Mathematics Commons^™

Identification Of Scientific Argumentation Ability Of High School Students On Optical Instrument Material, Rais Muktamar Amin, Parno Parno, Sentot Kusairi, Marlina Ali

Jurnal Pendidikan Sains

Optical instruments play a crucial role in physics education, providing essential material for students to understand complex concepts. This study aims to evaluate the scientific argumentation abilities of high school students regarding optical instruments. Conducted as a quantitative descriptive study, the research involved 60 eleventh-grade MIPA students from SMA Laboratorium UM. The research instrument was a scientific argumentation test comprising 12 essay questions, designed according to the Toulmin Argumentation Pattern (TAP) adaptation indicators, with a reliability coefficient of 0.332. Student responses were classified into five levels of scientific argumentation based on the TAP model, as developed by Sampson, Enderle, and …

Analyzing Physics Students’ Misconceptions About Simple Electrical Circuits, Sapta Adiguna, Shinta Dewi Susanti, Sentot Kusairi, Iwan Setiawan

Jurnal Pendidikan Sains

This study investigates the prevalence and types of misconceptions among first-year Physics Education students regarding simple electrical circuits using the Simple Electric Circuits Diagnostic Test (SECDT). Employing a quantitative descriptive approach, the research analyzes responses from a sample of 42 students, selected through convenience sampling. The SECDT, a three-tier diagnostic instrument with a reliability of 0.69, identifies student misconceptions by categorizing responses into scientific knowledge, misconceptions, no understanding, and lack of knowledge. The results indicate significant gender differences in the types and prevalence of misconceptions. Male students exhibited a higher percentage of misconceptions (77.5%) compared to female students (62.8%). Notably, …

The Influence Of Predict, Observe, And Explain (Poe) Learning Accompanied By Formative Assessment On Misconceptions And Mastery Of Students’ Concepts Of Temperature And Heat Material, Ahmad Ilmar, Sentot Kusairi, Khusaini Khusaini

Jurnal Pendidikan Sains

High misconceptions and students’ mastery of concepts that are low enough are detected in temperature and heat material. To overcome this, teachers must apply learning strategies that are able to actively involve students in observation activities, namely the POE learning strategy. However, POE learning is not always easy to apply, students are still weak in communicating the results of their experiments. Therefore, a way is needed that helps students during the learning process to be more confident and not afraid when asked to argue, namely with formative assessment. POE learning accompanied by formative assessment aims to enable students to understand …

Identifying Students’ Incorrect Common-Sense Knowledge In Forces And Motion: Recommendations For Developing Computer-Based Learning Media, Ahmad Ridlotul Adha, Sutopo Sutopo, Nasikhuddin Nasikhuddin

Jurnal Pendidikan Sains

Conceptual understanding is a crucial area in physics education research, focusing on students’ comprehension of fundamental principles. Force and motion, integral topics within this field, are inherently linked to students’ daily experiences. Numerous studies have identified the persistence of common sense knowledge among students. This research presents a literature review aimed at identifying such consistently held misconceptions. We analyzed 17 papers sourced from Publish or Perish 8, Google Scholar, and Scopus. Our analysis revealed that the concepts of impetus and active force are the most persistent forms of common sense knowledge, influenced by real-life experiences. Additionally, students’ difficulties with kinematics …

Sustainable Food House Area (Sfha): Analysis Of Community Knowledge And Behavior, Delvi Adri, Mimien Henie Irawati, Sueb Sueb

Jurnal Pendidikan Sains

This research aimed to assess the knowledge and behavior of the community regarding the Sustainable Reserve Food Garden (SRFG) program. The study was conducted in July 2016 in Jorong Lubuk Agam, Kenagarian Ampang Kuranji Koto Baru, Dharmasraya, West Sumatra. Utilizing a descriptive quantitative approach, data were collected using Accidental Random Sampling, involving 33 heads of families as respondents. The findings revealed that community knowledge and behavior related to the SRFG program were generally insufficient, with 44.1% and 47.27% of respondents, respectively, demonstrating a lack of understanding and practice. The study concludes that approximately one-third of the population has limited knowledge …

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …

Modeling The Population Dynamics And Movement Of Zebra Mussels, Alexanderia Lacy, Yu Jin, David Strayer, Suzanne Lenhart

Department of Mathematics: Faculty Publications

Zebra mussels have caused significant damage in many lakes and rivers. By using a hybrid population model with discrete-time equations and ordinary differential equations, we represent the zebra mussel’s life cycle, growth, and population movement. The dynamics of the larvae (unsettled and settled larvae) are represented during the summer months in a system of two ordinary differential equations, while the juvenile, small adult, and large adult stages are represented by a discrete model with yearly time steps. The goal is to investigate the effects of zebra mussel movement between three different spatial locations and possible control measures. Zebra mussel data …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

