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The Independence Polynomial Of A Graph At −1, Phoebe Rose Zielonka

Theses, Dissertations and Culminating Projects

No abstract provided.

Curriculum Connectivity In Montclair State University’S Undergraduate Mathematics Program, Ana G. Da Silva Jesus

Theses, Dissertations and Culminating Projects

According to Piaget’s cognitive development theory and the constructivism learning theory of education, real learning occurs when students establish long term connections between disciplines by either adapting or redefining previously acquired knowledge. These ideologies have important teaching and learning implications that directly influence curriculum development and the design of a course of study. This thesis explores the interconnectedness of the subjects required for the successful completion of an undergraduate math program at Montclair State University. More specifically, it models students’ unique connections through a learning network and investigates the correlation between the interconnectivity of subjects and students’ overall performance. Results …

The Full Degree Spanning Tree Problem, Sarah Acquaviva

Theses, Dissertations and Culminating Projects

Given a graph G, we study the problem of finding a spanning tree T that maximizes the number of vertices of full degree; that is, the number of vertices whose degree in T equals its degree in G. We prove a few general bounds and then analyze this parameter on various classes of graphs including grid graphs, hypercubes, and random regular graphs. We also explore a related problem that focuses on maximizing the number of leaves in a spanning tree of a graph.

Object Detection And Image Categorization By Transferring Commonsense Knowledge With Premises And Quantifiers, Irina Chernyavsky

Theses, Dissertations and Culminating Projects

Domestic, or household robots, are autonomous robots designed to make our home-life easier by performing chores and mundane tasks such as cleaning, or cooking. Currently domestic robots are specialized to complete a specific task and, therefore, are confined by factors such as mobility, size, and complexity. With the fast development of computer vision and robotics, the need for more compact, advanced and multi-task robots has emerged. Therefore, the robot needs to be multi-functional, able to discern the environment and the tasks. The aim of this paper is to categorize images in domestic robots as relevant to the culinary, laundry, vacuum …

Investigating Elementary School Students’ Reasoning About Dynamic Angles, Erell Germia

Theses, Dissertations and Culminating Projects

Angle measurement is a significant topic in almost all areas of mathematics learning and also in many disciplines outside mathematics education, such as engineering and architecture. According to the literature, there are three common conceptions of angles – as union of rays, rotations, and wedges. Researchers argued that students must consider these three angle concepts together to construct a meaningful understanding of angles. However, the curriculum standards for mathematics often present these angle conceptions separately to students, probably resulting in a fragmented understanding of the angle concept. In addition to this problem, the research literature documents multiple alternative conceptions that …

Using Teacher Noticing And Video-Mediated Professional Learning To Develop Preservice Teachers’ Knowledge For Teaching The Derivative, Alfred M. Limbere

Theses, Dissertations and Culminating Projects

This study investigated how problem-solving videos can be used in video-mediated professional learning to support secondary preservice mathematics teachers (PMTs) in developing teacher knowledge for noticing student thinking in the context of the derivative concept in calculus. A model of the trajectory of PMTs’ noticing was constructed as six PMTs viewed and analyzed videos of students’ problem solving. At the same time, the nature of video-mediated interactions that were found to be productive in supporting this knowledge development was examined. A design experiment was used as the research methodology. Data was collected from video recordings of eight semi-structured teaching episodes …

Independent Dominating Sets In Unicyclic Graphs, Rachel Lopez

Theses, Dissertations and Culminating Projects

Wilf found the maximum number of independent dominating sets of a tree using algebraic methods, while Sagan gave an elementary proof. In this thesis, we maximize the number of independent dominating sets of unicyclic graphs, giving a new proof of a result of Jou and Chang. In our proof, we are able to reduce the problem to finding independent dominating sets of single-legged caterpillar graphs. We also study the number of single-legged caterpillar graphs, both oriented and unoriented, which are related to the Fibonacci Sequence. Finally, this thesis also examines the domination ratio in unicyclic graphs. The domination ratio is …

Magic Squares Of Squares Of Order 5 Modulo A Prime Number, Imani L. Mosquera

Theses, Dissertations and Culminating Projects

In this paper, I examine magic squares of squares (MSS) of order 5 over Zp where p is a prime number. The first approach to the problem is to find how many distinct elements an MSS may have (called the degree of the MSS). In the next step, I study the relationship between the magic sum and the center entry of any MSS. In order to develop construction methods and configurations for magic squares of squares of order 5 with desired degrees, I study Pythagorean triples and sequences of consecutive quadratic residues modulo p. Properties of these sequences are provided …

A Network-Based Analysis Of Student Learning Trajectories And Andragogical Design, John Kerry O’Meara

Theses, Dissertations and Culminating Projects

The core goal of this thesis project is to formalize the complex system that exists naturally in a formal classroom environment. The three factors that are considered in this study are the roles of the student, the roles of the teacher, and the respective environments from which these members arise and how these act as determinants of curriculum development and design. At the curricular scale, educational practices should be treated as a complex system composed of various inherently connected concepts and exchanges of ideas and ways of knowing. This synthesis of previous work and ongoing research efforts employs a network …

Strict Prime-Intersective Polynomials For A Fixed Prime Number, Rob Rexler Baello

Theses, Dissertations and Culminating Projects

In this thesis, we examine intersective polynomials, which are polynomials with integer coefficients that have a root modulo any positive integer greater than 1. For any prime number p, a p-intersective polynomial is a polynomial with integer coefficients which has a root in Zp. We define a special type of p-intersective polynomial called strict p-intersective polynomial that can be factored as the product of a p-intersective polynomial and an irreducible polynomial mod p. The main results include methods of construction of strict p-intersective polynomials for certain prime numbers p and enumeration of such polynomials of certain degrees.

