Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Other Mathematics (23)
- Logic and Foundations (17)
- Algebraic Geometry (10)
- Analysis (10)
- Number Theory (10)
-
- Applied Mathematics (9)
- Discrete Mathematics and Combinatorics (8)
- Computer Sciences (7)
- Engineering (7)
- Computer Engineering (6)
- Other Computer Engineering (6)
- Other Computer Sciences (6)
- Education (5)
- Geometry and Topology (4)
- Numerical Analysis and Computation (4)
- Set Theory (4)
- Arts and Humanities (2)
- Curriculum and Instruction (2)
- Other Applied Mathematics (2)
- Physics (2)
- Science and Mathematics Education (2)
- Acoustics, Dynamics, and Controls (1)
- Art and Design (1)
- Business (1)
- Christianity (1)
- Computer-Aided Engineering and Design (1)
- Educational Administration and Supervision (1)
- Institution
-
- Chapman University (15)
- University of New Mexico (10)
- University of Nebraska - Lincoln (6)
- University of Richmond (5)
- Claremont Colleges (3)
-
- Utah State University (3)
- California State University, San Bernardino (2)
- Loyola Marymount University and Loyola Law School (2)
- Prairie View A&M University (2)
- California Polytechnic State University, San Luis Obispo (1)
- Calvin University (1)
- City University of New York (CUNY) (1)
- Dordt University (1)
- Georgia Southern University (1)
- Georgia State University (1)
- Lawrence University (1)
- Olivet Nazarene University (1)
- Portland State University (1)
- Technological University Dublin (1)
- Union College (1)
- University of Arkansas, Fayetteville (1)
- University of Denver (1)
- University of North Florida (1)
- University of Puget Sound (1)
- University of Tennessee, Knoxville (1)
- Western Kentucky University (1)
- Western Michigan University (1)
- Wofford College (1)
- Keyword
-
- Neutrosophic logic (7)
- Mathematics (5)
- Algebra (3)
- Complex variables (3)
- Abstract algebra (2)
-
- Algebraic structures (2)
- Convolution algebra (2)
- Education (2)
- Functional analysis (2)
- George Boole (2)
- Group theory (2)
- Nominal sets (2)
- Number theory (2)
- Operator algebras (2)
- Residuated lattice (2)
- Schur analysis (2)
- Subset (2)
- (Self-distributive (1)
- (commutative (1)
- *-even matrix polynomial (1)
- 15A23 Factorization of matrices (1)
- 2D lattice Z2 (1)
- 65F99 Numerical linear algebra (1)
- Abelian (1)
- Abeliangroup (1)
- Abstract Algebra -- Study and teaching (1)
- Academic -- UNF -- Master of Science in Mathematical Science; Dissertations (1)
- Academic -- UNF -- Mathematics; math; mathematics; singular values; linear algebra (1)
- Academic Achievement (1)
- Al-Khwarizmi (1)
- Publication
-
- Branch Mathematics and Statistics Faculty and Staff Publications (10)
- Mathematics, Physics, and Computer Science Faculty Articles and Research (9)
- Department of Mathematics: Dissertations, Theses, and Student Research (6)
- Engineering Faculty Articles and Research (6)
- Department of Math & Statistics Faculty Publications (5)
-
- How to... in 10 minutes or less (3)
- Applications and Applied Mathematics: An International Journal (AAM) (2)
- Dissertations (2)
- Mathematics Faculty Works (2)
- Theses Digitization Project (2)
- Arthur Vining Davis High Impact Fellows Projects (1)
- Articles (1)
- Dissertations and Theses (1)
- Doctoral Dissertations (1)
- Electronic Theses and Dissertations (1)
- Faculty Work Comprehensive List (1)
- Georgia State Undergraduate Research Conference (1)
- Graduate Theses and Dissertations (1)
- HMC Senior Theses (1)
- Honors Program Projects (1)
- Honors Theses (1)
- Journal of Humanistic Mathematics (1)
- Lawrence University Honors Projects (1)
- Mathematics Preprint Series (1)
- Publications and Research (1)
- STAR Program Research Presentations (1)
- Summer Research (1)
- The STEAM Journal (1)
- UNF Graduate Theses and Dissertations (1)
- University Faculty Publications and Creative Works (1)
- Publication Type
Articles 1 - 30 of 67
Full-Text Articles in Algebra
The Effects Of Standards-Based Grading On Student Performance In Algebra 2, Rachel Beth Rosales
The Effects Of Standards-Based Grading On Student Performance In Algebra 2, Rachel Beth Rosales
Dissertations
The use of standards-based grading in American public schools is increasing, offering students, parents, and teachers a new way of measuring and communicating about student achievement and performance. Parents indicate an appreciation for this method of grading, and students at the elementary grades (K-6) have improved standardized test scores in reading and math as a result of its implementation. This study seeks to determine whether standards-based grading has the same effect on students at the high school level (grades 9-12) by comparing end-of-course test scores and posttest scores of Algebra 2 students enrolled in a standards-based graded classroom with to …
Instability Indices For Matrix Polynomials, Todd Kapitula, Elizabeth Hibma, Hwa Pyeong Kim, Jonathan Timkovich
