Open Access. Powered by Scholars. Published by Universities.®
- Institution
-
- Indian Statistical Institute (204)
- Claremont Colleges (97)
- University of South Carolina (63)
- Illinois Math and Science Academy (44)
- University of South Florida (39)
-
- Minnesota State University Moorhead (38)
- University of New Mexico (34)
- Bryant University (30)
- Selected Works (28)
- University of Denver (27)
- Western Kentucky University (23)
- University of Richmond (19)
- Hamilton College (18)
- City University of New York (CUNY) (17)
- John Carroll University (17)
- The College of Wooster (12)
- Dordt University (11)
- Georgia Southern University (11)
- Lincoln University (11)
- Walden University (11)
- Bridgewater State University (10)
- California State University, San Bernardino (10)
- Central Washington University (10)
- University of Rhode Island (10)
- Brigham Young University (9)
- Providence College (9)
- Technological University Dublin (9)
- University of North Dakota (9)
- Dartmouth College (8)
- Old Dominion University (8)
- Publication
-
- Doctoral Theses (204)
- Faculty Publications (65)
- Journal of Humanistic Mathematics (55)
- Numeracy (39)
- Math Department Newsletters (38)
-
- Electronic Theses and Dissertations (36)
- Branch Mathematics and Statistics Faculty and Staff Publications (34)
- All HMC Faculty Publications and Research (26)
- Honors Projects in Mathematics (22)
- Open Educational Resources (21)
- Series (17)
- Department of Math & Statistics Faculty Publications (16)
- Masters Essays (16)
- Posters (16)
- Manuscript Collection Finding Aids (15)
- Theses and Dissertations (15)
- Senior Independent Study Theses (12)
- Faculty Work Comprehensive List (11)
- Math for Girls Day Documents (11)
- Walden Dissertations and Doctoral Studies (11)
- Mathematics & Computer Science Student Scholarship (9)
- Honors Program Theses and Projects (8)
- Honors Theses (8)
- Master's Theses (8)
- All Master's Theses (7)
- Articles (6)
- Dartmouth Scholarship (6)
- Electronic Thesis and Dissertation (6)
- Honors Projects (6)
- Limits (6)
- Publication Type
Articles 1 - 30 of 1120
Full-Text Articles in Entire DC Network
Ideals In Semigroups Of Partial Transformations With Invariant Set, Jitsupa Srisawat, Yanisa Chaiya
Ideals In Semigroups Of Partial Transformations With Invariant Set, Jitsupa Srisawat, Yanisa Chaiya
Turkish Journal of Mathematics
This paper explores the ideals and their structural properties in two generalizations of the partial transformationsemigroup. Furthermore, principal, maximal, and minimal ideals within these semigroups are elucidated.
Math 75: Introduction To Linear Algebra, Sarah K. Merz
Math 75: Introduction To Linear Algebra, Sarah K. Merz
Pacific Open Texts
This text is intended to use in a first course of Linear Algebra with a prerequisite of Calculus 1. Topics covered include systems of linear equations, matrix operations and inverses, linear transformations, Markov chains, determinants, eigenvalues and eigenvectors, diagonalization, vector geometry, projections and planes, homogeneous coordinates, subspaces, spanning sets, linear independence, orthogonality, fundamental subspaces, and least squares.
Building Blocks For W-Algebras Of Classical Types, Vladimir Kovalchuk
Building Blocks For W-Algebras Of Classical Types, Vladimir Kovalchuk
Electronic Theses and Dissertations
The universal 2-parameter vertex algebra W∞ of type W(2, 3, 4; . . . ) serves as a classifying object for vertex algebras of type W(2, 3, . . . ,N) for some N in the sense that under mild hypothesis, all such vertex algebras arise as quotients of W∞. There is an ℕ X ℕ family of such 1-parameter vertex algebras known as Y-algebras. They were introduced by Gaiotto and Rapčák are expected to be building blocks for all W-algebras in type A, i.e, every W-(super) algebra in …
Combinatorial Problems On The Integers: Colorings, Games, And Permutations, Collier Gaiser
Combinatorial Problems On The Integers: Colorings, Games, And Permutations, Collier Gaiser
Electronic Theses and Dissertations
This dissertation consists of several combinatorial problems on the integers. These problems fit inside the areas of extremal combinatorics and enumerative combinatorics.
