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Articles 1  30 of 1352
FullText Articles in Physical Sciences and Mathematics
"Who Wrote The Epistle, God Only Knows": A Statistical Authorial Analysis Of Hebrews In Comparison With Pauline And Lukan Literature, Benjamin J. Erickson
"Who Wrote The Epistle, God Only Knows": A Statistical Authorial Analysis Of Hebrews In Comparison With Pauline And Lukan Literature, Benjamin J. Erickson
Senior Honors Theses
The authorship of Hebrews has been a point of contention for scholars for the past two millennia. While the epistle is traditionally attributed to Paul, many scholars assert that it carries thematic, structural, and stylistic differences from the remainder of his extant epistles; therefore, many other possible authors have been proposed. Of these, only Luke has other New Testament writings. Therefore, this project conducts a statistical comparison of Hebrews to the Pauline and Lukan corpora using stylometric authorial analysis methods. This analysis demonstrates that Hebrews is stylistically closer to Lukan literature than Pauline (but not to a significant degree), and …
Mathematically Modeling How Trapping Regimes That Target Specific Crayfish Life Stages Impact Removal Efficacy, Rini Pattison
Mathematically Modeling How Trapping Regimes That Target Specific Crayfish Life Stages Impact Removal Efficacy, Rini Pattison
Seaver College Research And Scholarly Achievement Symposium
The red swamp crayfish, Procambarus clarkii, is an invasive species introduced into several streams within the Santa Monica Mountains (SMM) in Southern California. Crayfish predation decimates native aquatic species. Thus, the Mountains Restoration Trust (MRT) and Environmental Restoration Group have worked to remove crayfish through regular trapping in Malibu Creek.
To aid conservation efforts, former SURB students William Milligan and Dev Patel developed mathematical models of crayfish removal efficacy. Milligan created a differential equation model of how crayfish removal affects local newt populations. Patel expanded Milligan’s crayfish model by creating a discrete model of the crayfish life cycle that newly …
Quik Church, Route 3.141592, Sarah Voss
Quik Church, Route 3.141592, Sarah Voss
Journal of Humanistic Mathematics
The following set of poems are from one of ten sections in a collection of poetry called Quik Church: Short Poems that Travel Far. Each section illustrates one of many “streets” which individuals often take on their spiritual journey through life, e.g., the Old Gods Path, Nature Trail, Memory Skyway, Mystic Avenue, Pastoral Lane, and so on. This one, Route 3.141592, is the route of mathematics and the science that depends on mathematics.
Seven Properties Of Highly Effective Problems, Thomas Ales, Kevin Peterson, Constantine Roussos
Seven Properties Of Highly Effective Problems, Thomas Ales, Kevin Peterson, Constantine Roussos
Journal of Mathematics and Science: Collaborative Explorations
In an effort to provide more critical thinking opportunities in their courses, instructors are embracing the power of problem and projectbased learning (PBL). In this paper we address the importance of problem quality when utilizing PBL. We list seven important properties that a highquality problem should have. We conclude with an example of a problem that possesses all seven properties.
Bridging Biological Systems With Social Behavior, Conservation, Decision Making, And WellBeing Through Hybrid Mathematical Modeling, Maggie Renee Sullens
Bridging Biological Systems With Social Behavior, Conservation, Decision Making, And WellBeing Through Hybrid Mathematical Modeling, Maggie Renee Sullens
Faculty Publications and Other Works  Mathematics
This dissertation defense presentation highlights the power of hybrid mathematical modeling and addresses crucial issues such as:
1️. The Impact of Industry Collapse on Community Mental Health: A Complex Contagion ODE Model.
2️. Budget Allocation and Illegal Fishing: A Game Theoretic Model.
3️. Reactive Scope Model with an Energy Budget and Multiple Mediators: An ODE Model
The overarching theme of Hybrid Mathematical Modeling beautifully captures the essence of this work, demonstrating its potential to unravel ecological issues while addressing the intricate interactions between humans and the environment.
