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Articles 31 - 60 of 134
Full-Text Articles in Mathematics
Design Of Strips With Geometry Shapes And Mathematical Analysis, Somia Benali
Design Of Strips With Geometry Shapes And Mathematical Analysis, Somia Benali
Theses, Dissertations and Culminating Projects
In this research, I investigate different methods to create geometric designs for textile strips and study the geometric properties of the involved shapes. I develop three designs that contain circles, squares, and golden spiral pieces with repeating patterns and certain tangencies. One interesting part of the work is to find the tangent points and to calculate the areas of the regions to which different colors maybe assigned. The main figure for Design I is a circle inscribed in a square and that for Design II is a circle inscribed in an isosceles triangle. The last design integrates Golden Spirals into …
A Network Thermodynamic Game-Theoretic Approach To Modeling Amyloid-Beta Aggregation Along Competing Pathways, Joseph Pateras
A Network Thermodynamic Game-Theoretic Approach To Modeling Amyloid-Beta Aggregation Along Competing Pathways, Joseph Pateras
Theses, Dissertations and Culminating Projects
The formation of large AB fibril plaques in the human brain is considered important to the pathogenesis of Alzheimer's disease (AD), as protein aggregation elsewhere in the body underpins many human ailments. Now however, low-molecular weight intermediate AB oligomers, more than large fibrils, are thought to be a primary precursor in early AD etiology. The main obstacle in the study of AD is the lack of understanding we have pertaining to the evolution of the disease in a living brain. For this reason, a thorough study of AB aggregation begs exploration. Prior conjectures and new experiments emphasize the interaction between …
Video Case Materials And The Development Of Collective Professional Knowledge, Victoria D. Bonaccorso
Video Case Materials And The Development Of Collective Professional Knowledge, Victoria D. Bonaccorso
Theses, Dissertations and Culminating Projects
The dynamic nature of teaching means that teachers are making in-the-moment decisions on a daily basis. Video case study professional development can be used as a way to provide teachers an opportunity to analyze real teaching scenarios to prepare to make these decisions in practice. While work has been done to reveal the effectiveness of using case studies as a teaching tool, there has not been research conducted to determine if video case studies can be used to foster the development of collective professional knowledge. This study utilizes a particular professional development model using video case studies grounded in the …
Semi-Automated Image Segmentation And Synthesis Of Virtual Samples Using Generative Adversarial Networks And Fuzzy Sets, Reza Vafaee
Theses, Dissertations and Culminating Projects
Data-driven modeling has gained a lot of attention over the past few years. In most cases, such models use a big collection of inputs and the corresponding outputs to find the pattern in data. Prerequisite for applying these models is the availability of a large collection of data. Data-driven modeling has been employed to accomplish many tasks over the years. However, due to the lack of clinical data, the advancement of data-driven modeling in medical imaging has been relatively limited, mainly due to challenges involved with medical data collection and analysis. This is particularly true in ultrasound imaging for assessing …
Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya
Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya
Department of Mathematics Facuty Scholarship and Creative Works
Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way to arrange information so …
Storage Management Strategy In Mobile Phones For Photo Crowdsensing, En Wang, Zhengdao Qu, Xinyao Liang, Xiangyu Meng, Yongjian Yang, Dawei Li, Weibin Meng
Storage Management Strategy In Mobile Phones For Photo Crowdsensing, En Wang, Zhengdao Qu, Xinyao Liang, Xiangyu Meng, Yongjian Yang, Dawei Li, Weibin Meng
Department of Computer Science Faculty Scholarship and Creative Works
In mobile crowdsensing, some users jointly finish a sensing task through the sensors equipped in their intelligent terminals. In particular, the photo crowdsensing based on Mobile Edge Computing (MEC) collects pictures for some specific targets or events and uploads them to nearby edge servers, which leads to richer data content and more efficient data storage compared with the common mobile crowdsensing; hence, it has attracted an important amount of attention recently. However, the mobile users prefer uploading the photos through Wifi APs (PoIs) rather than cellular networks. Therefore, photos stored in mobile phones are exchanged among users, in order to …
Fluids In Music: The Mathematics Of Pan’S Flutes, Bogdan Nita, Sajan Ramanathan
Fluids In Music: The Mathematics Of Pan’S Flutes, Bogdan Nita, Sajan Ramanathan
Department of Mathematics Facuty Scholarship and Creative Works
We discuss the mathematics behind the Pan’s flute. We analyze how the sound is created, the relationship between the notes that the pipes produce, their frequencies and the length of the pipes. We find an equation which models the curve that appears at the bottom of any Pan’s flute due to the different pipe lengths.
