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Articles 1  30 of 1072
FullText Articles in Physical Sciences and Mathematics
Spectral Sequences And Khovanov Homology, Zachary J. Winkeler
Spectral Sequences And Khovanov Homology, Zachary J. Winkeler
Dartmouth College Ph.D Dissertations
In this thesis, we will focus on two main topics; the common thread between both will be the existence of spectral sequences relating Khovanov homology to other knot invariants. Our first topic is an invariant MKh(L) for links in thickened disks with multiple punctures. This invariant is different from but inspired by both the AsaedaPryzytyckiSikora (APS) homology and its specialization to links in the solid torus. Our theory will be constructed from a Z^nfiltration on the Khovanov complex, and as a result we will get various spectral sequences relating MKh(L) to Kh(L), AKh(L), and APS(L). Our …
Remarks On The Occasion Of The Retirement Of Distinguished Professor Guillermo Owen, Thor Martinsen
Remarks On The Occasion Of The Retirement Of Distinguished Professor Guillermo Owen, Thor Martinsen
Mathematica Militaris
The article is a tribute to Distinguished Professor Guillermo Owen who recently retired from the Naval Postgraduate School after 40 years of service.
Applying Expansive Framing To An Integrated MathematicsComputer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway
Applying Expansive Framing To An Integrated MathematicsComputer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway
Publications
In this research report for the National Council of Teachers of Mathematics 2022 Research Conference, we discuss the theory of Expansive Framing and its application to an interdisciplinary mathematicscomputer science curricular unit.
Variety And Variation, Christopher Goff, Erik R. Tou
Variety And Variation, Christopher Goff, Erik R. Tou
Euleriana
Welcome to Volume 2 of Issue 2 of Euleriana. While we occasionally discover themes that emerge from the articles and translations presented in a given issue, the wide range of Euler’s work more often results in a variety of topics for each issue. This is no less true for Issue 2.
Collation Model For Ljs 27: Algorismus., Dot Porter
Collation Model For Ljs 27: Algorismus., Dot Porter
Collation Models
Pedagogical treatise on commercial and practical arithmetic, with extensive use of arabic numerals and problems illustrated with scenes from daily life.
Introduction To Mathematical Analysis I  3rd Edition, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen
Introduction To Mathematical Analysis I  3rd Edition, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen
PDXOpen: Open Educational Resources
Video lectures explaining problem solving strategies are available
Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.
The lecture notes contain topics of real analysis usually covered in a 10week course: the completeness axiom, sequences and convergence, continuity, and differentiation. In addition, the notes include many carefully selected exercises of various levels …
Elegance Or Alchemy? An International CrossCase Analysis Of Faculty And Graduate Student Perceptions Of Mathematical Proofs, Brooke Nicole Denney
Elegance Or Alchemy? An International CrossCase Analysis Of Faculty And Graduate Student Perceptions Of Mathematical Proofs, Brooke Nicole Denney
Masters Theses
Artist Marcel Duchamp once said, ``The painter is a medium who doesn’t realize what he is doing. No translation can express the mystery of sensibility, a word, still unreliable, which is nonetheless the basis of painting or poetry, like a kind of alchemy" (Moffitt, 2012). Just as there is a puzzling aspect of creating art or writing poetry, the aesthetic quality of mathematical proofs is a mysterious and illdefined concept. Like many other subjective terms, it can be difficult to reach a consensus on what elegance means in a mathematical context. In this thesis, I try to better understand faculty …
Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram
Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram
Journal of Humanistic Mathematics
Soma cubes are an example of a dissection puzzle, where an object is broken down into pieces, which must then be reassembled to form either the original shape or some new design. In this paper, we present some interesting discoveries regarding the Soma Cube. Equivalence classes form aesthetically pleasing shapes in the solution set of the puzzle. These gems are identified by subgraph isomorphisms using SNAP!/Edgy, a simple blockbased computer programming language. Our preliminary findings offer several opportunities for researchers from middle school to undergraduate to utilize graphs, group theory, topology, and computer science to discover connections between computation and …
In Mathematics, As In Art, Andrew Granville
In Mathematics, As In Art, Andrew Granville
Journal of Humanistic Mathematics
The artist’s vision helps decide what should be created; the mathematician’s insight what can be created. Yet most people view art as merely decoration, or a reflection of existing reality, while they think of mathematics as just a tool for accurate scientific description. Can more people learn to value and enjoy both art and mathematics? And spend a lifetime exploring them and appreciating them for their own sakes?
