Open Access. Powered by Scholars. Published by Universities.®

Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

11,358 Full-Text Articles 9,697 Authors 1,601,107 Downloads 203 Institutions

All Articles in Mathematics

Faceted Search

11,358 full-text articles. Page 1 of 320.

Mathematical Analysis Ii, Ismail Nikoufar 2016 Payame Noor University

Mathematical Analysis Ii, Ismail Nikoufar

Ismail Nikoufar

No abstract provided.


Quaternion Algebras And Hyperbolic 3-Manifolds, Joseph Quinn 2016 Graduate Center, City University of New York

Quaternion Algebras And Hyperbolic 3-Manifolds, Joseph Quinn

All Graduate Works by Year: Dissertations, Theses, and Capstone Projects

I use a classical idea of Macfarlane to obtain a complex quaternion model for hyperbolic 3-space and its group of orientation-preserving isometries, analogous to Hamilton’s famous result on Euclidean rotations. I generalize this to quaternion models over number fields for the action of Kleinian groups on hyperbolic 3-space, using arithmetic invariants of the corresponding hyperbolic 3-manifolds. The class of manifolds to which this technique applies includes all cusped arithmetic manifolds and infinitely many commensurability classes of cusped non-arithmetic, compact arithmetic, and compact non-arithmetic manifolds. I obtain analogous results for actions of Fuchsian groups on the hyperbolic plane. I develop ...


The Remedy That's Killing: Cuny, Laguardia, And The Fight For Better Math Policy, Rachel A. Oppenheimer 2016 Graduate Center, City University of New York

The Remedy That's Killing: Cuny, Laguardia, And The Fight For Better Math Policy, Rachel A. Oppenheimer

All Graduate Works by Year: Dissertations, Theses, and Capstone Projects

Nationwide, there is a crisis in math learning and math achievement at all levels of education. Upwards of 80% of students who enter the City University of New York’s community colleges from New York City’s Department of Education high schools fail to meet college level math proficiencies and as a result, are funneled into the system’s remedial math system. Once placed into pre-college remedial arithmetic, pre-algebra, and elementary algebra courses, students fail at alarming rates and research indicates that students’ failure in remedial math has negative ripple effects on their persistence and degree completion. CUNY is not ...


P-Adic L-Functions And The Geometry Of Hida Families, Joseph Kramer-Miller 2016 Graduate Center, City University of New York

P-Adic L-Functions And The Geometry Of Hida Families, Joseph Kramer-Miller

All Graduate Works by Year: Dissertations, Theses, and Capstone Projects


A major theme in the theory of $p$-adic deformations of automorphic forms is how $p$-adic $L$-functions over eigenvarieties relate to the geometry of these eigenvarieties. In this talk we explain results in this vein for the ordinary part of the eigencurve (i.e. Hida families). We address how Taylor expansions of one variable $p$-adic $L$-functions varying over families can detect geometric phenomena: crossing components of a certain intersection multiplicity and ramification over the weight space. Our methods involve proving a converse to a result of Vatsal relating congruences between eigenforms to their algebraic special $L ...


Cohomology Of Certain Polyhedral Product Spaces, Elizabeth A. Vidaurre 2016 Graduate Center, City University of New York

Cohomology Of Certain Polyhedral Product Spaces, Elizabeth A. Vidaurre

All Graduate Works by Year: Dissertations, Theses, and Capstone Projects

The study of torus actions led to the discovery of moment-angle complexes and their generalization, polyhedral product spaces. Polyhedral products are constructed from a simplicial complex. This thesis focuses on computing the cohomology of polyhedral products given by two different classes of simplicial complexes: polyhedral joins (composed simplicial complexes) and $n$-gons. A homological decomposition of a polyhedral product developed by Bahri, Bendersky, Cohen and Gitler is used to derive a formula for the case of polyhedral joins. Moreover, methods from and results by Cai will be used to give a full description of the non-trivial cup products in a ...


Mathematical Reasoning And The Inductive Process: An Examination Of The Law Of Quadratic Reciprocity, Nitish Mittal 2016 California State University - San Bernardino

Mathematical Reasoning And The Inductive Process: An Examination Of The Law Of Quadratic Reciprocity, Nitish Mittal

Electronic Theses, Projects, and Dissertations

This project investigates the development of four different proofs of the law of quadratic reciprocity, in order to study the critical reasoning process that drives discovery in mathematics. We begin with an examination of the first proof of this law given by Gauss. We then describe Gauss’ fourth proof of this law based on Gauss sums, followed by a look at Eisenstein’s geometric simplification of Gauss’ third proof. Finally, we finish with an examination of one of the modern proofs of this theorem published in 1991 by Rousseau. Through this investigation we aim to analyze the different strategies used ...


The Logic Of Uncertain Justifications, Robert Milnikel 2016 Kenyon College

The Logic Of Uncertain Justifications, Robert Milnikel

Robert Milnikel

No abstract provided.


The Logic Of Uncertain Justifications, Robert Milnikel 2016 Kenyon College

The Logic Of Uncertain Justifications, Robert Milnikel

Robert Milnikel

No abstract provided.


Conservativity For Logics Of Justified Belief: Two Approaches, Robert Milnikel 2016 Kenyon College

Conservativity For Logics Of Justified Belief: Two Approaches, Robert Milnikel

Robert Milnikel

No abstract provided.


A New Angle On An Old Construction: Approximating Inscribed N-Gons, Robert Milnikel 2016 Kenyon College

A New Angle On An Old Construction: Approximating Inscribed N-Gons, Robert Milnikel

Robert Milnikel

No abstract provided.