Examining Students’ Covariational Reasoning Through Mathematical Modeling Activities Embedded In The Context Of The Greenhouse Effect, Debasmita Basu
Examining Students’ Covariational Reasoning Through Mathematical Modeling Activities Embedded In The Context Of The Greenhouse Effect, Debasmita Basu
Theses, Dissertations and Culminating Projects
The greenhouse effect is one of the most pressing environmental as well as social issues of the present age. In news media and weather reports, most of the essential information about the phenomenon is expressed in forms of graphs and pictures. However, the interpretation of such graphs is challenging for students; they often focus on the shape of the graphs, overlooking the covariational relationships between the concerned quantities. Building on the framework of critical mathematics literacy and social justice mathematics, in this study I aimed to explore the power of dynamic mathematical modeling activities for engaging students in covariational reasoning …
One Teacher's Transformation Of Practice Through The Development Of Covariational Thinking And Reasoning In Algebra : A Self-Study, Jacqueline Dauplaise
One Teacher's Transformation Of Practice Through The Development Of Covariational Thinking And Reasoning In Algebra : A Self-Study, Jacqueline Dauplaise
Theses, Dissertations and Culminating Projects
CCSSM (2010) describes quantitative reasoning as expertise that mathematics educators should seek to develop in their students. Researchers must then understand how to develop covariational reasoning. The problem is that researchers draw from students’ dialogue as the data for understanding quantitative relationships. As a result, the researcher can only conceive the students’ reasoning. The objective of using the self-study research methodology is to examine and improve existing teaching practices. To improve my practice, I reflected upon the implementation of my algebra curriculum through a hermeneutics cycle of my personal history and living educational theory. The critical friend provoked through dialogues …
Statistical Modeling Of Count Data With Over-Dispersion Or Zero-Inflation Problems, Chengxin Zhang
Statistical Modeling Of Count Data With Over-Dispersion Or Zero-Inflation Problems, Chengxin Zhang
Theses, Dissertations and Culminating Projects
In this study, we will analyze a supply retailing company’s data to model the relationship between their customer’s past purchase behavior to predict their future online purchase behavior. The data was divided into time periods from 2016: P1-P6(January 31st to July 30th) and P7(July 31st to August 27th ). Based on customer’s past purchase information from the P1-P6 period, such as money spent, number of cart additions, transactions type, number of unique purchase dates, number of unique purchase skus, number of page views, number browse dates, company size, and number of products purchased, we aim to find if these information …
Sampling Studies For Longitudinal Functional Data, Toni Jassel
Sampling Studies For Longitudinal Functional Data, Toni Jassel
Theses, Dissertations and Culminating Projects
We study the data setting consisting of functional data sets repeatedly observed over time. The focus is on the dynamic prediction of the future trajectory for a subject. Regression methods based on dynamic functional models are used for dynamic prediction of individual trajectories. We propose strategies for the selection of the study sampling design in the context of longitudinal functional data. An application to simulated child growth data is presented. The height-for-age z-score (HAZ) was the response variable in the functional dynamic models for prediction. The intent was to recommend four months for removal in our initial historic data set. …
Conventions, Habits, And U.S. Teachers’ Meanings For Graphs, Kevin C. Moore, Jason Silverman, Teo Paoletti, Dave Liss, Stacy Musgrave
Conventions, Habits, And U.S. Teachers’ Meanings For Graphs, Kevin C. Moore, Jason Silverman, Teo Paoletti, Dave Liss, Stacy Musgrave
Department of Mathematics Facuty Scholarship and Creative Works
In this paper, we use relevant literature and data to motivate a more detailed look into relationships between what we perceive to be conventions common to United States (U.S.) school mathematics and individuals’ meanings for graphs and related topics. Specifically, we draw on data from pre-service (PST) and in-service (IST) teachers to characterize such relationships. We use PSTs’ responses during clinical interviews to illustrate three themes: (a) some PSTs’ responses implied practices we perceive to be conventions of U.S. school mathematics were instead inherent aspects of PSTs’ meanings; (b) some PSTs’ responses implied they understood certain practices in U.S. school …
Pre-Service Teachers’ Figurative And Operative Graphing Actions, Kevin C. Moore, Irma E. Stevens, Teo Paoletti, Natalie L.F. Hobson, Biyao Liang
Pre-Service Teachers’ Figurative And Operative Graphing Actions, Kevin C. Moore, Irma E. Stevens, Teo Paoletti, Natalie L.F. Hobson, Biyao Liang
Department of Mathematics Facuty Scholarship and Creative Works