Towards Pedagogy Supporting Ethics In Modelling, Marie Oldfield
Towards Pedagogy Supporting Ethics In Modelling, Marie Oldfield
Journal of Humanistic Mathematics
Education for concepts such as ethics and societal responsibility that are critical in building robust and applicable mathematical and statistical models do currently exist in isolation but have not been incorporated into the mainstream curricula at the school or university level. This is partially due to the split between fields (such as mathematics, statistics, and computer science) in an educational setting but also the speed with which education is able to keep up with industry and its requirements. I argue that principles and frameworks of socially responsible modelling should begin at school level and that this would mean that ethics …
Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler
Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler
Journal of Humanistic Mathematics
Foundational philosophical beliefs about mathematics in the mathematical community may have an unappreciated yet profound impact on ethics in mathematical practice and mathematics education, which also affects practice. A philosophical and historical basis of the dominant platonic and formalist views of mathematics are described and evaluated, after which an alternative evidencebased foundation for mathematical thought is outlined. The dualistic nature of the platonic view based on intuition is then compared to parallel historical developments of universalizing ethics in Western thought. These background ideas set the stage for a discussion of the impact of traditional mathematical beliefs on ethics in the …
Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel
Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel
Journal of Humanistic Mathematics
Almost exactly fifty years ago, Friedrich Kambartel, in his classic essay “Ethics and Mathematics,” did pioneering work in an intellectual environment that almost selfevidently assumed a strict separation of the two fields. In our first section we summarize and discuss that classical paper. The following two sections are devoted to complement and contrast Kambartel’s picture. In particular, the second section is devoted to ethical aspects of the indirect and direct mathematization of modern societies. The final section gives a short categorization of various philosophical positions with respect to the rationality of ethics and the mutual relation between ethics and mathematics.
Oer Ancient Egyptian Numerals And Arithmetic Activity, Cynthia Huffman Ph.D.
Oer Ancient Egyptian Numerals And Arithmetic Activity, Cynthia Huffman Ph.D.
Faculty Submissions
Many people are fascinated with ancient Egypt. The amazing, unique culture influenced many other civilizations and cultures. If you study the history of math, you will see how this influence included mathematics. Ancient Egypt also lasted an incredibly long time – over 3000 years. According to Egyptologist Bob Brier, “No civilization lasted so long, contributed so much, or repeatedly amazed as did ancient Egypt.”
In this Open Educational Resource activity, students will have the opportunity to learn about ancient Egyptian numerals and basic arithmetic. For motivation, the setting is a scribal school with each student using a clipboard, paper, and …
Temporal Sentiment Mapping System For TimeSynchronized Data, Jiachen Ma
Temporal Sentiment Mapping System For TimeSynchronized Data, Jiachen Ma
Dissertations (1934 )
Temporal sentiment labels are used in various multimedia studies. They are useful for numerous classification and detection tasks such as video tagging, segmentation, and labeling. However, generating a largescale sentiment dataset through manual labeling is usually expensive and challenging. Some recent studies explored the possibility of using online TimeSync Comments (TSCs) as the primary source of their sentiment maps. Although the approach has positive results, existing TSCs datasets are limited in scale and content categories. Guidelines for generating such data within a constrained budget are yet to be developed and discussed. This dissertation tries to address the above issues by …
Understanding College Students' Use Of Written Feedback In Mathematics, Erin Loraine Carroll
Understanding College Students' Use Of Written Feedback In Mathematics, Erin Loraine Carroll
Theses and Dissertations
Many teachers want to help their students develop a growth mindset about their ability to do mathematics. Research has shown, however, that teachers simply do not know how to promote growth mindsets in their classrooms. Existing research suggests that one way teachers can support students' development of a growth mindset is through the written feedback they provide students. This study combines the research done on students' mindsets and written feedback to examine the interaction between student mindset and written feedback by analyzing written feedback provided to students in a College Algebra class and how students used that feedback based on …