A Bi-Stable Switch In Virus Dynamics Can Explain The Differences In Disease Outcome Following Siv Infections In Rhesus Macaques, Stanca Ciupe, Christopher Miller, Jonathan Forde 2016 Virginia Tech

A Bi-Stable Switch In Virus Dynamics Can Explain The Differences In Disease Outcome Following Siv Infections In Rhesus Macaques, Stanca Ciupe, Christopher Miller, Jonathan Forde

Biology and Medicine Through Mathematics Conference

No abstract provided.


Hill's Diagrammatic Method And Reduced Graph Powers, Gregory D. Smith, Richard Hammack 2016 The College of William & Mary

Hill's Diagrammatic Method And Reduced Graph Powers, Gregory D. Smith, Richard Hammack

Biology and Medicine Through Mathematics Conference

No abstract provided.


Growth Dynamics For Pomacea Maculata, Lihong Zhao, Karyn L. Sutton, Jacoby Carter 2016 University of Louisiana at Lafayette

Growth Dynamics For Pomacea Maculata, Lihong Zhao, Karyn L. Sutton, Jacoby Carter

Biology and Medicine Through Mathematics Conference

No abstract provided.


Wilson-Cowan Coupled Dynamics In A Model Of The Cortico-Striato-Thalamo-Cortical Circuit, Anca R. Radulescu 2016 State University of New York at New Paltz

Wilson-Cowan Coupled Dynamics In A Model Of The Cortico-Striato-Thalamo-Cortical Circuit, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.


Robust Traveling Waves In Chains Of Simple Neural Oscillators, Stanislav M. Mintchev 2016 The Cooper Union for the Advancement of Science and Art

Robust Traveling Waves In Chains Of Simple Neural Oscillators, Stanislav M. Mintchev

Biology and Medicine Through Mathematics Conference

No abstract provided.


A Proof Of Concept Study Of Function-Based Statistical Analysis Of Fnirs Data: Syntax Comprehension In Children With Specific Language Impairment Compared To Typically-Developing Controls, Guifang Fu, Nicholas J. Wan, Joseph M. Baker, James Montgomery, Julia L. Evans, Ronald Gillam 2016 Utah State University

A Proof Of Concept Study Of Function-Based Statistical Analysis Of Fnirs Data: Syntax Comprehension In Children With Specific Language Impairment Compared To Typically-Developing Controls, Guifang Fu, Nicholas J. Wan, Joseph M. Baker, James Montgomery, Julia L. Evans, Ronald Gillam

Mathematics and Statistics Faculty Publications

Functional near infrared spectroscopy (fNIRS) is a neuroimaging techonology that enables investigators to indirectly monitor brain activity in vivo through relative changes in the concentration of oxygenated and deoxygenated hemoglobin. One of the key features of fNIRS is its superior temporal resolution, with dense measurements over very short periods of time (100ms increments). Unfortunately, most statistical analysis approaches in the existing literature have not fully utilized the high temporal resolution of fNIRS. For example, many analysis procedures are based on linearity assumptions that only extract partial information, thereby neglecting the overall dynamic trends in fNIRS trajectories. The main goal of ...


On The Reduction Of Matrix Polynomials To Hessenberg Form, Thomas R. Cameron 2016 Washington State University

On The Reduction Of Matrix Polynomials To Hessenberg Form, Thomas R. Cameron

Electronic Journal of Linear Algebra

It is well known that every real or complex square matrix is unitarily similar to an upper Hessenberg matrix. The purpose of this paper is to provide a constructive proof of the result that every square matrix polynomial can be reduced to an upper Hessenberg matrix, whose entries are rational functions and in special cases polynomials. It will be shown that the determinant is preserved under this transformation, and both the finite and infinite eigenvalues of the original matrix polynomial can be obtained from the upper Hessenberg matrix.


Totally Positive Density Matrices And Linear Preservers, David Kribs, Jeremy Levick, Rajesh Pereira 2016 University of Guelph

Totally Positive Density Matrices And Linear Preservers, David Kribs, Jeremy Levick, Rajesh Pereira

Electronic Journal of Linear Algebra

The intersection between the set of totally nonnegative matrices, which are of interest in many areas of matrix theory and its applications, and the set of density matrices, which provide the mathematical description of quantum states, are investigated. The single qubit case is characterized, and several equivalent conditions for a quantum channel to preserve the set in that case are given. Higher dimensional cases are also discussed.


The Power Of X, Darren B. Glass 2016 Gettysburg College

The Power Of X, Darren B. Glass

Math Faculty Publications

In his recent book, The Math Myth: And Other STEM Delusions, political scientist Andrew Hacker argues, among other things, that we should not require high school students to take algebra.

Part of his argument, based on data some have questioned, is that algebra courses are a major contributor to students dropping out of high school. He also argues that algebra is nothing more than an "enigmatic orbit of abstractions" that most people will never use in their jobs. [excerpt]


The Distance Spectral Radius Of Graphs With Given Number Of Odd Vertices, Hongying Lin, Bo Zhou 2016 South China Normal University

The Distance Spectral Radius Of Graphs With Given Number Of Odd Vertices, Hongying Lin, Bo Zhou

Electronic Journal of Linear Algebra

The graphs with smallest, respectively largest, distance spectral radius among the connected graphs, respectively trees with a given number of odd vertices, are determined. Also, the graphs with the largest distance spectral radius among the trees with a given number of vertices of degree 3, respectively given number of vertices of degree at least 3, are determined. Finally, the graphs with the second and third largest distance spectral radius among the trees with all odd vertices are determined.


Digital Commons powered by bepress