We first study monochromatic solutions to equations when integers are colored with finitely many colors in Chapter 2. By looking at subsets of {1, 2, . . . , n} whose least common multiple is small, we improved a result of Brown and Rödl on the smallest integer n such that every 2-coloring of {1, 2, . . . , n} has a monochromatic solution to equations with unit fractions. Using a recent result of Boza, …
Circling The Square: Computing Radical Two, Isaiah Mellace, Joshua Kroeker
Circling The Square: Computing Radical Two, Isaiah Mellace, Joshua Kroeker
NEXUS: The Liberty Journal of Interdisciplinary Studies
Discoveries of equations for irrational numbers are not new. From Newton’s Method to Taylor Series,there are many ways to calculate the square root of two to arbitrary precision. The following method is similar in this way, but it is also a fascinating derivation from geometry that has applications to other irrationals. Additionally, the equation derived has some properties that may lead to fast computation. The first part of this paper is dedicated to deriving the equation, and the second is focused on computer science implementations and optimizations.
Khovanov Homology And Legendrian Simple Knots, Ryan J. Maguire
Khovanov Homology And Legendrian Simple Knots, Ryan J. Maguire
Dartmouth College Ph.D Dissertations
The Jones polynomial and Khovanov homology are powerful invariants in knot theory. Their computations are known to be NP-Hard and it can be quite a challenge to directly compute either of them for a general knot. We develop explicit algorithms for the Jones polynomial and discuss the implementation of an algorithm for Khovanov homology. Using this we tabulate the invariants for millions of knots, generate statistics on them, and formulate conjectures for Legendrian and transversely simple knots.
A Thesis, Or Digressions On Sculptural Practice: In Which, Concepts & Influences Thereof Are Explained, Set Forth, Catalogued, Or Divulged By Way Of Commentaries To A Poem, First Conceived By The Artist, Fed Through Chatg.P.T., And Re-Edited By The Artist, To Which Are Added, Annotated References, Impressions And Ruminations Thereof, Also Including Private Thoughts & Personal Accounts Of The Artist, Jaimie An
Masters Theses
This thesis is an exercise in, perhaps a futile, attempt to trace just some of the ideas, stories, and musings I might meander through in my process. It’s not quite a map, nor is it a neat catalogue; it is a haphazard collection of tickets and receipts from a travel abroad, carelessly tossed in a carry-on, only to be stashed upon returning home. These ideas are derived from much greater thinkers and authors than myself; I am a mere collector or a translator, if that, and not a very good one, for much is lost. I do not claim comprehensive …
A Brief Introduction To General Topology, Richard P. Millspaugh
A Brief Introduction To General Topology, Richard P. Millspaugh
Open Educational Resources
The material in this text is intended to be accessible to undergraduates who have had an introduction to elementary set theory and proof techniques. It includes sufficient material from general topology to prove the two main topological results found in a standard first semester calculus course: the Intermediate Value Theorem and the Extreme Value Theorem. This material can be found in Chapters 2 through 6 and makes up the bulk of the text. Rather than approaching these topics through use of the standard euclidean metric, it defines the standard topology on R in terms of the usual order on R. …
Conceptual Understanding Of Linear Relationships Across Various Mathematics Courses, Melissa Manley
Conceptual Understanding Of Linear Relationships Across Various Mathematics Courses, Melissa Manley
Theses and Dissertations
This cross-sectional study investigated the conceptual understanding of linear relationships for 195 students enrolled in a single school in a large, urban district across five mathematics courses: Grade 7 Math (n = 24), Grade 8 Math (n = 52), Geometry (n = 43), Algebra 1 (n = 31), and Algebra 2 (n = 45). The following questions guided this study: (1) What differences exist in students’ conceptual understanding of linear relationships across mathematics courses? (2) What are common strengths and weaknesses in students’ conceptual understanding of linear relationships?