The Impact Of Virtual Learning Modalities On The Academic Success Of Students In One Arkansas School District, Diane F. Richards
The Impact Of Virtual Learning Modalities On The Academic Success Of Students In One Arkansas School District, Diane F. Richards
ATU Theses and Dissertations
The COVID19 pandemic changed the way Arkansas public schools’ offered students an education. While moving through this pandemic, many Arkansas schools implemented optional methods of delivery for their students. Some schools tried to maintain facetoface classes, while others offered completely online classes. Still, others offered a hybrid format where students attended some facetoface classes and online classes. One Arkansas school district offered all three options. School districts need guidance as to which teaching methods worked well. The longterm effects of the educational impact of COVID19 are not known at this time. Schools could benefit from a guide with useful strategies …
The Efficacy Of The Covid19 Vaccine In Mississippi, Ilyse Miriam Levy
The Efficacy Of The Covid19 Vaccine In Mississippi, Ilyse Miriam Levy
Honors Theses
The Efficacy of The COVID19 Vaccine in Mississippi
(Under the direction of Dr. Xin Dang)
By tracking and analyzing fiftythree weeks of COVID19 data, this thesis analyzes the efficacy of the COVID19 vaccine within the State of Mississippi. Over the course of these fiftythree weeks, I have also been able to calculate the confidence intervals for vaccination efficacy and the risk reduction due to vaccination by using data regarding the correlations between deaths and vaccination status, provided to me by the Mississippi Office of Epidemiology. My analysis demonstrates that the COVID19 vaccine is effective not only in Mississippi but also …
The Executive’S Guide To Getting Ai Wrong, Jerrold Soh
The Executive’S Guide To Getting Ai Wrong, Jerrold Soh
Asian Management Insights
It’s all math. Really.
Mathematical Modeling Suggests Cooperation Of PlantInfecting Viruses, Joshua Miller, Vitaly V. Ganusov, Tessa BurchSmith
Mathematical Modeling Suggests Cooperation Of PlantInfecting Viruses, Joshua Miller, Vitaly V. Ganusov, Tessa BurchSmith
Chancellor’s Honors Program Projects
No abstract provided.
Positive Solutions To Semilinear Elliptic Equations With LogisticType Nonlinearities And Harvesting In Exterior Domains, Eric Jameson
Positive Solutions To Semilinear Elliptic Equations With LogisticType Nonlinearities And Harvesting In Exterior Domains, Eric Jameson
UNLV Theses, Dissertations, Professional Papers, and Capstones
Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistictype nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques forsolving these equations in the whole space RN can be applied to the exterior domain with some …
A Computer Programming Intervention For Second Grade Math Students, Eric B. Bagley
A Computer Programming Intervention For Second Grade Math Students, Eric B. Bagley
All Graduate Theses and Dissertations
The multiplication algorithms taught to elementary students are made to help students find answers quickly, but why the algorithm works and how it relates to multiplication is not widely known. For example, one intuitive meaning of multiplication is that of iterated, or, repeated, addition. In this paper, we look at the ways a visual, blockbased, programming activity uses the concept of iteration to help secondgraders learn multiplication. The results of the study observing secondgrade students use visual programming and iteration to setup and solve multiplication story problems. We found that generally students enjoyed these activities and found them helpful during …
The Influence Of A Course On Assessment For Inservice Secondary Mathematics Teachers, Natalie M. Anderson
The Influence Of A Course On Assessment For Inservice Secondary Mathematics Teachers, Natalie M. Anderson
All Graduate Theses and Dissertations
Many mathematics teachers are not prepared to design valid and usable measurements of their students’ mathematical achievements. There are relatively few opportunities for mathematics teachers to improve their assessment literacy. The purpose of this study is to (1) design a course on assessment for inservice mathematics teachers and (2) evaluate the effectiveness of the course. This paper recounts the development of the course and its influence on 16 teachers. Teachers who completed the course submitted a unit outline with learning objectives, a test blueprint, and a unit test. These artifacts influenced my evaluation on the effectiveness of the course. All …
