Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Algebra (7)
- Geometry and Topology (6)
- Education (4)
- Logic and Foundations (4)
- Analysis (3)
-
- Applied Mathematics (3)
- Discrete Mathematics and Combinatorics (3)
- Number Theory (3)
- Other Mathematics (3)
- Curriculum and Instruction (2)
- Educational Methods (2)
- Other Education (2)
- Science and Mathematics Education (2)
- Architectural History and Criticism (1)
- Architecture (1)
- Arts and Humanities (1)
- Dynamical Systems (1)
- Educational Psychology (1)
- Junior High, Intermediate, Middle School Education and Teaching (1)
- Medicine and Health Sciences (1)
- Non-linear Dynamics (1)
- Physics (1)
- Quantum Physics (1)
- Secondary Education (1)
- Statistics and Probability (1)
- Teacher Education and Professional Development (1)
- Institution
-
- University of New Mexico (4)
- Claremont Colleges (3)
- Andrews University (2)
- Loyola Marymount University and Loyola Law School (2)
- Bowling Green State University (1)
-
- Chapman University (1)
- City University of New York (CUNY) (1)
- GALILEO, University System of Georgia (1)
- Georgia Southern University (1)
- Gettysburg College (1)
- Illinois Math and Science Academy (1)
- Merrimack College (1)
- Portland State University (1)
- Prairie View A&M University (1)
- Selected Works (1)
- University of Massachusetts Amherst (1)
- University of Nebraska - Lincoln (1)
- Western University (1)
- Keyword
-
- Geometry (5)
- Algebra (3)
- Tropical geometry (3)
- Algebraic geometry (2)
- Education (2)
-
- Math (2)
- Mathematics (2)
- Vertices (2)
- (Semi)topological BCC-algebra (1)
- 14T05 (1)
- Algebraic Geometry (1)
- Analytic functions in the unit disk (1)
- Architecture (1)
- Arithmetic statistics (1)
- Asymptotics (1)
- Automorphic forms (1)
- Bergman kernel (1)
- Beurling-Lax theorem (1)
- Book embeddings (1)
- Bounded domains (1)
- Category Theory (1)
- Catholic middle school mathematics (1)
- Cheat sheet (1)
- Combinatorics (1)
- Complete graphs (1)
- Coordinate geometry (1)
- Curves (1)
- De Branges Rovnyak spaces (1)
- Descartes (1)
- Enumerative geometry (1)
- Publication
-
- Branch Mathematics and Statistics Faculty and Staff Publications (4)
- Faculty Publications (2)
- HMC Senior Theses (2)
- Applications and Applied Mathematics: An International Journal (AAM) (1)
- Blake Mellor (1)
-
- Department of Mathematics: Dissertations, Theses, and Student Research (1)
- Dissertations, Theses, and Capstone Projects (1)
- Doctoral Dissertations (1)
- Electronic Theses and Dissertations (1)
- Electronic Thesis and Dissertation Repository (1)
- Honors Projects (1)
- Honors Thesis (1)
- Journal of Catholic Education (1)
- Journal of Humanistic Mathematics (1)
- Math Faculty Publications (1)
- Mathematics Faculty Publications (1)
- Mathematics Grants Collections (1)
- Mathematics, Physics, and Computer Science Faculty Articles and Research (1)
- Professional Learning Day (1)
- Student Research Symposium (1)
Articles 1 - 25 of 25
Full-Text Articles in Algebraic Geometry
A Categorical Formulation Of Algebraic Geometry, Bradley Willocks
A Categorical Formulation Of Algebraic Geometry, Bradley Willocks
Doctoral Dissertations
We construct a category, $\Omega$, of which the objects are pointed categories and the arrows are pointed correspondences. The notion of a ``spec datum" is introduced, as a certain relation between categories, of which one has been given a Grothendieck topology. A ``geometry" is interpreted as a sub-category of $\Omega$, and a formalism is given by which such a subcategory is to be associated to a spec datum, reflecting the standard construction of the category of schemes from the category of rings by affine charts.
Graph Structures In Bipolar Neutrosophic Environment, Florentin Smarandache, Muhammad Akram, Muzzamal Sitara
Graph Structures In Bipolar Neutrosophic Environment, Florentin Smarandache, Muhammad Akram, Muzzamal Sitara
Branch Mathematics and Statistics Faculty and Staff Publications
A bipolar single-valued neutrosophic (BSVN) graph structure is a generalization of a bipolar fuzzy graph. In this research paper, we present certain concepts of BSVN graph structures. We describe some operations on BSVN graph structures and elaborate on these with examples. Moreover, we investigate some related properties of these operations.
