Mathematics Commons^™

Growth Mindset In The Mathematics Classroom: Studying The Effects Of A Growth Mindset Intervention On High School Students In A Geometry Classroom, Katelyn Strauss

Mathematics Graduate Theses

Having a growth mindset is crucial to being successful in a mathematics classroom. However, many students believe themselves to be either “mathematics people” or “not mathematics people”. When students believe they are not a mathematics person, they are far less likely to engage in material where they face struggles, and thus they miss out on valuable learning. A review of the literature has show that students have been able to shift their mindset from fixed to growth through a series of interventions. I used a unit in Geometry to see how a growth mindset intervention would affect the mindset of …

Dimension Of Subalgebras Of Fomin-Kirillov Algebras, Taro Ikeda, Sirous Homayouni

Annual Student Research Poster Session

One of the central open problems concerning the Fomin-Kirillov algebras was whether their dimension is finite or infinite. This question was recently resolved in one research by C. Barligea, where it was shown that FK(n) is infinite-dimensional for all n ≥ 6. In our work, we investigate the dimension of a certain subalgebra of FK(6).

(Si15-084) Application Of Differentiation Matrices Corresponding To Scaling And Wavelet Functions To Integral Equations, Viresh Kumar, Rakesh Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper, we have studied the technique by which a differentiation matrix corresponding to scaling and wavelet function is helpful in representing an integral equation in discrete form. In this technique, only finite times continuously differentiable scaling and wavelet functions were used for the differentiation matrix. This method explores the applications of compactly supported wavelets in discretization of Fredholm integral equation and provides us with a bridge for the solution of integral equations via compactly supported finitely differentiable wavelets.

(Si15-017) Modeling Construction Project Uncertainty Using Fuzzy Inference And Nature-Inspired Metaheuristic Knowledge-Based Algorithms, M. Kapoor, B. K. Pathak, R. Kumar

Applications and Applied Mathematics: An International Journal (AAM)

Construction projects are influenced by various uncertain factors, including supervisory knowledge, labor expertise, and weather conditions. These uncertain factors have linguistic properties that are challenging to quantify with the help of traditional set theory. To address this, the study applies fuzzy inference systems, specifically the Mamdani fuzzy inference system, to model and evaluate the impact of these uncertainties on construction projects. This fuzzy inference system provides a more nuanced understanding of these factors compared to traditional set theory methods. Experimental results indicate that uncertainties significantly impact construction projects. These findings establish a valuable framework for developing adaptive strategies, enhancing project …

(Si15-140) Designing Bayesian Double Sampling Plans Based On Zero Inflated Poisson Distribution, Priyadharshini R., Shalini K., Hemalatha R., Sangeetha S.

Applications and Applied Mathematics: An International Journal (AAM)

The implementation of attribute-based sampling inspection serves as a quality control technique used across numerous industries to evaluate items or workflow processes. When the data exhibits a substantial number of zero counts, the zero-inflated Poisson (ZIP) distribution serves as an effective model for accommodating this zero-inflation. Double sampling plan (DSP) is a quality check method where the decision to approve or decline a batch comes after examining two samples, providing more conclusive information compared to a single sample plan (SSP). In practice, effective decision-making regarding submitted lots considers both within-lot and between-lot variations, which can be addressed through the use …

(Si15-142) Selection Of Single Sampling Plans Based On Zero Inflated Binomial Distribution Using Cost Optimization, Sangeetha S., Shalini K., Hemalatha R., Priyadharshini R.

Applications and Applied Mathematics: An International Journal (AAM)

Economic design of sampling plans involves creating sampling plans that minimize the total cost associated with the inspection process while ensuring quality. It aims to address the quality risk concerns of both producer and consumer, ensuring product quality while minimizing inspection costs. This article’s objective is to design single sampling plans by attributes based on Zero-inflated Binomial (ZIB) distribution, using cost optimization principles by developing an economic model aimed at achieving optimal total cost by considering the Average Total Inspection (ATI). Numerical illustration is provided to illustrate the selection of single sampling plans under ZIB distribution that minimizes producer’s total …