How To Intercept A High-Speed Rocket With A Pair Of Compasses And A Straightedge?, Yagub N. Aliyev

CODEE Journal

In this paper a nonlinear differential equation arising from an elementary geometry problem is discussed. This geometry problem was inspired by one of the proofs of the first remarkable limit discussed in a typical first semester undergraduate Calculus course. It is known that the involved differential equation can be reduced to Abel’s differential equation of the first kind. In this paper the problem was solved using an approximate geometric method which constructs a piecewise linear solution approximation for the curve. The compass tool of GeoGebra was extensively used for these constructions. At the end of the paper, some generalizations are …

Difference Of Facial Achromatic Numbers Between Two Triangular Embeddings Of A Graph, Kengo Enami, Yumiko Ohno

Theory & Applications of Graphs

A facial $3$-complete $k$-coloring of a triangulation $G$ on a surface is a vertex $k$-coloring such that every triple of $k$-colors appears on the boundary of some face of $G$. The facial $3$-achromatic number $\psi_3(G)$ of $G$ is the maximum integer $k$ such that $G$ has a facial $3$-complete $k$-coloring. This notion is an expansion of the complete coloring, that is, a proper vertex coloring of a graph such that every pair of colors appears on the ends of some edge.

For two triangulations $G$ and $G'$ on a surface, $\psi_3(G)$ may not be equal to $\psi_3(G')$ even if $G$ …

The Ricci Curvature On Simplicial Complexes, Taiki Yamada

Theory & Applications of Graphs

We define the Ricci curvature on simplicial complexes modifying the definition of the Ricci curvature on graphs, and prove upper and lower bounds of the Ricci curvature. These properties are generalizations of previous studies. Moreover, we obtain an estimate of the eigenvalues of the Laplacian on simplicial complexes by the Ricci curvature.

Shock-Wave Tolerant Phase Reconstruction Algorithm For Shack–Hartmann Wavefront Sensor Data, Thomas E. Defoor, Matthew Kalensky, Matthew R. Kemnetz, Timothy J. Bukowski, Mark F. Spencer

Faculty Publications

We develop a phase reconstruction algorithm for the Shack–Hartmann wavefront sensor (SHWFS) that is tolerant to phase discontinuities, such as the ones imposed by shock waves. In practice, this algorithm identifies SHWFS locations where the resultant tilt information is affected by the shock and improves the tilt information in these locations using the local SHWFS observation-plane irradiance patterns. The algorithm was shown to work well over the range of conditions tested with both simulated and experimental data. In turn, the reconstruction algorithm will enable robust wavefront sensing in transonic, supersonic, and hypersonic environments.

Social Justice Mathematics: Classroom Practices That Give Students Rigor While Building Agency, Emily Marquise

Masters Theses (Archived)

The purpose of this study is to examine the impact of a social justice approach to mathematics instruction. While many students have math aversion, students in low socioeconomic communities exhibit this to a higher degree putting them at a disadvantage as they progress through their educational career. More than 3.4 million K-12 students in the United States come from families that earn less than the median income yet achieve scores in the top percentile (Wyner et al., 2007). This raises the question of why so many students in low-socioeconomic settings are not given rigorous content that will keep them competitive …

Building Community, Competency, And Creativity In Calculus 2: Summary Of A Pilot Year Of Project Implementation, Jennifer Beichman, Candice R. Price

Feminist Pedagogy

In light of the COVID-19 pandemic, instructional modes at our institution moved to fully online and remote, then fully online but on campus, and back to in-person learning in fall 2021. To combat perceived issues in student engagement, we piloted using group projects in place of exams at the natural content break points in Calculus 2.

Limit Distributions Of Products Of Independent And Identically Distributed Random 2 × 2 Stochastic Matrices: A Treatment With The Reciprocal Of The Golden Ratio, Santanu Chakraborty

School of Mathematical & Statistical Sciences Faculty Publications

Consider a sequence (Xn)n≥1 of i.i.d. 2×2 stochastic matrices with each Xn distributed as μ. This μ is described as follows. Let (Cn,Dn)T denote the first column of Xn and for a given real r with 012 is very challenging. Considering the extreme nontriviality of this case, we stick to a very special such r, namely, r=√5−12 (the reciprocal of the golden ratio), briefly mention the challenges in this nontrivial case, and completely identify λ for a very special situation.