Neutrosophic Commutative N-Ideals In Bck-Algebras, Florentin Smarandache, Seok-Zun Song, Young Bae Jun
Neutrosophic Commutative N-Ideals In Bck-Algebras, Florentin Smarandache, Seok-Zun Song, Young Bae Jun
Branch Mathematics and Statistics Faculty and Staff Publications
The notion of a neutrosophic commutative N -ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N -ideal and a neutrosophic commutative N -ideal are discussed. Characterizations of a neutrosophic commutative N -ideal are considered.
Ideal Containments Under Flat Extensions And Interpolation On Linear Systems In P2, Solomon Akesseh
Ideal Containments Under Flat Extensions And Interpolation On Linear Systems In P2, Solomon Akesseh
Department of Mathematics: Dissertations, Theses, and Student Research
Fat points and their ideals have stimulated a lot of research but this dissertation concerns itself with aspects of only two of them, broadly categorized here as, the ideal containments and polynomial interpolation problems.
Ein-Lazarsfeld-Smith and Hochster-Huneke cumulatively showed that for all ideals I in k[Pn], I(mn) ⊆ Im for all m ∈ N. Over the projective plane, we obtain I(4)< ⊆ I2. Huneke asked whether it was the case that I(3) ⊆ I2. Dumnicki, Szemberg and Tutaj-Gasinska show that if I is the saturated homogeneous radical ideal of the 12 …
Descartes Comes Out Of The Closet, Nora E. Culik
Descartes Comes Out Of The Closet, Nora E. Culik
Journal of Humanistic Mathematics
While “Descartes Comes Out of the Closet” is ostensibly about a young woman’s journey to Paris, the descriptive detail borrows language and images from Cartesian coordinate geometry, dualistic philosophy, neuroanatomy (the pineal), and projections of three dimensions onto planes. This mathematical universe is counterpointed in the natural language of the suppressed love story that locates the real in the human. Thus, at the heart of the story is the tension between competing notions of mathematics, i.e., as either an independent realm apart from history or as a culturally produced and historical set of practices. Of course, the central character proves …
College Algebra, Trigonometry, And Precalculus (Clayton), Chaogui Zhang, Scott Bailey, Billie May, Jelinda Spotorno, Kara Mullen
College Algebra, Trigonometry, And Precalculus (Clayton), Chaogui Zhang, Scott Bailey, Billie May, Jelinda Spotorno, Kara Mullen
Mathematics Grants Collections
This Grants Collection for College Algebra, Trigonometry, and Precalculus was created under a Round Five ALG Textbook Transformation Grant.
Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.
Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:
- Linked Syllabus
- Initial Proposal
- Final Report
Counting Rational Points, Integral Points, Fields, And Hypersurfaces, Joseph Gunther
Counting Rational Points, Integral Points, Fields, And Hypersurfaces, Joseph Gunther
Dissertations, Theses, and Capstone Projects
This thesis comes in four parts, which can be read independently of each other.
In the first chapter, we prove a generalization of Poonen's finite field Bertini theorem, and use this to show that the obvious obstruction to embedding a curve in some smooth surface is the only obstruction over perfect fields, extending a result of Altman and Kleiman. We also prove a conjecture of Vakil and Wood on the asymptotic probability of hypersurface sections having a prescribed number of singularities.
In the second chapter, for a fixed base curve over a finite field of characteristic at least 5, we …
On (Semi)Topological Bcc-Algebras, F. R. Setudeh, N. Kouhestani
On (Semi)Topological Bcc-Algebras, F. R. Setudeh, N. Kouhestani
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we introduce the notion of (semi)topological BCC-algebras and derive here conditions that imply a BCC-algebra to be a (semi)topological BCC-algebra. We prove that for each cardinal number α there is at least a (semi)topological BCC-algebra of order α: Also we study separation axioms on (semi)topological BCC-algebras and show that for any infinite cardinal number α there is a Hausdorff (semi)topological BCC-algebra of order α with nontrivial topology.
Klein Four Actions On Graphs And Sets, Darren B. Glass
Klein Four Actions On Graphs And Sets, Darren B. Glass
Math Faculty Publications
We consider how a standard theorem in algebraic geometry relating properties of a curve with a (ℤ/2ℤ)2-action to the properties of its quotients generalizes to results about sets and graphs that admit (ℤ/2ℤ)2-actions.
