-Uvarov method. This approach is demonstrated through the analysis of quarkonium systems …

Mathematics And Determinism: Chaos, Quantum Mechanics, And The Limits Of Predictive Structure, Jackson T. Salumbides

CMC Senior Theses

This thesis examines the relationship between mathematics and determinism by analyzing how chaos theory, quantum mechanics, and formal mathematical limits challenge traditional conceptions of predictability and causal structure. Chaos theory shows that deterministic systems can exhibit practical unpredictability due to sensitivity to initial conditions. Quantum mechanics introduces probabilistic outcomes that complicate deterministic interpretation, though alternative frameworks such as Bohmian mechanics and superdeterminism attempt to restore determinism at conceptual cost. Additionally, results from mathematical logic, including Gödel’s incompleteness theorems and Turing’s undecidability, demonstrate intrinsic limitations on what can be deduced or computed, even in fully deterministic systems. By synthesizing these areas, …

The Effect Of Electrode Geometry On Excited Species Production In Atmospheric Pressure Air-Hydrogen Streamer Discharge, Shirshak Kumar Dhali, Stuart Reyes

Electrical & Computer Engineering Faculty Publications

When a gas is overvolted at or near atmospheric pressure, it results in a streamer discharge formation. Electrode geometries exert significant impact on the electrical breakdown of gases by altering the spatial profile of the electric field. In many applications the efficient generation of radicals is critical and is determined by the characteristics of the streamer discharge. We examine the effect of electrode geometry on the streamer characteristics and the production of radicals. This is performed for three different electrode geometries: plane–plane, pin–plane, and pin–pin. A two-dimensional rotationally symmetric fluid model is used for the streamer discharge simulation in the …

0th Order Solutions Of The Wavefunctions For The Quantum Elliptical Box And Microstrip Antenna, Nishtha Tikalal

Honors Undergraduate Theses

For a quantum particle confined to a two-dimensional elliptical box or electromagnetic wave in a microstrip antenna, geometrical and boundary condition interplay result in a spectrum of spatial patterns. Due to the asymmetrical nature of the ellipse, we are faced with continuous symmetry reductions, leaving both degenerate and nondegenerate solutions. Here, we present a complete derivation of an analytical solution and visualizations of the fundamental wavefunctions for both Dirichlet and Neumann boundary conditions respectively corresponding to the quantum elliptical box and the elliptical microstrip antenna.

We demonstrate that the eigenmodes, governed by eccentricity, directly correspond to the modal field distributions …

Isochronous And Period-Doubling Diagrams For Symplectic Maps Of The Plane, T. Zolkin, S. Nagaitsev, I. Morozov, S. Kladov, Y. -K. Kim

Physics Faculty Publications

Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the interpretation of how systems evolve under varying conditions. While the area-preserving quadratic Hénon map has received significant theoretical attention, a comprehensive description of its mixed parameter-space dynamics remain lacking. This limitation arises from early attempts to reduce the full two-dimensional phase space to a one-dimensional projection, a simplification that resulted in the loss of important dynamical features. Consequently, there is a clear need for a more …

Local-Neutrosophic Logic And Local-Neutrosophic Sets: Incorporating Locality With Applications, Florentin Smarandache, Takaaki Fujita

Branch Mathematics and Statistics Faculty and Staff Publications

The study of uncertainty has been a significant area of research, with concepts such as fuzzy sets [87], fuzzy graphs [51], and neutrosophic sets [58] receiving extensive attention. In Neutrosophic Logic, indeterminacy often arises from real-world complexities. This paper explores the concept of locality as a key factor in determining indeterminacy, building upon the framework introduced by F. Smarandache in [73]. Locality refers to processes constrained within a specific region, where an object or system is directly influenced by its immediate surroundings. In contrast, nonlocality involves effects that transcend spatial or temporal boundaries, where changes in one location have direct …

Reasoning Through Change: Exploring Covariational Thinking In Student Exponential Graph Interpretation, Samantha Lynn Pearson

Honors Theses and Capstones

This study explores how life science students reason about exponential functions in the context of an introductory physics course. While exponential functions are essential in both physics and biology—appearing in scenarios like population growth and temperature cooling—students often encounter challenges in interpreting them. Using a resources framework, we examined the cognitive resources these students bring to exponential reasoning, focusing on what ideas and strategies they already possess. Our methodology involved conducting think-aloud interviews with nine students from PHYS 402. Interviews were coded using a framework informed by prior research on covariational reasoning and exponential understanding. Results show that students generally …

Students’ Concept Maps Profile On Environmental Pollution Material During The Covid-19 Pandemic, Sunarni Sunarni, Sri Widoretno, Puguh Karyanto, Bowo Sugiharto, Sri Dwiastuti, Chandra Adi Prabowo

Jurnal Pendidikan Sains

The study investigates the performance of students in constructing Concept Maps (CM) related to environmental pollution material during the COVID-19 pandemic. The data reveals that the overall achievement in CM construction was suboptimal, with no component reaching more than half of its maximum potential. The highest achievement was recorded in the valid relationship component, which attained 9.75% of its maximum possible score. This was followed by the hierarchy component, achieving 7.34%, and the branching component at 3.42%. The pattern component ranked fourth with 1.31%, closely followed by the example component at 1.30%. The lowest performance was observed in the crosslink …

Analysis Of Students’ Problem-Solving Skills In Newton’S Law With 5e Learning Cycle, Nidya Desyana, Sutopo Sutopo, Nandang Mufti

Jurnal Pendidikan Sains

The aim of this study is to identify students’ problem-solving skills in Newton’s laws through the implementation of the 5E learning cycle in the classroom. A pre-experimental design with a one-group pretest-posttest approach was employed. Data on problem-solving skills were collected from students’ pre-test and post-test responses to two essay questions. The indicator with the highest percentage of problem-solving skills was useful description (83% of students), while the indicator with the lowest percentage was specific application of physics (33% of students). Due to the non-normal distribution of the data, the Wilcoxon test was utilized. The results indicated a significant difference …

Development Of Conceptual Scaffolding-Assisted Formative Assessment For Enhancing Understanding Of Temperature And Heat, Ana Lailatul Fitriyah, Sentot Kusairi, Markus Diantoro

Jurnal Pendidikan Sains

This research aims to develop formative assessment media assisted by conceptual scaffolding to improve students’ understanding of temperature and heat, test its validity and practicality, and gauge student responses. Utilizing the ADDIE model, the research follows five stages: Analysis, Design, Development, Implementation, and Evaluation. In the Analysis stage, a literature review was conducted to identify critical components, including formative assessment, conceptual scaffolding, concept mastery, and previous research. The Design stage involved identifying users, defining competencies and indicators, creating a storyboard, integrating assessment components, and determining mastery levels. During the Development stage, the assessment media were developed into a functional product. …