Regular Ideals, Ideal Intersections, And Quotients, Jonathan H. Brown, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff

Department of Mathematics: Faculty Publications

Let B ⊆ A be an inclusion of C^∗ -algebras. We study the relationship between the regular ideals of B and regular ideals of A.We show that if B ⊆ A is a regular C^∗ -inclusion and there is a faithful invariant conditional expectation from A onto B, then there is an isomorphism between the lattice of regular ideals of A and invariant regular ideals of B. We study properties of inclusions preserved under quotients by regular ideals. This includes showing that if D ⊆ A is a Cartan inclusion and J is a regular ideal in A, …

Toughness Of Recursively Partitionable Graphs, Calum Buchanan, Brandon Du Preez, K. E. Perry, Puck Rombach

Theory & Applications of Graphs

A simple graph G = (V,E) on n vertices is said to be recursively partitionable (RP) if G ≃ K1, or if G is connected and satisfies the following recursive property: for every integer partition a₁, a₂, . . . , a_k of n, there is a partition {A₁,A₂, . . . ,A_k} of V such that each |A_i| = a_i, and each induced subgraph G[A_i] is RP (1 ≤ i ≤ k). We show that if S is a …

An Empirical Study Of Machine Learning Techniques For Accurate Stock Price Forecasting, Daniel Paliulis, Hari Patchigolla

Honors Scholar Theses

This paper presents a comprehensive approach to predicting future stock prices of companies using machine learning and time series analysis. The research problem is centered around addressing the complexity and emotion-driven nature of stock investment decisions. To create an objective determinant in stock decisions, we propose a machine learning model utilizing time series data from major companies, including Amazon, Apple, Google, Nvidia, Meta, Tesla, Salesforce, Intel, and Microsoft. We explore the use of Long Short-Term Memory (LSTM) neural networks, to capture the temporal dynamics of stock prices. These models are designed to process sequential data, maintaining short term and long …

The Tor Algebra Of Trimmings Of Gorenstein Ideals, Luigi Ferraro, Alexis Hardesty

School of Mathematical & Statistical Sciences Faculty Publications

Let (R,\mathfrak m,\Bbbk ) be a regular local ring of dimension 3. Let I be a Gorenstein ideal of R of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric matrix of odd size such that I is generated by the sub-maximal pfaffians of this matrix. Let J be the ideal obtained by multiplying some of the pfaffian generators of I by \mathfrak m; we say that J is a trimming of I. Building on a recent paper of Vandebogert, we construct an explicit free resolution of R/J and compute a partial DG algebra structure on this …

First Order Approximation On The Basilica Julia Set, Xintan Xia, Taryn Flock

Mathematics, Statistics, and Computer Science Honors Projects

We consider the basilica Julia set of the quadratic polynomial P (z) = z^2 - 1, with its successive graph approximations defined in terms of the external ray parametrization of the set. Following the model of Kigami and later Strichartz, we exploit these graph approximations to define derivatives of functions defined on the fractal, an endeavor complicated by asymmetric neighborhood behaviors at approximated vertex points across levels, and by the topology of these vertices. We hence differentiate even and odd levels of approximations of the Julia set and construct, accordingly, normal derivatives corresponding to each level category at the vertices, …

A Mathematical Model For Frogeye Leaf Spot Epidemics In Soybean, Chayu Yang, Jin Wang

Department of Mathematics: Faculty Publications

We propose a new mathematical model based on differential equations to investigate the transmission and spread of frogeye leaf spot, a major soybean disease caused by the fungus Cercospora sojina. The model incorporates the primary and secondary transmission routes of the disease as well as the intrinsic dynamics of the pathogen in the contaminated soil. We conduct detailed equilibrium and stability analyses for this model using theories of dynamical systems. We additionally conduct numerical simulations to verify the analytical predictions and to implement the model for a practical application.

Optimal Stopping And Related Topics, Jackson Scott Hebner

Honors Scholar Theses

Suppose we are observing a randomly evolving system and have the ability to freeze it at any time. If we want to maximize some function of the state of the system, how can we determine the best time to freeze the system based on observations only up until the present moment? That is, without seeing the future, how can we form a rule for stopping the system such that we optimize the expected value of the function of interest to us? This is an informal statement of the concept of optimal stopping, a topic with deep theory and numerous applications. …

Wiener Index In Graphs Given Girth, Minimum, And Maximum Degrees, Fadekemi J. Osaye, Liliek Susilowati, Alex S. Alochukwu, Cadavious Jones

Theory & Applications of Graphs

Let $G$ be a connected graph of order $n$. The Wiener index $W(G)$ of $G$ is the sum of the distances between all unordered pairs of vertices of $G$. The well-known upper bound $\big( \frac{n}{\delta+1}+2\big) {n \choose 2}$ on the Wiener index of a graph of order $n$ and minimum degree $\delta$ by Kouider and Winkler \cite{Kouider} was improved significantly by Alochukwu and Dankelmann \cite{Alex} for graphs containing a vertex of large degree $\Delta$ to $W(G) \leq {n-\Delta+\delta \choose 2} \big( \frac{n+2\Delta}{\delta+1}+4 \big)$. In this paper, we give upper bounds on the Wiener index of $G$ in terms of order …