Instability Indices For Matrix Polynomials, Todd Kapitula, Elizabeth Hibma, Hwa Pyeong Kim, Jonathan Timkovich
University Faculty Publications and Creative Works
There is a well-established instability index theory for linear and quadratic matrix polynomials for which the coefficient matrices are Hermitian and skew-Hermitian. This theory relates the number of negative directions for the matrix coefficients which are Hermitian to the total number of unstable eigenvalues for the polynomial. Herein we extend the theory to *-even matrix polynomials of any finite degree. In particular, unlike previously known cases we show that the instability index depends upon the size of the matrices when the degree of the polynomial is greater than two. We also consider Hermitian matrix polynomials, and derive an index which …
Relation Between Hilbert Algebras And Be–Algebras, A. Rezaei, A. B. Saeid, R. A. Borzooei
Relation Between Hilbert Algebras And Be–Algebras, A. Rezaei, A. B. Saeid, R. A. Borzooei
Applications and Applied Mathematics: An International Journal (AAM)
Hilbert algebras are introduced for investigations in intuitionistic and other non - classical logics and BE -algebra is a generalization of dual BCK -algebra. In this paper, we investigate the relationship between Hilbert algebras and BE -algebras. In fact, we show that a commutative implicative BE -algebra is equivalent to the commutative self distributive BE -algebra, therefore Hilbert algebras and commutative self distributive BE -algebras are equivalent.
The Quantum Gromov-Hausdorff Propinquity, Frédéric Latrémolière
The Quantum Gromov-Hausdorff Propinquity, Frédéric Latrémolière
Mathematics Preprint Series
We introduce the quantum Gromov-Hausdorff propinquity, a new distance between quantum compact metric spaces, which extends the GromovHausdorff distance to noncommutative geometry and strengthens Rieffel’s quantum Gromov-Hausdorff distance and Rieffel’s proximity by making *-isomorphism a necessary condition for distance zero, while being well adapted to Leibniz seminorms. This work offers a natural solution to the long-standing problem of finding a framework for the development of a theory of Leibniz Lip-norms over C*- algebras.
The Kronecker-Weber Theorem: An Exposition, Amber Verser
The Kronecker-Weber Theorem: An Exposition, Amber Verser
Lawrence University Honors Projects
This paper is an investigation of the mathematics necessary to understand the Kronecker-Weber Theorem. Following an article by Greenberg, published in The American Mathematical Monthly in 1974, the presented proof does not use class field theory, as the most traditional treatments of the theorem do, but rather returns to more basic mathematics, like the original proofs of the theorem. This paper seeks to present the necessary mathematical background to understand the proof for a reader with a solid undergraduate background in abstract algebra. Its goal is to make what is usually an advanced topic in the study of algebraic number …
A Primer For Mathematical Modeling, Marla A. Sole
A Primer For Mathematical Modeling, Marla A. Sole
Publications and Research
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school with the mathematics they will use outside of school. Instructors have found mathematical modeling difficult to teach. To successfully incorporate modeling activities I believe that curricular changes should be accompanied by professional development for curriculum developers, classroom teachers, and higher education professionals. This article serves as an introduction to modeling by …
Characterization Of The Drilling Via The Vibration Augmenter Of Rotary-Drills And Sound Signal Processing Of Impacted Pipe As A Potential Water Height Assessment Tool, Nicholas Morris
STAR Program Research Presentations
The focus of the internship has been on two topics: a) Characterize the drilling performance of a novel percussive augmenter – this drill was developed by the JPL’s Advanced Technologies Group and its performance was characterized; and b) Examine the feasibility of striking a pipe as a means of assessing the water height inside the pipe. The purpose of this investigation is to examine the possibility of using a simple method of applying impacts to a pipe wall and determining the water height from the sonic characteristic differences including damping, resonance frequencies, etc. Due to multiple variables that are relevant …
Decompositions Of Betti Diagrams, Courtney Gibbons
Decompositions Of Betti Diagrams, Courtney Gibbons
Department of Mathematics: Dissertations, Theses, and Student Research
In this dissertation, we are concerned with decompositions of Betti diagrams over standard graded rings and the information about that ring and its modules that can be recovered from these decompositions. In Chapter 2, we study the structure of modules over short Gorenstein graded rings and determine a necessary condition for a matrix of nonnegative integers to be the Betti diagram of such a module. We also describe the cone of Betti diagrams over the ring k[x,y]/(x2,y2), and we provide an algorithm for decomposing Betti diagrams, even for modules of infinite projective dimension. Chapter 3 …