(Si15-067) Ahp And Moora Decision Making Methods On Bipolar Fuzzy Sets, S. Anita Shanthi, R. Preethi

Applications and Applied Mathematics: An International Journal (AAM)

Decision making, in the present contemporary world, has been inherently complicated. Nowadays, the major challenge is the selection of an appropriate option. The arrival of numerous brands and models makes a purchase challenging. Hence, in this paper, four different models of the same branded laptops are considered, for the selection of an appropriate option, using the Analytic Hierarchy Process (AHP) and Multi-Objective Optimization on the basis of Ratio Analysis (MOORA), with bipolar fuzzy sets, which help decision makers arrive at the most logical choice based on their preferences. The bipolar fuzzy Analytic Hierarchy Process efficaciously supports decision making in cases …

(Si15-022) Five Efficient Cryptography Authentication Schemes With Functional Relation On General Spaces, L. Sreenivasulu Reddy, S. Lakshmisri

Applications and Applied Mathematics: An International Journal (AAM)

This work addresses the growing demand for diversification in cryptographic schemes to secure communication. This work proposes a novel suite of algorithms, including two block ciphers (TPBlock and TAP-Block), two stream ciphers (TP-Stream and TAP-Stream), and a zero-knowledge proof scheme (F-zero knowledge proof). All schemes leverage functional relations defined over the real number space with a dimension greater than one for encryption, decryption, and key generation, offering an alternative to the number-theoretical aspects and algebraic structures commonly used in existing schemes. The main goal of this work is to introduce and propose these five novel cryptographic schemes to provide authentication …

(Si15-010) On Perturbations Of Gabor Frames, Jamkhongam Touthang

Applications and Applied Mathematics: An International Journal (AAM)

Stability plays a crucial role in frame theory and its applications. The present paper studies the interaction between Gabor frames and perturbations, presenting perturbation results related to small changes of the frame parameters and the window functions both in regular and irregular settings. Examples are provided for illustration. Additionally, the paper briefly discusses algorithms pertinent to Gabor frames under perturbations and highlights challenging areas in the field.

(Si15-064) Permutation Pentanomials Over Finite Fields With Even Characteristic, Shalini Gupta, Sushil Kumar, Ashima .

Applications and Applied Mathematics: An International Journal (AAM)

Permutation polynomials over finite fields constitute an active area of research and play an important role in diverse domains, including finite geometry, combinatorial design, coding theory, and cryptography. The study of these polynomials has a long history, and many results have been obtained in recent years. This paper presents new classes of permutation pentanomials based on permutation over the unit circle of finite fields with even characteristic that contribute to the theoretical development of permutation polynomials.

(Si15-120) Exploring Fractional Difference Equations And Their Applications With Mahgoub-Transform, Tharmalingam Gunasekar, Periyasamy Udhayasankar, Prabakaran Raghavendran, Kamalendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

We discuss the introduction and study of the nabla discrete Mahgoub transform along with its defining properties. The transform of fractional sums and fractional differences are derived, demonstrating the applicability of the transform from the computational viewpoint. Employing the transform, fractional difference equations with initial value problems are solved, thereby enhancing the knowledge of their closed forms. As a side-effect of the Mahgoub-transforms, an attractive connection is established, showing that the discrete Mittag-Leffler function acts as the eigenfunction for the Caputo-type fractional difference operator nabla. These results strengthen the core basis for fractional calculus and herald industrial applications in various …

Coefficients Of The Characteristic Polynomial Of A Hypergraph And Their Combinatorial Properties, Utku Okur

Theses and Dissertations

We investigate the combinatorial properties of the characteristic polynomial $\phi_\mathcal{H}\ev{t}$ of a hypergraph $\mathcal{H}$, in particular, its coefficients. Due to a classical result of Jacobi, the generating function of closed walks at a vertex $u$ in a graph $G$ is determined by the rational function $\phi_{G-u}(t) / \phi_G(t)$. The connection between closed walks of $G$ and its characteristic polynomial has a known elegant proof via an application of Viennot's Heaps of Pieces framework, where cycles are taken as pieces and the concurrence relation is sharing a vertex. Here, we prove a bijection between heaps with a unique maximal piece containing …