A Generalized Kodaira Vanishing Theorem For Lie Algebroids And A Riemann–Roch Theorem For Singular Foliation, Tengzhou Hu

Arts & Sciences Graduate Student Theses and Dissertations

A Lie algebroid is a generalization of Lie algebra that provides a general framework to describe the symmetries of a manifold. In this thesis, we first generalize the Kodaira vanishing theorem, which is a basic result in complex geometry, to K\"{a}hler Lie algebroids. The generalization of the Kodaira vanishing theorem states that the kernel of the Lie algebroid Laplace operator on Lie algebroid positive line bundle-valued $(p,q)$-forms vanishes when $p+q$ is sufficiently large. The most difficult part of the proof of the generalized Kodaira vanishing theorem is the generalization of the K\"{a}hler identities to Lie algebroids. Secondly, we introduce Lie …

On The Hardness Of The Balanced Connected Subgraph Problem For Families Of Regular Graphs, Harsharaj Pathak

Theory & Applications of Graphs

The Balanced Connected Subgraph problem (BCS) was introduced by Bhore et al. In the BCS problem we are given a vertex-colored graph G = (V, E) where each vertex is colored “red” or “blue”. The goal is to find a maximum cardinality induced connected subgraph H of G such that H contains an equal number of red and blue vertices. This problem is known to be NP-hard for general graphs as well as many special classes of graphs. In this work we explore the time complexity of the BCS problem in case of regular graphs. We prove that the BCS …

The Vulnerabilities To The Rsa Algorithm And Future Alternative Algorithms To Improve Security, James Johnson

Cybersecurity Undergraduate Research Showcase

The RSA encryption algorithm has secured many large systems, including bank systems, data encryption in emails, several online transactions, etc. Benefiting from the use of asymmetric cryptography and properties of number theory, RSA was widely regarded as one of most difficult algorithms to decrypt without a key, especially since by brute force, breaking the algorithm would take thousands of years. However, in recent times, research has shown that RSA is getting closer to being efficiently decrypted classically, using algebraic methods, (fully cracked through limited bits) in which elliptic-curve cryptography has been thought of as the alternative that is stronger than …

Renormalized Stress-Energy Tensor For Scalar Fields In Hartle-Hawking, Boulware, And Unruh States In The Reissner-Nordström Spacetime, Julio Arrechea, Cormac Breen, Adrian Ottewill, Peter Taylor

Articles

In this paper, we consider a quantum scalar field propagating on the Reissner-Nordström black hole spacetime. We compute the renormalized stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh states. When the field is in the Hartle-Hawking state, we renormalize using the recently developed “extended coordinate” prescription. This method, which relies on Euclidean techniques, is very fast and accurate. Once, we have renormalized in the Hartle-Hawking state, we compute the stress-energy tensor in the Boulware and Unruh states by leveraging the fact that the difference between stress-energy tensors in different quantum states is already finite. We consider a …

A Review On Possible Physical Meaning Of Elastic-Electromagnetic Mathematical Equivalences, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

It is known, despite special theory of relativity has been widely accepted, in our recent draft submitted to this journal it is shown that some experiments have been carried out suggesting superluminal wave propagation, which make Minkowski lightcone not valid anymore. Therefore, it seems worth to reconsider the connection between elastic wave and electromagnetic wave equations, as in their early development. In this paper we will start with Maxwell-Dirac isomorphism, then we will find its connection with elastic wave equations.

Every Relu-Based Neural Network Can Be Described By A System Of Takagi-Sugeno Fuzzy Rules: A Theorem, Barnabas Bede, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

While modern deep-learning neural networks are very successful, sometimes they make mistakes, and since their results are "black boxes" -- no explanation is provided -- it is difficult to determine which recommendations are erroneous. It is therefore desirable to make the resulting computations explainable, i.e., to describe their results by using commonsense rules. In this paper, we use "fuzzy" techniques -- techniques developed by Lotfi Zadeh to deal with commonsense rules formulated by using imprecise ("fuzzy") words from natural language -- to show that such a rule-based representation is always possible. Our result does not yet provide the desired explainability, …

Smooth Non-Additive Integrals And Measures And Their Potential Applications, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we explain why non-additive integrals and measures are needed, how non-additive integrals and measures are related, how to use them in decision making, and how they can help in fundamental physics. These four topics are covered, correspondingly, in Sections 2-5 of this paper.