How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli
How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli
The Review: A Journal of Undergraduate Student Research
The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …
The Biggest Loser: How Tanking In Professional Sports Impacts Fan Perception, Julia Ayres
The Biggest Loser: How Tanking In Professional Sports Impacts Fan Perception, Julia Ayres
Honors Projects in Mathematics
Professional sports teams are adored nationwide for their talents and the pride they bring to their city for their efforts. However, not all teams take this responsibility seriously and will lose on purpose, or tank, to gain a higher draft pick in the future. Although the longterm goals of tanking are to help the organization, many people take issue with athletes not putting in their best efforts in every game. Teams in both the NBA and NFL are guilty of tanking to gain better draft picks but not all have found success in this process. This leads to important questions …
Vampires And Other Diseases: Stochastic Infection Dynamics Of Small Populations, Marijn Jaarsma
Vampires And Other Diseases: Stochastic Infection Dynamics Of Small Populations, Marijn Jaarsma
Honors Projects in Science and Technology
Mathematical models are powerful tools often applied in the field of epidemiology. The type and shape of the model will differ between different types of diseases. In this study, stochastic dynamical models are applied to the entertaining example of vampires, and the results of this analysis are compared to reallife diseases with small populations of infected. The data used comes from popculture depictions of vampires in literature, television shows, movies, and fan pages associated with these depictions. The aim of this study is to serve as an educational tool for modeling diseases with small populations to predict and control the …
Applied Math In Introductory Chemistry, Ji Kim, Grace Pai
Applied Math In Introductory Chemistry, Ji Kim, Grace Pai
Open Educational Resources
Students, particularly those who are nonscience majors, often struggle with collegelevel science courses required for graduation due to the applied mathematics needed to successfully complete the course. This resource includes four activities on the topics of units and measurements, dimensional analysis, density, and gases. These topics were specifically designed to teach the mathematics embedded in these topics in a culturally responsive way. Throughout the activities, we incorporate these four elements of culturally relevant pedagogy (LadsonBillings, 2009) in order to engage students in successfully solving basic mathematics in chemistry while promoting their interest in learning chemistry.
Mathematical Analysis Of An Sir Disease Model With NonConstant Transmission Rate, Emma Bollinger, Tayler Valdez, Swarup Ghosh, Sunil Giri
Mathematical Analysis Of An Sir Disease Model With NonConstant Transmission Rate, Emma Bollinger, Tayler Valdez, Swarup Ghosh, Sunil Giri
Student Research
 Epidemiology: A branch of medicine that studies causes, transmission, and control methods of diseases at the population level.
 Mathematical epidemiology deals with creating a model for a disease through the study of incidence and distribution of the disease throughout a population.
 Here, we have examined the behavior of a measleslike disease[2] that is characterized by a nonconstant transmission rate.
Ranked Choice Voting: Who’S The Real Winner?, Brendan Magill '23
Ranked Choice Voting: Who’S The Real Winner?, Brendan Magill '23
Posters
Ranked choice voting is a voting system in which voters rank candidates in order or preference. The winning candidate is determined by eliminating candidates and reassigning their votes until one has a majority. It provides solutions to some of the fundamental issues with traditional voting. But is it more fair? Should it be instituted in American democratic elections?
CrossSectoral Climate Change Modeling, Jeremy Gordon '22
CrossSectoral Climate Change Modeling, Jeremy Gordon '22
Posters
Although climate data originates from various integrated sectors, it continues to be evaluated in isolation. By using crosssectoral modeling, climate change modeling can more effectively represent data, and the possible consequences of misjudging future models.
Accessible And Intuitive Mathematical Notation, Anthony Christiana '22
Accessible And Intuitive Mathematical Notation, Anthony Christiana '22
Posters
For math learners with disabilities, engagement with traditional mathematical notation can be difficult or impossible. Here, we explore two examples of the ways that notation can fail disabled students. We also note how accommodating for these disabilities allows us to imagine better ways of serving all students through notational practices.