A Spiral Workbook For Discrete Mathematics 2nd Edition, Harris Kwong
A Spiral Workbook For Discrete Mathematics 2nd Edition, Harris Kwong
Milne Open Textbooks
This updated text covers the standard topics in a sophomorelevel course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Handson exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is …
PreCalculus: Thinking Deeply About Simple Things, Jacob Carter
PreCalculus: Thinking Deeply About Simple Things, Jacob Carter
Graduate Research Showcase
“PreCalculus: Thinking Deeply About Simple Things” is a researchbased creative endeavor focused on designing a highschool precalculus course. This course aims to foster deep, meaningful thinking, as well as an appreciation of the values of diversity, equity, and inclusion in the math classroom. The course leverages students’ funds of knowledge to employ culturally responsive teaching methods to connect mathematical concepts to the students’ backgrounds, interests, and reallife situations. This course also integrates socialemotional learning to create an engaging and supportive learning environment for all students. By combining Peter Liljedahl’s “Building Thinking Classroom in Mathematics” approach with problembased learning, the course …
Proof Of The KreschTamvakis Conjecture, John Caughman, Taiyo S. Terada
Proof Of The KreschTamvakis Conjecture, John Caughman, Taiyo S. Terada
Mathematics and Statistics Faculty Publications and Presentations
In this paper we resolve a conjecture of Kresch and Tamvakis.
Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron
Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron
Honors College Theses
The properties of ncolor compositions have been studied parallel to those of regular compositions. The conjugate of a composition as defined by MacMahon, however, does not translate well to ncolor compositions, and there is currently no established analogous concept. We propose a conjugation rule for cyclic ncolor compositions. We also count the number of selfconjugates under these rules and establish a couple of connections between these and regular compositions.
Social Justice Mathematics: Classroom Practices That Give Students Rigor While Building Agency, Emily Marquise
Social Justice Mathematics: Classroom Practices That Give Students Rigor While Building Agency, Emily Marquise
Masters Theses
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 K12 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 lowsocioeconomic settings are not given rigorous content that will keep them competitive …
The Negative Stigma Surrounding Mathematics, Marissa A. Greisen
The Negative Stigma Surrounding Mathematics, Marissa A. Greisen
PSU McNair Scholars Online Journal
There is a negative stigma that surrounds mathematics in our education system. It is important to bring notice to this for the benefit of future students. There is a lot of research claiming that math is looked down on, but they do not answer why, or what we can do to fix it. Why is there a greater negative stigma around math and not other subjects? What roles to teachers, parents, and peers play in this stigma? In this article, I created a survey for people to answer questions regarding their opinion on math, who they believe typically does well …
Benford’S Law And Its Applications To Accounting, Lucy Wilson
Benford’S Law And Its Applications To Accounting, Lucy Wilson
Mathematics Student Projects
In this paper, we introduce the concept of Benford’s Law, which is the mathematical observation that in many naturally occurring numerical datasets, the leading digits are not evenly distributed. We actually find that smaller leading digits appear more often than larger ones. We will explore when and why this phenomenon occurs and how we can use statistical tests to determine how well a dataset conforms to Benford’s Law. We will also see how Benford’s Law can be used by auditors in the accounting field to catch potential fraud.
The Traveling Salesman Problem At Taylor University, Jonathan Jinoo Pawley
The Traveling Salesman Problem At Taylor University, Jonathan Jinoo Pawley
Mathematics Student Projects
What is the shortest route to walk to every residence hall on campus, beginning and ending with the same hall? This question can be considered by applying the Traveling Salesman Problem, an easy to understand yet hard to solve problem in the realm of discrete combinatorial optimization. The Traveling Salesman Problem is useful as an introduction to optimization problems, and it also has immensely practical applications. This paper will serve as an introduction to the computational difficulty of the Traveling Salesman Problem and will also explore various approximation algorithms. We will subsequently apply our new understanding of the theory to …
Assessing Controls On Ice Dynamics At Crane Glacier, Antarctic Peninsula, Using A Numerical Ice Flow Model, Rainey Aberle, Ellyn M. Enderlin, HansPeter Marshall, Michal Kopera, Tate G. Meehan
Assessing Controls On Ice Dynamics At Crane Glacier, Antarctic Peninsula, Using A Numerical Ice Flow Model, Rainey Aberle, Ellyn M. Enderlin, HansPeter Marshall, Michal Kopera, Tate G. Meehan
Geosciences Faculty Publications and Presentations
The Antarctic Peninsula's widespread glacier retreat and ice shelf collapse have been attributed to atmospheric and oceanic warming. Following the initial postcollapse period of retreat, several former tributary glaciers of the Larsen A and B ice shelves have been slowly readvancing for more than a decade. Here, we use a flowline model of Crane Glacier to gauge the sensitivity of former tributary glaciers to future climate change following this period of longterm dynamic adjustment. The glacier's longterm geometry and speed changes are similar to those of other former Larsen A and B tributaries, suggesting that Crane Glacier is a reasonable …
Differential Calculus: From Practice To Theory, Eugene Boman, Robert Rogers
Differential Calculus: From Practice To Theory, Eugene Boman, Robert Rogers
Milne Open Textbooks
Differential Calculus: From Practice to Theory covers all of the topics in a typical first course in differential calculus. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas. Only after skill with the computational tools of calculus has been developed is the question of rigor seriously broached. At that point, the …
Investigation Of Student Understanding Of Representations Of Probability Concepts In Quantum Mechanics, William D. Riihiluoma
Investigation Of Student Understanding Of Representations Of Probability Concepts In Quantum Mechanics, William D. Riihiluoma
Electronic Theses and Dissertations
The ability to relate physical concepts and phenomena to multiple mathematical representations—and to move fluidly between these representations—is a critical outcome expected of physics instruction. In upperdivision quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered. Thus, developing the ability to generate and translate expressions in these notations is of great importance, and the extent to which students can relate these expressions to physical quantities and phenomena is crucial to understand.