We report on semi-structured clinical interviews to describe U.S. pre-service secondary mathematics teachers’ graphing meanings. Our primary goal is to draw on Piagetian notions of figurative and operative thought to identify marked differences in the students’ meanings. Namely, we illustrate students’ meanings dominated by fragments of sensorimotor experience and compare those with students’ meanings dominated by the coordination of mental actions in the form of covarying quantities. Our findings suggest students’ meanings that foreground operative aspects of thought are more generative with respect to graphing. Our findings also indicate that students can encounter perturbations due to potential incompatibilities between figurative …
Assimilating Mathematical Thinking To The Learning Of Shadows, Taheeda Shwana Street-Conaway
Assimilating Mathematical Thinking To The Learning Of Shadows, Taheeda Shwana Street-Conaway
Theses, Dissertations and Culminating Projects
This study focuses on a teaching experiment with 33 six-graders in a Kearny public school in Hudson County, New Jersey, during the 2017-2018 academic year. More specifically, this study explored a) the types of tasks and tools that can be used to develop students’ covariational and correspondence reasoning in learning about shadows and b) the nature of students’ reasoning about covariation and correspondence relationships as students engage in the use of tools and tasks. The results showed that the simulation and the tasks I designed had the students engaged in the learning process. Students were able to reason about the …
Cause And Consequence Of Aβ – Lipid Interactions In Alzheimer Disease Pathogenesis, Vijayaraghavan Rangachari, Dexter N. Dean, Pratip Rana, Ashuwin Vaidya, Preetam Ghosh
Cause And Consequence Of Aβ – Lipid Interactions In Alzheimer Disease Pathogenesis, Vijayaraghavan Rangachari, Dexter N. Dean, Pratip Rana, Ashuwin Vaidya, Preetam Ghosh
Department of Mathematics Facuty Scholarship and Creative Works
Self-templating propagation of protein aggregate conformations is increasingly becoming a significant factor in many neurological diseases. In Alzheimer disease (AD), intrinsically disordered amyloid-β (Aβ) peptides undergo aggregation that is sensitive to environmental conditions. High-molecular weight aggregates of Aβ that form insoluble fibrils are deposited as senile plaques in AD brains. However, low-molecular weight aggregates called soluble oligomers are known to be the primary toxic agents responsible for neuronal dysfunction. The aggregation process is highly stochastic involving both homotypic (Aβ-Aβ) and heterotypic (Aβ with interacting partners) interactions. Two of the important members of interacting partners are membrane lipids and surfactants, to …
An Enthalpy Model For The Dynamics Of A Deltaic System Under Base-Level Change, William Anderson
An Enthalpy Model For The Dynamics Of A Deltaic System Under Base-Level Change, William Anderson
Theses, Dissertations and Culminating Projects
Fluvial deltas are composites of two primary sedimentary environments: a depositional fluvial region and an offshore region. The fluvial region is defined by two geomorphic moving boundaries: an alluvial-bedrock transition (ABT), which separates the sediment prism from the non-erodible bedrock basement, and the shoreline (SH), where the delta meets the ocean. The trajectories of these boundaries in time and space define the evolution of the shape of the sedimentary prism, and are often used as stratigraphic indicators, particularly in seismic studies, of changes in relative sea level and the identification of stratigraphic sequences. In order to better understand the relative …
Interlace Polynomials Of Cycles With One Additional Chord, Jhonny Almeida
Interlace Polynomials Of Cycles With One Additional Chord, Jhonny Almeida
Theses, Dissertations and Culminating Projects
In this research, we investigate the interlace polynomial of a certain type of cycle graph with additional edges, called chords. We focus on the graphs resulted by adding one chord to cycle graphs. Consider the cycle Cn with n edges. When adding one chord to it, two sub-cycles were created which share one edge. If the length of one sub-cycle is r (r ≥ 3), then the other length is n - r+2. All cycles with one chord resulting in a sub-cycle of length r, where r ≤ n - r + 2, are isomorphic, denoted by J(n,r). When n …
A Greedy Algorithm For Finding A Large 2-Matching On A Random Cubic Graph, Deepak Bal, Patrick Bennett, Tom Bohman, Alan Frieze
A Greedy Algorithm For Finding A Large 2-Matching On A Random Cubic Graph, Deepak Bal, Patrick Bennett, Tom Bohman, Alan Frieze
Department of Mathematics Facuty Scholarship and Creative Works
A 2-matching of a graph G is a spanning subgraph with maximum degree two. The size of a 2-matching U is the number of edges in U and this is at least n-k(U) where n is the number of vertices of G and κ denotes the number of components. In this article, we analyze the performance of a greedy algorithm 2greedy for finding a large 2-matching on a random 3-regular graph. We prove that with high probability, the algorithm outputs a 2-matching U with k(U)=Θ(n1/5).
Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi
Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi
Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works
We investigate masked financial instability caused by wealth inequality. When an economic sector is decomposed into two subsectors that possess a severe wealth inequality, the sector in entirety can look financially stable while the two subsectors possess extreme financially instabilities of opposite nature, one from excessive equity, the other from lack thereof. The unstable subsector can result in further financial distress and even trigger a financial crisis. The market instability indicator, an early warning system derived from dynamical systems applied to agent-based models, is used to analyze the subsectoral financial instabilities. Detailed mathematical analysis is provided to explain what financial …
Teacher Questioning And Invitations To Participate In Advanced Mathematics Lectures, Teo Paoletti, Victoria Krupnik, Dimitrios Papadopoulos, Joseph Olsen, Tim Fukawa-Connelly, Keith Weber
Teacher Questioning And Invitations To Participate In Advanced Mathematics Lectures, Teo Paoletti, Victoria Krupnik, Dimitrios Papadopoulos, Joseph Olsen, Tim Fukawa-Connelly, Keith Weber
Department of Mathematics Facuty Scholarship and Creative Works
In this study, we were interested in exploring the extent to which advanced mathematics lecturers provide students opportunities to play a role in considering or generating course content. To do this, we examined the questioning practices of 11 lecturers who taught advanced mathematics courses at the university level. Because we are unaware of other studies examining advanced mathematics lecturers’ questioning, we first analyzed the data using an open coding scheme to categorize the types of content lecturers solicited and the opportunities they provided students to participate in generating course content. In a second round of analysis, we examined the extent …
Adjunct Instructors’ Opportunities For Learning Through Engagement With A Research-Based Mathematics Curriculum, Zareen Gul Rahman
Adjunct Instructors’ Opportunities For Learning Through Engagement With A Research-Based Mathematics Curriculum, Zareen Gul Rahman
Theses, Dissertations and Culminating Projects
There is a growing need to retain students in STEM fields and majors in the U.S. Improving students’ experience in early mathematics courses like Precalculus can influence students’ decisions to remain in STEM fields. Teachers can play an important role in providing effective learning experiences to the students. Supporting teachers and providing professional development can help the teachers in facilitating student learning. When it comes to implementing research-based mathematics curricula, teachers are key players in making the curriculum come alive inside their classrooms. The challenges that teachers face when implementing a research-based mathematics curriculum can provide opportunities for their own …
The Dispersion Process For Particles On Graphs, Adam Cartisano
The Dispersion Process For Particles On Graphs, Adam Cartisano
Theses, Dissertations and Culminating Projects
In this thesis, we study a process called Dispersion, in which M particles are dispersed among the vertices of a graph G. All particles initially occupy a single vertex called the origin vertex. At each discrete time step, all particles which share a vertex with at least one other, move to a randomly (though not necessarily uniformly) chosen neighbor of the currently occupied vertex. The process ends when each vertex is occupied by at most one particle. We will explore various aspects of the Dispersion process. One of these is the expected time to completion, E[TDisp] for 3 …
Candy Sharing And Chip Firing Games On Graphs, Joseph Degaetani
Candy Sharing And Chip Firing Games On Graphs, Joseph Degaetani
Theses, Dissertations and Culminating Projects
The Candy Game begins with a finite number of players sitting in a circle, each with an initial amount of candy. At each time step, each player passes half of their pile to the player on their left (with odd sized stacks receiving an extra piece of candy). The original question was whether every initial distribution of candy results in every player holding the same number of pieces after a finite number of turns. For arbitrary initial distributions, we prove asymptotically tight bounds on the final amount of candy. The diffusion chip firing game assigns integral chip amounts to each …
Gravitational-Wave Memory From Black Hole And Neutron Star Mergers, Matthew Karlson
Gravitational-Wave Memory From Black Hole And Neutron Star Mergers, Matthew Karlson
Theses, Dissertations and Culminating Projects
The detection of gravitational waves from binary black hole and binary neutron star mergers has ushered in a new age of observational astronomy. Anticipation of detection from these coalescing compact binaries has led to the development of models for comparison using analytical and numerical techniques. Typically, these methods model gravitational-wave signals as small oscillations that grow over time, reach some maximum value, and eventually decay to zero. However, these models are incomplete: compact binaries can emit gravitational waves that decay to a non-zero value. This phenomenon is known as the gravitational-wave memory. In particular, the signal from compact binaries displays …