Closure And Homological Properties Of (Auto)Stackable Groups, Ashley Johnson
Closure And Homological Properties Of (Auto)Stackable Groups, Ashley Johnson
Department of Mathematics: Dissertations, Theses, and Student Research
Let G be a finitely presented group with Cayley graph Γ. Roughly, G is a stackable group if there is a maximal tree T in Γ and a function φ, defined on the edges in Γ, for which there is a natural ‘flow’ on the edges in Γ\T towards the identity. Additionally, if graph (φ), which consists of pairs (e; φ(e)) for e an edge in Γ, forms a regular language, then G is autostackable. In 2011, Brittenham and Hermiller introduced stackable groups in [4], in part, as a means …
Geometric Study Of The Category Of Matrix Factorizations, Xuan Yu
Geometric Study Of The Category Of Matrix Factorizations, Xuan Yu
Department of Mathematics: Dissertations, Theses, and Student Research
We study the geometry of matrix factorizations in this dissertation.
It contains two parts. The first one is a Chern-Weil style
construction for the Chern character of matrix factorizations; this
allows us to reproduce the Chern character in an explicit,
understandable way. Some basic properties of the Chern character are
also proved (via this construction) such as functoriality and that
it determines a ring homomorphism from the Grothendieck group of
matrix factorizations to its Hochschild homology. The second part is
a reconstruction theorem of hypersurface singularities. This is
given by applying a slightly modified version of Balmer's tensor
triangular geometry …
Embedding And Nonembedding Results For R. Thompson's Group V And Related Groups, Nathan Corwin
Embedding And Nonembedding Results For R. Thompson's Group V And Related Groups, Nathan Corwin
Department of Mathematics: Dissertations, Theses, and Student Research
We study Richard Thompson's group V, and some generalizations of this group. V was one of the first two examples of a finitely presented, infinite, simple group. Since being discovered in 1965, V has appeared in a wide range of mathematical subjects. Despite many years of study, much of the structure of V remains unclear. Part of the difficulty is that the standard presentation for V is complicated, hence most algebraic techniques have yet to prove fruitful.
This thesis obtains some further understanding of the structure of V by showing the nonexistence of the wreath product Z wr Z^2 as …
A New Implementation Of Gmres Using Generalized Purcell Method, Morteza Rahmani, Sayed H. Momeni-Masuleh
A New Implementation Of Gmres Using Generalized Purcell Method, Morteza Rahmani, Sayed H. Momeni-Masuleh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a new method based on the generalized Purcell method is proposed to solve the usual least-squares problem arising in the GMRES method. The theoretical aspects and computational results of the method are provided. For the popular iterative method GMRES, the decomposition matrices of the Hessenberg matrix is obtained by using a simple recursive relation instead of Givens rotations. The other advantages of the proposed method are low computational cost and no need for orthogonal decomposition of the Hessenberg matrix or pivoting. The comparisons for ill-conditioned sparse standard matrices are made. They show a good agreement with available …
An Algebraic Approach To Number Theory Using Unique Factorization, Mark Sullivan
An Algebraic Approach To Number Theory Using Unique Factorization, Mark Sullivan
Honors Theses
Though it may seem non-intuitive, abstract algebra is often useful in the study of number theory. In this thesis, we explore some uses of abstract algebra to prove number theoretic statements. We begin by examining the structure of unique factorization domains in general. Then we introduce number fields and their rings of algebraic integers, whose structures have characteristics that are analogous to some of those of the rational numbers and the rational integers. Next we discuss quadratic fields, a special case of number fields that have important applications to number theoretic problems. We will use the structures that we introduce …
Al-Khwarizmi: Founder Of Classical Algebra, Calvin Jongsma
Al-Khwarizmi: Founder Of Classical Algebra, Calvin Jongsma
Faculty Work Comprehensive List
Adopting a historically defensible definition of “algebra,” we will begin by exploring a few examples of algebra prior to al-Khwarizmi. We will then examine what algebra became through al-Khwarizmi’s work. In conclusion, we will assess the historical importance of al-Khwarizmi’s contributions for developments in European algebra.
