Mathematical Analysis Ii, 2016 Payame Noor University

Quaternion Algebras And Hyperbolic 3-Manifolds, 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, 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, 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, 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, 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, 2016 Kenyon College

#### The Logic Of Uncertain Justifications, Robert Milnikel

*Robert Milnikel*

No abstract provided.

The Logic Of Uncertain Justifications, 2016 Kenyon College

#### The Logic Of Uncertain Justifications, Robert Milnikel

*Robert Milnikel*

No abstract provided.

Conservativity For Logics Of Justified Belief: Two Approaches, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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.