Magic Squares Of Cubes Modulo A Prime Number, Yevgeniy Sokolovskiy
Magic Squares Of Cubes Modulo A Prime Number, Yevgeniy Sokolovskiy
Theses, Dissertations and Culminating Projects
This work is dedicated to the properties of the 3 × 3 magic squares of cubes modulo a prime number. Its central concept is the number of distinct entries of these squares and the properties associated with this number. We call this number the degree of a magic square. The necessary conditions for the magic square of cubes with degrees 3, 5, 7, and 9 are examined. It was established that there are infinitely many primes for which magic squares of cubes with degrees 3, 5, 7, and 9 exist. I apply n-tuples of consecutive cubic residues to prove that …
Magic Squares Of Squares Of Order Three Over Finite Fields, Giancarlo Labruna
Magic Squares Of Squares Of Order Three Over Finite Fields, Giancarlo Labruna
Theses, Dissertations and Culminating Projects
A magic square M over an integral domain D is a 3 x 3 matrix with entries from D such that the elements from each row, column, and diagonal add to the same sum. If all the entries in M are perfect squares in D, we call M a magic square of squares over D. Martin LaBar raised an open question in 1984, which states, “Is there a magic square of squares over the ring Z of the integers which has all the nine entries distinct?” We approach to answering a similar question in case D is a finite field. …
Simplicity And Sustainability: Pointers From Ethics And Science, Mehrdad Massoudi, Ashuwin Vaidya
Simplicity And Sustainability: Pointers From Ethics And Science, Mehrdad Massoudi, Ashuwin Vaidya
Department of Mathematics Facuty Scholarship and Creative Works
In this paper, we explore the notion of simplicity. We use definitions of simplicity proposed by philosophers, scientists, and economists. In an age when the rapidly growing human population faces an equally rapidly declining energy/material resources, there is an urgent need to consider various notions of simplicity, collective and individual, which we believe to be a sensible path to restore our planet to a reasonable state of health. Following the logic of mathematicians and physicists, we suggest that simplicity can be related to sustainability. Our efforts must therefore not be spent so much in pursuit of growth but in achieving …
Simplicity And Sustainability: Pointers From Ethics And Science, Mehrdad Massoudi, Ashwin Vaidya
Simplicity And Sustainability: Pointers From Ethics And Science, Mehrdad Massoudi, Ashwin Vaidya
Department of Mathematics Facuty Scholarship and Creative Works
In this paper, we explore the notion of simplicity. We use definitions of simplicity proposed by philosophers, scientists, and economists. In an age when the rapidly growing human population faces an equally rapidly declining energy/material resources, there is an urgent need to consider various notions of simplicity, collective and individual, which we believe to be a sensible path to restore our planet to a reasonable state of health. Following the logic of mathematicians and physicists, we suggest that simplicity can be related to sustainability. Our efforts must therefore not be spent so much in pursuit of growth but in achieving …
Minimizing The Number Of Independent Sets In Triangle-Free Regular Graphs, Jonathan Cutler, A. J. Radcliffe
Minimizing The Number Of Independent Sets In Triangle-Free Regular Graphs, Jonathan Cutler, A. J. Radcliffe
Department of Mathematics Facuty Scholarship and Creative Works
Recently, Davies, Jenssen, Perkins, and Roberts gave a very nice proof of the result (due, in various parts, to Kahn, Galvin–Tetali, and Zhao) that the independence polynomial of a d-regular graph is maximized by disjoint copies of Kd,d. Their proof uses linear programming bounds on the distribution of a cleverly chosen random variable. In this paper, we use this method to give lower bounds on the independence polynomial of regular graphs. We also give a new bound on the number of independent sets in triangle-free cubic graphs.
Inverse Function: Pre-Service Teachers’ Techniques And Meanings, Teo Paoletti, Irma E. Stevens, Natalie L.F. Hobson, Kevin C. Moore, Kevin R. Laforest
Inverse Function: Pre-Service Teachers’ Techniques And Meanings, Teo Paoletti, Irma E. Stevens, Natalie L.F. Hobson, Kevin C. Moore, Kevin R. Laforest
Department of Mathematics Facuty Scholarship and Creative Works
Researchers have argued teachers and students are not developing connected meanings for function inverse, thus calling for a closer examination of teachers’ and students’ inverse function meanings. Responding to this call, we characterize 25 pre-service teachers’ inverse function meanings as inferred from our analysis of clinical interviews. After summarizing relevant research, we describe the methodology and theoretical framework we used to interpret the pre-service teachers’ activities. We then present data highlighting the techniques the pre-service teachers used when responding to tasks that involved analytical and graphical representations of functions and inverse functions in both decontextualized and contextualized situations and discuss …