An assessment was created to assess three constructs of conceptual understanding of …
Mathematics Majors In Medical School Admissions: A Comparative Evaluation Of Mcat And Gpa Performance, Morgan Baker
Mathematics Majors In Medical School Admissions: A Comparative Evaluation Of Mcat And Gpa Performance, Morgan Baker
Theses/Capstones/Creative Projects
Choosing a major as an incoming undergraduate student can be very stressful. This study investigates the differences in success that come with choice of undergraduate major, particularly focusing on the performance of mathematics majors. A large majority of medical school applicants come from a biological sciences background. Despite this preference, there is evidence that students from nontraditional majors produce higher Medical College Admission Test (MCAT) scores and superior grade point averages (GPAs). Utilizing data visualization and analysis through R programming, this research examines public data from the Association of American Medical Colleges (AAMC) to understand the benefits of pursuing a …
An Investigation Into Problem Solving In The Calculus Iii Classroom, Joseph Godinez
An Investigation Into Problem Solving In The Calculus Iii Classroom, Joseph Godinez
Honors College
The importance of tertiary education has grown to new heights, especially in the United States. A critical component of successful modern professionals remains the ability to employ problem-solving strategies and techniques. This study seeks to investigate initial problem-solving strategies employed by post-secondary students enrolled in Calculus II when presented with problems common to integral calculus. In- person pair-wise interviews were conducted asking six participants to sort integrals into categories based on the technique they would use to solve it. Participant responses were analyzed using a concept image composed of general and topic-specific symbolic forms, related conceptual images and concept definitions, …
New Algorithms For The Multiplication Table Problem, Evan Blom
New Algorithms For The Multiplication Table Problem, Evan Blom
Undergraduate Honors Thesis Collection
In 1955, Paul Erdős initiated the study of a function that counts the number of distinct integers in an (n × n) multiplication table. That is, he studied M(n) = |{i · j, 1 ≤ i, j ≤ n}|. Much research has been done in regards to both asymptotic and exact approximations of M(n) for increasingly large values of n. Recently, Brent et. al. investigated the algorithmic cost in computing this function. Instead of computing M(n) directly, their approach was to compute it incrementally. That is, given M(n−1), they could quickly compute M(n) using another function δ(n) to count the …
The Mathematics Of Financial Portfolio Optimization Incorporating Environmental, Social, And Governance Score Information, Ian Driskill
The Mathematics Of Financial Portfolio Optimization Incorporating Environmental, Social, And Governance Score Information, Ian Driskill
Master's Theses
We numerically investigate the effects that Environmental, Social, and Governance (ESG) scores have on portfolio optimization with Modern Portfolio Theory assumptions and how ESG scores correlate with the market returns of a rated company's stock. Additionally, we review and analyze a research paper published in the Journal of Financial Economics regarding ESG investing titled “Responsible investing: The ESG-efficient frontier” by Pedersen, Fitzgibbons, and Lukasz. Our overall goal is provide insight for socially responsible inclined investors, to help them understand what ESG scores tell us and how those scores may effect their overall investment returns."
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.