Cox Processes For Visual Object Counting, Yongming Ma
Cox Processes For Visual Object Counting, Yongming Ma
Student Research Symposium
We present a model that utilizes Cox processes and CNN classifiers in order to count the number of instances of an object in an image. Poisson processes are well suited to events that occur randomly in space, like the location of objects in an image, as well as to the task of counting. Mixed Poisson processes also offer increased flexibility, however they do not easily scale with image size: they typically require O(n3) computation time and O(n2) storage, where n is the number of pixels. To mitigate this problem, we employ Kronecker algebra which takes advantage of the direct product …
Integrating Non-Euclidean Geometry Into High School, John Buda
Integrating Non-Euclidean Geometry Into High School, John Buda
Honors Thesis
The purpose of this project is to provide the framework for integrating the study of non-Euclidean geometry into a high school math class in such a way that both aligns with the Common Core State Standards and makes use of research-based practices to enhance the learning of traditional geometry. Traditionally, Euclidean geometry has been the only strand of geometry taught in high schools, even though mathematicians have developed several other strands. The non-Euclidean geometry that I focus on in this project is what is known as taxicab geometry. With the Common Core Standards for Math Practice pushing students to “model …
Beurling-Lax Type Theorems In The Complex And Quaternionic Setting, Daniel Alpay, Irene Sabadini
Beurling-Lax Type Theorems In The Complex And Quaternionic Setting, Daniel Alpay, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
We give a generalization of the Beurling–Lax theorem both in the complex and quaternionic settings. We consider in the first case functions meromorphic in the right complex half-plane, and functions slice hypermeromorphic in the right quaternionic half-space in the second case. In both settings we also discuss a unified framework, which includes both the disk and the half-plane for the complex case and the open unit ball and the half-space in the quaternionic setting.
Student-Created Test Sheets, Samuel Laderach
Student-Created Test Sheets, Samuel Laderach
Honors Projects
Assessment plays a necessary role in the high school mathematics classroom, and testing is a major part of assessment. Students often struggle with mathematics tests and examinations due to math and test anxiety, a lack of student learning, and insufficient and inefficient student preparation. Practice tests, teacher-created review sheets, and student-created test sheets are ways in which teachers can help increase student performance, while ridding these detrimental factors. Student-created test sheets appear to be the most efficient strategy, and this research study examines the effects of their use in a high school mathematics classroom.
On Vector-Valued Automorphic Forms On Bounded Symmetric Domains, Nadia Alluhaibi
On Vector-Valued Automorphic Forms On Bounded Symmetric Domains, Nadia Alluhaibi
Electronic Thesis and Dissertation Repository
The objective of the study is to investigate the behaviour of the inner products of vector-valued Poincare series, for large weight, associated to submanifolds of a quotient of the complex unit ball and how vector-valued automorphic forms could be constructed via Poincare series. In addition, it provides a proof of that vector-valued Poincare series on an irreducible bounded symmetric domain span the space of vector-valued automorphic forms.
Polygons, Pillars And Pavilions: Discovering Connections Between Geometry And Architecture, Sean Patrick Madden
Polygons, Pillars And Pavilions: Discovering Connections Between Geometry And Architecture, Sean Patrick Madden
Journal of Catholic Education
Crowning the second semester of geometry, taught within a Catholic middle school, the author's students explored connections between the geometry of regular polygons and architecture of local buildings. They went on to explore how these principles apply famous buildings around the world such as the monuments of Washington, D.C. and the elliptical piazza of Saint Peter's Basilica at Vatican City within Rome, Italy.
Classification Of Rectifying Space-Like Submanifolds In Pseudo-Euclidean Spaces, Bang Yen Chan, Yun Myung Oh
Classification Of Rectifying Space-Like Submanifolds In Pseudo-Euclidean Spaces, Bang Yen Chan, Yun Myung Oh
Faculty Publications
The notions of rectifying subspaces and of rectifying submanifolds were introduced in [B.-Y. Chen, Int. Electron. J. Geom 9 (2016), no. 2, 1–8]. More precisely, a submanifold in a Euclidean m-space Em is called a rectifying submanifold if its position vector field always lies in its rectifying subspace. Several fundamental properties and classification of rectifying submanifolds in Euclidean space were obtained in [B.-Y. Chen, op. cit.]. In this present article, we extend the results in [B.-Y. Chen, op. cit.] to rectifying space- like submanifolds in a pseudo-Euclidean space with arbitrary codimension. In particular, we completely classify all rectifying space-like submanifolds …
Session A-3: Three-Act Math Tasks, Lindsey Herlehy
Session A-3: Three-Act Math Tasks, Lindsey Herlehy
Professional Learning Day
Participants will engage in a Three-Act Math task highlighting the application of properties of geometrical figures. Developed by Dan Meyer, an innovative and highly regarded mathematics instructor, Three-Act Math tasks utilize pedagogical skills that elicit student curiosity, collaboration and questioning. By posing a mathematical problem through active storytelling, this instructional approach redefines real-world mathematics and clarifies the role that a student plays in the learning process. Participants will be given multiple resources where they can access Three-Act Math tasks appropriate for upper elementary grades through Algebra and Geometry courses.