Chapter 1 gives …

The Independence Polynomial Of A Graph At −1, Kyle Robbins

Theses, Dissertations and Culminating Projects

No abstract provided.

Interlace Polynomials Of Certain Graphs, Cheyenne Petzold

Theses, Dissertations and Culminating Projects

In this research, we investigated the interlace polynomials of a shell graph as well as other related graphs. A shell graph, Tn is constructed by adding edges to a cycle graph such that all vertices are adjacent to one vertex. The main results of this thesis include iterative and explicit formulas for the interlace polynomial of a shell graph, denoted q(Tn; x). A linear algebra application using the adjacency matrices of the chosen graphs is also explored.

Secondary Teachers’ Noticing Of Students’ Mathematical Thinking As They Participate In A Professional Development Program Centered On Task-Based Student Interviews, Gurkan Kose

Theses, Dissertations and Culminating Projects

Teacher’s noticing of students’ mathematical thinking has been an important focus of research in the past two decades (e.g., Jacobs et al., 2010; Sherin et al., 2011). Noticing matters, but it is not an end in itself (Schoenfeld, 2011). It is operationalized within the context of teachers’ dispositions and knowledge which shape decisions teachers make while responding to student thinking and planning the next instructional steps. In order for teachers to adapt productive beliefs about how children learn and shift to student-centered instruction, they need to acknowledge the importance of understanding students' existing conceptions of mathematical ideas (Carpenter & Lehrer, …

Fostering Mathematical Creativity Among Middle School Mathematics Teachers, Ceire H. Monahan

Theses, Dissertations and Culminating Projects

The purpose of this research was to understand in-service teachers’ experiences with and ideas about mathematical creativity after participating in a targeted professional development program. The professional development program encouraged participants to think creatively and foster students’ creativity. In this study I present the results from the main unit of analysis, 12 participants in a professional development program, along with a deep analysis of three exemplar teachers from each of the identified groups, adherence to traditional teaching practices (traditional), appreciation for teaching for creativity (creative but hesitant), and teaching for creativity (creative). The findings of this study highlight the combination …

Bipartite, Size, And Online Ramsey Numbers Of Some Cycles And Paths, Eliyahu Schudrich

Theses, Dissertations and Culminating Projects

The basic premise of Ramsey Theory states that in a sufficiently large system, complete disorder is impossible. One instance from the world of graph theory says that given two fixed graphs F and H, there exists a finitely large graph G such that any red/blue edge coloring of the edges of G will produce a red copy of F or a blue copy of H. Much research has been conducted in recent decades on quantifying exactly how large G must be if we consider different classes of graphs for F and H. In this thesis, we explore several Ramsey- type …

Transitioning Secondary Mathematics Pedagogy Towards Reform-Oriented Practice Through Coteaching, Jessica Tybursky Nuzzi

Theses, Dissertations and Culminating Projects

Reform standards in mathematics education have called for classrooms that are student-centered and that incorporate problem solving and reasoning for meaningful learning. After decades of reform efforts involving multiple stakeholders, research indicates that most classrooms remain teacher-centered and procedurally focused, due to the complexity of concerns and competing intentions that teachers face in their work. Coteaching, a commitment between two teachers to coplan, coenact, and coreflect on lessons, can serve as an ongoing, sustained, focused, integrated, reflective professional development structure that supports teachers towards growth. The theoretical constructs used to describe possible growth towards reform orientations in teaching secondary mathematics …

A Community Of Learning In An Elementary School Mathematics Classroom, Megan Louise Roeder

Theses, Dissertations and Culminating Projects

The goal of this study was to investigate opportunities for cultivating a community of learning in an elementary school mathematics classroom using four guiding principles for productive disciplinary engagement. A community of learning involves teachers and students participating equally in negotiating, sharing, and producing knowledge as co-learners, coteachers, and co-collaborators in the classroom. Characteristics of a community of learning align with effective teaching and learning practices described by national governing bodies and researchers in the field of mathematics education. The essence of a community of learning is beneficial in an elementary mathematics classroom because it invokes deep learning about disciplinary …

The Role Of Covariational Reasoning In Pre-Service Teachers’ Meanings For Quadratic And Exponential Relationships, Madhavi Vishnubhotla

Theses, Dissertations and Culminating Projects

Researchers have indicated that students have difficulties recognizing quadratic and exponential change and do not maintain productive meanings for these relationships. Other researchers have documented that students are capable of developing productive meanings for mathematical ideas via covariational reasoning. This dissertation reports the results of an investigation into ways in which preservice teachers can leverage covariational reasoning to develop meanings for quadratic and exponential relationships. I collected data by engaging two preservice teachers in semi-structured clinical interviews and a semester long teaching experiment. My analyses reveal that whereas in the pre-interviews, the participants did not have meanings that supported differentiating …

Bounds For The Number Of Independent And Dominating Sets In Trees, Daniel K. Arabia

Theses, Dissertations and Culminating Projects

In this work, we investigate bounds on the number of independent sets in a graph and its complement, along with the corresponding question for number of dominating sets. Nordhaus and Gaddum gave bounds on χ(G)+χ(G) and χ(G) χ(G), where G is any graph on n vertices and χ(G) is the chromatic number of G. Nordhaus-Gaddum- type inequalities have been studied for many other graph invariants. In this work, we concentrate on i(G), the number of independent sets in G, and ∂(G), the number of dominating sets in G. We focus our attention on Nordhaus-Gaddum-type inequalities over trees on a fixed …

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

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

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 …

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 …

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. …

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

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 …

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 …

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

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 …