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 sophomore-level 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. Hands-on 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 …
Inexact Fixed-Point Proximity Algorithm For The ℓ₀ Sparse Regularization Problem, Ronglong Fang, Yuesheng Xu, Mingsong Yan
Inexact Fixed-Point Proximity Algorithm For The ℓ₀ Sparse Regularization Problem, Ronglong Fang, Yuesheng Xu, Mingsong Yan
Mathematics & Statistics Faculty Publications
We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the ℓ₀ norm. Specifically, the ℓ₀ model has an objective function that is the sum of a convex fidelity term and a Moreau envelope of the ℓ₀ norm regularization term. Such an ℓ₀ model is non-convex. Existing exact algorithms for solving the problems require the availability of closed-form formulas for the proximity operator of convex functions involved in the objective function. When such formulas are not available, numerical computation of the proximity operator becomes inevitable. This leads to inexact iteration algorithms. We investigate in this …
Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron
Counting Conjugates Of Colored Compositions, Jesus Omar Sistos Barron
Honors College Theses
The properties of n-color 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 n-color compositions, and there is currently no established analogous concept. We propose a conjugation rule for cyclic n-color compositions. We also count the number of self-conjugates under these rules and establish a couple of connections between these and regular compositions.
Pre-Calculus: Thinking Deeply About Simple Things, Jacob Carter
Pre-Calculus: Thinking Deeply About Simple Things, Jacob Carter
Graduate Research Showcase
“Pre-Calculus: Thinking Deeply About Simple Things” is a research-based creative endeavor focused on designing a high-school pre-calculus 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 real-life situations. This course also integrates social-emotional learning to create an engaging and supportive learning environment for all students. By combining Peter Liljedahl’s “Building Thinking Classroom in Mathematics” approach with problem-based learning, the course …
Finding Maximal Cap Sizes For Quad Card Decks Using Share Strings, Oliver William Pawelek
Finding Maximal Cap Sizes For Quad Card Decks Using Share Strings, Oliver William Pawelek
Senior Projects Spring 2024
This project introduces the concept of share strings and how they can be used to figure out maximal cap sizes for different decks of the card game EvenQuads. We prove that all caps must map to a share string with respect to a basis and that if no share strings exist for cap size k in a given dimension d, then the maximal cap size of that dimension M (d) must be less than k. We prove the maximal cap sizes up to dimension 7 and show that there are at most 8 possible share strings for 19-caps of dimension …
College Algebra, Leslie Bain
College Algebra, Leslie Bain
ATU Faculty OER Book Reviews
Review of OER College Algebra textbook by Carl Stitz, available at https://open.umn.edu/opentextbooks/textbooks/college-algebra
Bridging Biological Systems With Social Behavior, Conservation, Decision Making, And Well-Being Through Hybrid Mathematical Modeling, Maggie Renee Sullens
Bridging Biological Systems With Social Behavior, Conservation, Decision Making, And Well-Being 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.
Zeckendorf Representation Analysis On Third Order Fibonacci Sequences That Do Not Satisfy The Uniqueness Property, Samuel A. Aguilar
Zeckendorf Representation Analysis On Third Order Fibonacci Sequences That Do Not Satisfy The Uniqueness Property, Samuel A. Aguilar
Honors College Theses
Zeckendorf's Theorem states that every natural number can be expressed uniquely as the sum of distinct non-consecutive terms of the shifted Fibonacci sequence (i.e. 1, 2, 3, 5, ...). This theorem has motivated the study of representation of integers by the sum of non-adjacent terms of Nth order Fibonacci sequences, including the characterization of the uniqueness of Zeckendorf representation based on the initial terms of the sequence. Moreover, when this uniqueness property is satisfied for third order Fibonacci sequences, the ratio of integers less than a given number X that have a Zeckendorf representation has been estimated by Dr. Sungkon …
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 K-12 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 low-socioeconomic 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 …
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 …
Examining The Effectiveness Of Using Point-Of-View 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 & Rubinstein-Ávila, 2018), the need for evidence-based math interventions focused on the math development of individuals with LD also increases. Although VM is recognized as an Evidence-based 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. Monte-Serrat, Carlo Cattani
Towards Ethical Ai: Mathematics Influences Human Behavior, Dioneia M. Monte-Serrat, 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 audio-recorded 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 …