# Mathematics Commons™

## All Articles in Mathematics

10916 full-text articles. Page 1 of 293.

2016 Western Michigan University

#### The Creation Of A Video Review Guide For The Free-Response Section Of The Advanced Placement Calculus Exam, Jeffrey Brown

##### Honors Theses

The Creation of a Video Review Guide for the Free-Response Section of the Advanced Placement Calculus Exam follows the creation of a resource to help students prepare for the College Board’s Advanced Placement Calculus Exam. This project originated out of the authors personal experiences in preparing for this exam. The goal of the project was to create an accessible resource that reviews content, provides insights into the Advanced Placement exam, and creates successful habits in student responses. This paper, chronologically, details the development of the resource and a reflection on the final product and future uses.

2016 University of Tennessee, Chattanooga

#### Common Core In Tennessee: An Analysis Of Eighth Grade Mathematics Standards, Hayley Little

##### Honors Theses

Since their introduction in 2010, the Common Core State Standards (CCSS) have been a highly controversial topic in educational reform. Though the standards are not a product of the federal government and are not federally mandated, they do represent a push towards national academic standards in America. For states such as Tennessee, educational policies of the past pushed them to lower their academic standards in order to create the illusion of success. Those states are now some of the places that have seen the most change with the adoption of the CCSS. It still remains somewhat unclear, however, which changes ...

Mathematical Analysis Ii, 2016 Payame Noor University

#### Mathematical Analysis Ii, Ismail Nikoufar

##### Ismail Nikoufar

No abstract provided.

Some 2-Categorical Aspects In Physics, 2016 The Graduate Center, City University of New York

#### Some 2-Categorical Aspects In Physics, Arthur Parzygnat

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

2-categories provide a useful transition point between ordinary category theory and infinity-category theory where one can perform concrete computations for applications in physics and at the same time provide rigorous formalism for mathematical structures appearing in physics. We survey three such broad instances. First, we describe two-dimensional algebra as a means of constructing non-abelian parallel transport along surfaces which can be used to describe strings charged under non-abelian gauge groups in string theory. Second, we formalize the notion of convex and cone categories, provide a preliminary categorical definition of entropy, and exhibit several examples. Thirdly, we provide a universal description ...

An Extremal Problem For Finite Lattices, 2016 West Virginia University

#### An Extremal Problem For Finite Lattices, John Goldwasser, Brendan Nagle, Andres Saez

##### John Copeland Nagle

For a fixed M x N integer lattice L(M,N), we consider the maximum size of a subset A of L(M,N) which contains no squares of prescribed side lengths k(1),...,k(t). We denote this size by ex(L(M,N), {k(1),...,k(t)}), and when t = 1, we abbreviate this parameter to ex(L(M,N), k), where k = k(1). Our first result gives an exact formula for ex(L(M,N), k) for all positive integers k, M, and N, where ex(L(M,N), k) = ((3/4) + o(1)) MN holds ...

Gender Representation On Journal Editorial Boards In The Mathematical Sciences, 2016 Macalester College

#### Gender Representation On Journal Editorial Boards In The Mathematical Sciences, Chad M. Topaz, Shilad Sen

No abstract provided.

Gender Representation On Journal Editorial Boards In The Mathematical Sciences, 2016 Macalester College

#### Gender Representation On Journal Editorial Boards In The Mathematical Sciences, Chad M. Topaz, Shilad Sen

No abstract provided.

For A Given, Time Independent, System Of Equations Of Motion, Any Non-Trivial Constant Of Motion Is Locally A Hamiltonian, 2016 University of North Georgia

#### For A Given, Time Independent, System Of Equations Of Motion, Any Non-Trivial Constant Of Motion Is Locally A Hamiltonian, Piotr W. Hebda Ph.D., Beata Hebda Dr.

##### Faculty Publications

Given time-independent system of equations of motion and given a local, non-trivial constant of motion for these equations, it is shown that there exists a locally defined system of dynamical brackets, such that this given constant of motion, used together with these dynamical brackets, becomes a local Hamiltonian for the given system of equations of motion.

Gender Representation On Journal Editorial Boards In The Mathematical Sciences, 2016 Macalester College

#### Gender Representation On Journal Editorial Boards In The Mathematical Sciences, Chad M. Topaz, Shilad Sen

##### Faculty Publications

No abstract provided.

Introduction To Classical Field Theory, 2016 Department of Physics, Utah State University

#### Introduction To Classical Field Theory, Charles G. Torre

##### Charles G. Torre

This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.

2016 The University of Western Ontario

#### K-Theory Of Root Stacks And Its Application To Equivariant K-Theory, Ivan Kobyzev

##### Electronic Thesis and Dissertation Repository

We give a definition of a root stack and describe its most basic properties. Then we recall the necessary background (Abhyankar’s lemma, Chevalley-Shephard-Todd theorem, Luna’s etale slice theorem) and prove that under some conditions a quotient stack is a root stack. Then we compute G-theory and K-theory of a root stack. These results are used to formulate the theorem on equivariant algebraic K-theory of schemes.

2016 The University of Western Ontario

#### Moduli Space And Deformations Of Special Lagrangian Submanifolds With Edge Singularities, Josue Rosario-Ortega

##### Electronic Thesis and Dissertation Repository

Special Lagrangian submanifolds are submanifolds of a Calabi-Yau manifold calibrated by the real part of the holomorphic volume form. In this thesis we use elliptic theory for edge- degenerate differential operators on singular manifolds to study general deformations of special Lagrangian submanifolds with edge singularities. We obtain a general theorem describing the local structure of the moduli space. When the obstruction space vanishes the moduli space is a smooth, finite dimensional manifold.