Classification Of Book Representations Of K6, Dana Rowland
Classification Of Book Representations Of K6, Dana Rowland
Mathematics Faculty Publications
A book representation of a graph is a particular way of embedding a graph in three dimensional space so that the vertices lie on a circle and the edges are chords on disjoint topological disks. We describe a set of operations on book representations that preserves ambient isotopy, and apply these operations to K6, the complete graph with six vertices. We prove there are exactly 59 distinct book representations for K6, and we identify the number and type of knotted and linked cycles in each representation. We show that book representations of K6 contain between one and seven links, and …
Drawing A Triangle On The Thurston Model Of Hyperbolic Space, Curtis D. Bennett, Blake Mellor, Patrick D. Shanahan
Drawing A Triangle On The Thurston Model Of Hyperbolic Space, Curtis D. Bennett, Blake Mellor, Patrick D. Shanahan
Blake Mellor
In looking at a common physical model of the hyperbolic plane, the authors encountered surprising difficulties in drawing a large triangle. Understanding these difficulties leads to an intriguing exploration of the geometry of the Thurston model of the hyperbolic plane. In this exploration we encounter topics ranging from combinatorics and Pick’s Theorem to differential geometry and the Gauss-Bonnet Theorem.
Random Tropical Curves, Magda L. Hlavacek
Random Tropical Curves, Magda L. Hlavacek
HMC Senior Theses
In the setting of tropical mathematics, geometric objects are rich with inherent combinatorial structure. For example, each polynomial $p(x,y)$ in the tropical setting corresponds to a tropical curve; these tropical curves correspond to unbounded graphs embedded in $\R^2$. Each of these graphs is dual to a particular subdivision of its Newton polytope; we classify tropical curves by combinatorial type based on these corresponding subdivisions. In this thesis, we aim to gain an understanding of the likeliness of the combinatorial type of a randomly chosen tropical curve by using methods from polytope geometry. We focus on tropical curves corresponding to quadratics, …
Tropical Derivation Of Cohomology Ring Of Heavy/Light Hassett Spaces, Shiyue Li
Tropical Derivation Of Cohomology Ring Of Heavy/Light Hassett Spaces, Shiyue Li
HMC Senior Theses
The cohomology of moduli spaces of curves has been extensively studied in classical algebraic geometry. The emergent field of tropical geometry gives new views and combinatorial tools for treating these classical problems. In particular, we study the cohomology of heavy/light Hassett spaces, moduli spaces of heavy/light weighted stable curves, denoted as $\calm_{g, w}$ for a particular genus $g$ and a weight vector $w \in (0, 1]^n$ using tropical geometry. We survey and build on the work of \citet{Cavalieri2014}, which proved that tropical compactification is a \textit{wonderful} compactification of the complement of hyperplane arrangement for these heavy/light Hassett spaces. For $g …
Neutrosophic Triplet Groups And Their Applications To Mathematical Modelling, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K.
Neutrosophic Triplet Groups And Their Applications To Mathematical Modelling, Florentin Smarandache, W.B. Vasantha Kandasamy, Ilanthenral K.
Branch Mathematics and Statistics Faculty and Staff Publications
The innovative notion of neutrosophic triplet groups, introduced by Smarandache and Ali in 2014-2016, happens to yield the anti-element and neutral element once the element is given. It is established that the neutrosophic triplet group collection forms the classical group under product for Zn, for some specific n. However the collection is not even closed under sum. These neutrosophic triplet groups are built using only modulo integers or Cayley tables. Several interesting properties related with them are defined. It is pertinent to record that in Zn, when n is a prime number, we cannot get a neutral element which can …
Curiozităţi Ale Funcţiilor Supermatematice, Florentin Smarandache, Mircea Eugen Selariu
Curiozităţi Ale Funcţiilor Supermatematice, Florentin Smarandache, Mircea Eugen Selariu
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
Characterization Of Rectifying And Sphere Curves In R^3, Yun Myung Oh, Julie Logan
Characterization Of Rectifying And Sphere Curves In R^3, Yun Myung Oh, Julie Logan
Faculty Publications
Studies of curves in 3D-space have been developed by many geometers and it is known that any regular curve in 3D space is completely determined by its curvature and torsion, up to position. Many results have been found to characterize various types of space curves in terms of conditions on the ratio of torsion to curvature. Under an extracondition on the constant curvature, Y.L. Seo and Y. M. Oh found the series solution when the ratio of torsion to curvature is a linear function. Furthermore, this solution is known to be a rectifying curve by B. Y. Chen’s work. This …
A Journey To Fuzzy Rings, Brett T. Ernst
A Journey To Fuzzy Rings, Brett T. Ernst
Electronic Theses and Dissertations
Enumerative geometry is a very old branch of algebraic geometry. In this thesis, we will describe several classical problems in enumerative geometry and their solutions in order to motivate the introduction of tropical geometry. Finally, fuzzy rings, a powerful algebraic framework for tropical and algebraic geometry is introduced.