To investigate student understanding of the expressions used in these notations and the ways they relate, clinical thinkaloud interviews were conducted …
Parents' Perceptions Of The Importance Of Teaching Mathematics: A QStudy, Ashlynn M. Holley
Parents' Perceptions Of The Importance Of Teaching Mathematics: A QStudy, Ashlynn M. Holley
Theses and Dissertations
Mathematics education has gone through multiple reform efforts over the last century and continues to be the target of improvement efforts. Past changes in curriculum and goals have sometimes led to heated debates between various stakeholders. Knowing the views of different stakeholders can help determine what common ground there is between these different groups and where areas of disagreement might arise. Parents are especially important to understand because they have been influential in past reform efforts. Despite the importance of parents' opinions, little research has been conducted concerning their perspectives on the importance of mathematics teaching. Using Qmethodology, I was …
Examining The Effectiveness Of Using PointOfView Video Modeling On Mathematics Improvement In Students With Learning Disabilities In Saudi Arabia, Tirad Alsaluli
Electronic Theses and Dissertations
Video Modeling (VM) is one of the most widely used approaches by researchers to improve many skills, such as academic skills in students with Learning Disabilities (LD; Boon et al., 2020). As the incidence rate of individuals with LD in Saudi Arabia increase (Almedlij & RubinsteinÁvila, 2018), the need for evidencebased math interventions focused on the math development of individuals with LD also increases. Although VM is recognized as an Evidencebased Practice (EBPs), a limited number of studies have implemented VM as an intervention to improve mathematic skills. Implementing VM as a math intervention strategy would explore its effects on …
Towards Ethical Ai: Mathematics Influences Human Behavior, Dioneia M. MonteSerrat, Carlo Cattani
Towards Ethical Ai: Mathematics Influences Human Behavior, Dioneia M. MonteSerrat, Carlo Cattani
Journal of Humanistic Mathematics
Mathematics plays an important role in the linguistic structure of artificial in telligence (AI). We describe the linguistic process as a unique structure present both in human cognition and in cognitive computing. The close relationship with both AI and human cognition is due to this unique structure, which paves the way for AI to interfere with the behavior of those who interact with it. We highlight the role of mathematicians in designing algorithms—the core of the AI linguistic process—and in defining steps and instructions for AI. Because al gorithms, through AI, interfere with the thought of those who interact with …
Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers
Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers
Journal of Humanistic Mathematics
In this paper we address the questions: What is synesthesia? What support(s) can teachers provide for their students who have synesthesia? Nicole, a future mathematics teacher who possesses this synesthesia “superpower”, describes how it impacted her learning. We collected data for this case study through an audiorecorded and transcribed interview, as well as from subsequent email correspondence between the three authors. We asked Nicole three kinds of questions: questions she is frequently asked, questions she would like to be asked, and questions teachers (like Shelly and Beth) might ask. Results indicate that synesthesia may have helped Nicole learn English as …
#Disruptjmm: Online Social Justice Advocacy And Community Building In Mathematics, Rachel Roca, Carrie Diaz Eaton, Drew Lewis, Joseph Hibdon, Stefanie Marshall
#Disruptjmm: Online Social Justice Advocacy And Community Building In Mathematics, Rachel Roca, Carrie Diaz Eaton, Drew Lewis, Joseph Hibdon, Stefanie Marshall
Journal of Humanistic Mathematics
In 2019, \#DisruptJMM, a Twitter hashtag, began circulating after an Inclusion/Exclusion blog by Dr. Piper H pointing to the need to make commonplace conversations about human suffering in the Joint Mathematics Meetings (JMM). While the \#DisruptJMM hashtag has been used since 2019, the vast majority of use was in the JMM 2020 meetings. Twitter hashtags are used by activists to push forward conversations, join communities around a single idea, and create change. In this article, we draw on frameworks from community building seen in other equity and inclusion advocacy hashtags such as \#GirlsLikeUs [7] to qualitatively code and analyze tweets …
Mathematics Behind Machine Learning, Rim Hammoud
Mathematics Behind Machine Learning, Rim Hammoud
Electronic Theses, Projects, and Dissertations
Artificial intelligence (AI) is a broad field of study that involves developing intelligent
machines that can perform tasks that typically require human intelligence. Machine
learning (ML) is often used as a tool to help create AI systems. The goal of ML is