Investigating The Influence Of Instructional Strategies On The Development Of Procedural And Conceptual Knowledge In Advanced Algebra Ii Students, Maura Frances Yinger

Theses and Dissertations

This mixed-methods action research study investigated the influence of instructional strategies shown to improve students’ procedural and conceptual understanding in a rational expressions and equations unit in Advanced Algebra II. The instructional strategies used in the study include comparing, self-explaining, and exploring before instruction. The students (N=27) completed a pre-test and a post-test, both of which were followed by questions asking students to justify their responses on two questions. All students also responded to six digital self-explanation journal prompts. Randomly selected students were placed into three homogenous groups to participate in performance task observations. Analysis of the data …

Art Forms: Born Out Of Necessity, Urmi Duttagupta

Publications and Research

This collection of artworks expresses the artist’s profound passion for mathematics and life’s complex balance. As a female mathematician, she uses artistic expression and intricate patterns to evoke mathematical beauty and feminine strength, celebrating the presence and resilience of women in mathematics.

Memoir On A General Property Of A Very Extensive Class Of Transcendental Functions, Niels Henrik Abel 1802--1829, John Little

Mathematics and Computer Science Department Faculty Scholarship

We present this new commentary and translation anticipating the 200th anniversary of the work, commonly known as Abel's ``Paris memoir.'' This is recognized today as one of Abel's most original and influential works. It is significant mostly because it marked the first appearance of a form of a result in the theory of algebraic curves and Riemann surfaces that has come to be known as ``Abel's theorem.'' However, Abel's original understanding of the meaning and context of his result was quite different from the typical modern formulation and the development of the modern understanding has been a long and tortuous …

Packing Independent Cliques Into Planar Graphs, Csaba Biró, Gabriel Collado, Oscar Zamora

Theory & Applications of Graphs

The indeque number of a graph is largest set of vertices that induce an independent set of cliques. We study the extremal value of this parameter for the class and subclasses of planar graphs, most notably for forests and graphs of pathwidth at most $2$.

The Calvin University Math Department History 1920-2020, Michael Stob

University Histories

No abstract provided.

Energy Statistic-Based Goodness-Of-Fit Test For The Lindley Distribution With Application To Lifetime Data, Joseph Njuki, Ryan Avallone

Mathematics and Statistics

In this article, we propose a goodness-of-fit test for a one-parameter Lindley distribution based on energy statistics. The Lindley distribution has been widely used in reliability studies and survival analysis, especially in applied sciences. The proposed test procedure is simple and more powerful against general alternatives. Under different settings, Monte Carlo simulations show that the proposed test is able to be well controlled for any given nominal levels. In terms of power, the proposed test outperforms other existing similar methods in different settings. We then apply the proposed test to real-life datasets to demonstrate its competitiveness and usefulness.

This article …

Fourier Analyses Of Optical Profilometry As An Inferential Measurement For Impact Coverage., Langdon Feltner, Paul Mort

15th International Conference on Shot Peening

A critical consideration in peening process design is achieving sufficient impact coverage. Conventional methods for assessing coverage rely on manual inspection, which is time-consuming and poorly suited for automated control. In this work, we investigate the use of frequency-domain analysis to quantify surface modification in peened samples using optical profilometry (OP) data. Three-dimensional surface maps of Almen strips were acquired using a high-resolution OP system and analyzed via fast Fourier transform (FFT) to compute spatial power spectral densities (PSDs). PSD maps and radially averaged profiles reveal consistent amplification of harmonic components similar to the nominal particle size, with increasing intensity …

Constructions Of Compact Dupin Hypersurfaces With Non-Constant Lie Curvatures, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

A hypersurface M in the unit sphere Sⁿ ⊂ Rⁿ⁺¹ is Dupin if along each curvature surface of M, the corresponding principal curvature is constant. If the number g of distinct principal curvatures is constant on M, then M is called proper Dupin. In this expository paper, we give a detailed description of two important types of constructions of compact proper Dupin hypersurfaces in Sⁿ. One construction was published in 1989 by Pinkall and Thorbergsson [35], and the second was published in 1989 by Miyaoka and Ozawa [26]. Both types of examples have the …