Establishing Foundations For Investigating Inquiry-Oriented Teaching, Estrella Maria Salas Johnson
Establishing Foundations For Investigating Inquiry-Oriented Teaching, Estrella Maria Salas Johnson
Dissertations and Theses
The Teaching Abstract Algebra for Understanding (TAAFU) project was centered on an innovative abstract algebra curriculum and was designed to accomplish three main objectives: to produce a set of multi-media support materials for instructors, to understand the challenges faced by mathematicians as they implemented this curriculum, and to study how this curriculum supports student learning of abstract algebra. Throughout the course of the project I took the lead investigating the teaching and learning in classrooms using the TAAFU curriculum. My dissertation is composed of three components of this research. First, I will report on a study that aimed to describe …
Structured Matrices And The Algebra Of Displacement Operators, Ryan Takahashi
Structured Matrices And The Algebra Of Displacement Operators, Ryan Takahashi
HMC Senior Theses
Matrix calculations underlie countless problems in science, mathematics, and engineering. When the involved matrices are highly structured, displacement operators can be used to accelerate fundamental operations such as matrix-vector multiplication. In this thesis, we provide an introduction to the theory of displacement operators and study the interplay between displacement and natural matrix constructions involving direct sums, Kronecker products, and blocking. We also investigate the algebraic behavior of displacement operators, developing results about invertibility and kernels.
Comparing The Impact Of Traditional And Modeling College Algebra Courses On Student Performance In Survey Of Calculus, Jerry West
Graduate Theses and Dissertations
Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to maximize students' potential in utilizing mathematics and gaining skills required in subsequent math-based courses when necessary. The Committee for Undergraduate Programs in Mathematics has gone through extensive work to help mathematics departments reform their college algebra courses in order to help students gain interest in the utilization of mathematics …
Multiplicative Sets Of Atoms, Ashley Nicole Rand
Multiplicative Sets Of Atoms, Ashley Nicole Rand
Doctoral Dissertations
It is possible for an element to have both an atom factorization and a factorization that will always contain a reducible element. This leads us to consider the multiplicatively closed set generated by the atoms and units of an integral domain. We start by showing that for a nice subset S of the atoms of R, there exists an integral domain containing R with set of atoms S. A multiplicatively closed set is saturated if the factors of each element in the set are also elements in the set. Considering polynomial and power series subrings, we find necessary and sufficient …
Symbolic Powers Of Ideals In K[PN], Michael Janssen
Symbolic Powers Of Ideals In K[PN], Michael Janssen
Department of Mathematics: Dissertations, Theses, and Student Research
Let I ⊆ k[PN] be a homogeneous ideal and k an algebraically closed field. Of particular interest over the last several years are ideal containments of symbolic powers of I in ordinary powers of I of the form I(m) ⊆ Ir, and which ratios m/r guarantee such containment. A result of Ein-Lazarsfeld-Smith and Hochster-Huneke states that, if I ⊆ k[PN], where k is an algebraically closed field, then the symbolic power I(Ne) is contained in the ordinary power Ie, and thus, whenever …
Periodic Modules Over Gorenstein Local Rings, Amanda Croll
Periodic Modules Over Gorenstein Local Rings, Amanda Croll
Department of Mathematics: Dissertations, Theses, and Student Research
It is proved that the minimal free resolution of a module M over a Gorenstein local ring R is eventually periodic if, and only if, the class of M is torsion in a certain Z[t,t^{-1}] associated to R. This module, denoted (R), is the free Z[t,t^{-1}]-module on the isomorphism classes of finitely generated R-modules modulo relations reminiscent of those defining the Grothendieck group of R. The main result is a structure theorem for J(R) when R is a complete Gorenstein local ring; the link between periodicity and torsion stated above is a corollary.