to create models that can learn and improve to make predictions or decisions based on given data. The goal of this thesis is to build a clear and rigorous exposition of the mathematical underpinnings of support vector machines (SVM), a popular platform used in ML. As we will explore later on in the thesis, SVM can be implemented …
Engaging Students With HighStakes Problems, Deepak Basyal
Engaging Students With HighStakes Problems, Deepak Basyal
Mathematics and Statistics
Engaging students in meaningful mathematics problemsolving is the intention of many education stakeholders around the world. Research suggests that the implementation of highstakes problems in mathematics teaching is one way to strengthen students’ conceptual understanding. Many carefully crafted openended problems constitute highstakes problems, and proper use of such problems in teaching and learning not only encourages learners’ flexible thinking but also helps detect their misconceptions. However, what is less practiced and understood is: how exactly one should aim to implement such problems in a classroom setting. Teaching preservice middle school teachers for a few years using highstakes (mostly openended problems) …
Imperfect Immunity And The Stability Of A Modified KermackMckendrick Model, Kaylee Sims
Imperfect Immunity And The Stability Of A Modified KermackMckendrick Model, Kaylee Sims
Honors Theses
The classic KermackMcKendrick model of mathematical epidemiology suggests that a population is only in equilibrium when there is no disease present. In the modern era, we have several cyclic infectious diseases that show no signs of eradication, despite global health measures. In this thesis, we introduce a coefficient of waning immunity in order to produce a modified KermackMcKendrick model and analyze whether the model yields system stability with a certain amount of infection present. Ultimately, the model is incongruent with realworld case data, with its most glaring failure being exponential dampening of the height of each disease case peak due …
An Application Of The Pagerank Algorithm To Ncaa Football Team Rankings, Morgan Majors
An Application Of The Pagerank Algorithm To Ncaa Football Team Rankings, Morgan Majors
Honors Theses
We investigate the use of Google’s PageRank algorithm to rank sports teams. The PageRank algorithm is used in web searches to return a list of the websites that are of most interest to the user. The structure of the NCAA FBS football schedule is used to construct a network with a similar structure to the world wide web. Parallels are drawn between pages that are linked in the world wide web with the results of a contest between two sports teams. The teams under consideration here are the members of the 2021 Football Bowl Subdivision. We achieve a total ordering …
Book Review Of Inside Mathforum.Org: Analysis Of An Internet Based Education Community., Jose Ponce
Book Review Of Inside Mathforum.Org: Analysis Of An Internet Based Education Community., Jose Ponce
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Inside Mathforum.org: Analysis of an InternetBased Education Community, Wesley Shumar, Cambridge University Press, September 7, 2017, 1st Edition, 204 pages, ISBN: 9781108518345 (ebook).
What Is A Number?, Nicholas Radley
What Is A Number?, Nicholas Radley
HON499 projects
This essay is, in essence, an attempt to make a case for mathematical platonism. That is to say, that we argue for the existence of mathematical objects independent of our perception of them. The essay includes a somewhat informal construction of number systems ranging from the natural numbers to the complex numbers.
Tribute To Gene Chase, Calvin Jongsma
Tribute To Gene Chase, Calvin Jongsma
Faculty Work Comprehensive List
Gene’s academic work was always one of service to God, his students, and his colleagues, and his intellectual passion was to promote the development of Christian perspectives on various aspects of the field. His contributions to the ACMS have been much appreciated and, God willing, may still bear fruit into the future.
Incorporating Perspectival Elements In A Discrete Mathematics Course, Calvin Jongsma
Incorporating Perspectival Elements In A Discrete Mathematics Course, Calvin Jongsma
Faculty Work Comprehensive List
Discrete mathematics is a vast field that can be explored along many different paths. Opening with a unit on logic and proof and then taking up some additional core topics (induction, set theory, combinatorics, relations, Boolean algebra, graph theory) allows one to bring in a wealth of relevant material on history, philosophy, axiomatics, and abstraction in very natural ways. This talk looks at how my 2019 textbook on discrete mathematics, focused in this way, came to be, and it highlights the various perspectival elements the book includes.
Curriculum Connectivity In Montclair State University’S Undergraduate Mathematics Program, Ana G. Da Silva Jesus
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 …