Potentially Eventually Positive Star Sign Patterns, 2016 Huaiyin Institute of Technology

#### Potentially Eventually Positive Star Sign Patterns, Yu Ber-Lin, Huang Ting-Zhu, Jie Cui, Deng Chunhua

##### Electronic Journal of Linear Algebra

An $n$-by-$n$ real matrix $A$ is eventually positive if there exists a positive integer $k_{0}$ such that $A^{k}>0$ for all $k\geq k_{0}$. An $n$-by-$n$ sign pattern $\mathcal{A}$ is potentially eventually positive (PEP) if there exists an eventually positive real matrix $A$ with the same sign pattern as $\mathcal{A}$. An $n$-by-$n$ sign pattern $\mathcal{A}$ is a minimal potentially eventually positive sign pattern (MPEP sign pattern) if $\mathcal{A}$ is PEP and no proper subpattern of $\mathcal{A}$ is PEP. Berman, Catral, Dealba, et al. [Sign patterns that ...

2016 Kennesaw State University

#### Definition Of A Method For The Formulation Of Problems To Be Solved With High Performance Computing, Ramya Peruri

##### Master of Science in Computer Science Theses

Computational power made available by current technology has been continuously increasing, however today’s problems are larger and more complex and demand even more computational power. Interest in computational problems has also been increasing and is an important research area in computer science. These complex problems are solved with computational models that use an underlying mathematical model and are solved using computer resources, simulation, and are run with High Performance Computing. For such computations, parallel computing has been employed to achieve high performance. This thesis identifies families of problems that can best be solved using modelling and implementation techniques of ...

2016 University of Nebraska - Lincoln

#### Homological Characterizations Of Quasi-Complete Intersections, Jason M. Lutz

##### Dissertations, Theses, and Student Research Papers in Mathematics

Let R be a commutative ring, (f) an ideal of R, and E = K(f; R) the Koszul complex. We investigate the structure of the Tate construction T associated with E. In particular, we study the relationship between the homology of T, the quasi-complete intersection property of ideals, and the complete intersection property of (local) rings.

Advisers: Luchezar L. Avramov and Srikanth B. Iyengar

Multilevel Models For Longitudinal Data, 2016 East Tennessee State University

#### Multilevel Models For Longitudinal Data, Aastha Khatiwada

##### Electronic Theses and Dissertations

Longitudinal data arise when individuals are measured several times during an ob- servation period and thus the data for each individual are not independent. There are several ways of analyzing longitudinal data when different treatments are com- pared. Multilevel models are used to analyze data that are clustered in some way. In this work, multilevel models are used to analyze longitudinal data from a case study. Results from other more commonly used methods are compared to multilevel models. Also, comparison in output between two software, SAS and R, is done. Finally a method consisting of fitting individual models for each ...

Breaking Spaces And Forms For The Dpg Method And Applications Including Maxwell Equations, 2016 Humboldt-Universität zu Berlin

#### Breaking Spaces And Forms For The Dpg Method And Applications Including Maxwell Equations, Carsten Carstensen, Leszek Demkowicz, Jay Gopalakrishnan

##### Mathematics and Statistics Faculty Publications and Presentations

Discontinuous Petrov Galerkin (DPG) methods are made easily implementable using `broken' test spaces, i.e., spaces of functions with no continuity constraints across mesh element interfaces. Broken spaces derivable from a standard exact sequence of first order (unbroken) Sobolev spaces are of particular interest. A characterization of interface spaces that connect the broken spaces to their unbroken counterparts is provided. Stability of certain formulations using the broken spaces can be derived from the stability of analogues that use unbroken spaces. This technique is used to provide a complete error analysis of DPG methods for Maxwell equations with perfect electric boundary ...

2016 University of Nebraska - Lincoln

#### Applications Of Discrete Mathematics For Understanding Dynamics Of Synapses And Networks In Neuroscience, Caitlyn Parmelee

##### Dissertations, Theses, and Student Research Papers in Mathematics

Mathematical modeling has broad applications in neuroscience whether we are modeling the dynamics of a single synapse or the dynamics of an entire network of neurons. In Part I, we model vesicle replenishment and release at the photoreceptor synapse to better understand how visual information is processed. In Part II, we explore a simple model of neural networks with the goal of discovering how network structure shapes the behavior of the network.

Vision plays an important role in how we interact with our environments. To fully understand how visual information is processed requires an understanding of the way signals are ...

An Algorithm For The Machine Calculation Of Minimal Paths, 2016 East Tennessee State University

#### An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger

##### Electronic Theses and Dissertations

Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R3, but also to the general case of finding minimal functionals on hypersurfaces in Rn associated with an arbitrary metric.

Bridge Spectra Of Cables Of 2-Bridge Knots, 2016 University of Nebraska-Lincoln

#### Bridge Spectra Of Cables Of 2-Bridge Knots, Nicholas John Owad

##### Dissertations, Theses, and Student Research Papers in Mathematics

We compute the bridge spectra of cables of 2-bridge knots. We also give some results about bridge spectra and distance of Montesinos knots.

Advisors: Mark Brittenham and Susan Hermiller