Advisor: Srikanth Iyengar
Finances & Algebra Too!, Anne J. Catlla, Jonathan Foster, Charlene Frazier
Finances & Algebra Too!, Anne J. Catlla, Jonathan Foster, Charlene Frazier
Arthur Vining Davis High Impact Fellows Projects
The focus of this project is to provide an application-based approach to teaching algebra 2. Students will study algebraic concepts and functions through the lens of personal finance. After each unit of study, students will complete a financial application project that will go into each student’s “financial” portfolio.
Weighted Shifts Of Finite Multiplicity, Daniel S. Sievewright
Weighted Shifts Of Finite Multiplicity, Daniel S. Sievewright
Dissertations
We will discuss the structure of weighted shift operators on a separable, infinite dimensional, complex Hilbert space. A weighted shift is said to have multiplicity n when all the weights are n x n matrices. To study these weighted shifts, we will investigate which operators can belong to the Deddens algebras and spectral radius algebras, which can be quite large. This will lead to the necessary and sufficient conditions for these algebras to have a nontrivial invariant subspace.
Slicing A Puzzle And Finding The Hidden Pieces, Martha Arntson
Slicing A Puzzle And Finding The Hidden Pieces, Martha Arntson
Honors Program Projects
The research conducted was to investigate the potential connections between group theory and a puzzle set up by color cubes. The goal of the research was to investigate different sized puzzles and discover any relationships between solutions of the same sized puzzles. In this research, first, there was an extensive look into the background of Abstract Algebra and group theory, which is briefly covered in the introduction. Then, each puzzle of various sizes was explored to find all possible color combinations of the solutions. Specifically, the 2x2x2, 3x3x3, and 4x4x4 puzzles were examined to find that the 2x2x2 has 24 …
Propeller, Joel Kahn
Propeller, Joel Kahn
The STEAM Journal
This image is based on several different algorithms interconnected within a single program in the language BASIC-256. The fundamental structure involves a tightly wound spiral working outwards from the center of the image. As the spiral is drawn, different values of red, green and blue are modified through separate but related processes, producing the changing appearance. Algebra, trigonometry, geometry, and analytic geometry are all utilized in overlapping ways within the program. As with many works of algorithmic art, small changes in the program can produce dramatic alterations of the visual output, which makes lots of variations possible.
Polynomial Functions Over Finite Fields, John J. Hull
Polynomial Functions Over Finite Fields, John J. Hull
Georgia State Undergraduate Research Conference
No abstract provided.
How To Find A Levi Decomposition Of A Lie Algebra, Ian M. Anderson
How To Find A Levi Decomposition Of A Lie Algebra, Ian M. Anderson
How to... in 10 minutes or less
We show how to compute the Levi decomposition of a Lie algebra in Maple using the command LeviDecomposition. A worksheet and corresponding PDF can be found below.
How To Create A Jordan Algebra, Ian M. Anderson, Thomas J. Apedaile
How To Create A Jordan Algebra, Ian M. Anderson, Thomas J. Apedaile
How to... in 10 minutes or less
We show how to create a Jordan algebra in Maple using the commands AlgebraLibraryData and AlgebraData.
How To Create The Quaternion & Octonion Algebras, Ian M. Anderson, Thomas J. Apedaile
How To Create The Quaternion & Octonion Algebras, Ian M. Anderson, Thomas J. Apedaile
How to... in 10 minutes or less
We show how to create the quaternion and octonion algebras with the DifferentialGeometry software. For each algebra, there is a split-form also available.
On Contemplation In Mathematics, Frank Lucas Wolcott
On Contemplation In Mathematics, Frank Lucas Wolcott
Journal of Humanistic Mathematics
In a section about research, we make the case that intentional, structured reflection on the mathematical research process, by mathematical researchers themselves, would result in better mathematicians doing better mathematics. As supporting evidence, we describe the Flavors and Seasons project. In a section about teaching, we describe the contemplative education movement and share personal experiences using meditation in the math classroom. We conclude with an explicit proposal for elucidating the experiential context of mathematics, in both research and teaching environments.
Relation Lifting, With An Application To The Many-Valued Cover Modality, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jirí Velebil
Relation Lifting, With An Application To The Many-Valued Cover Modality, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jirí Velebil
Engineering Faculty Articles and Research
We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the existence of a distributive law of T over the “powerset monad” on categories, one is the preservation by T of “exactness” of certain squares. Both characterisations are generalisations of the “classical” results known for set functors: the first characterisation generalises the existence of a distributive law over the genuine powerset monad, the second generalises preservation of weak pullbacks.
The results presented in this paper …