One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, 2014 Dublin Institute of Technology

#### One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov

*Articles*

In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the integrable KdV and Degasperis-Procesi equations.

Algebraic Properties Of Ext-Modules Over Complete Intersections, 2014 University of Nebraska - Lincoln

#### Algebraic Properties Of Ext-Modules Over Complete Intersections, Jason Hardin

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

We investigate two algebraic properties of Ext-modules over a complete intersection R of codimension c. Given an R-module M, Ext(M,k) can be viewed as a graded module over a polynomial ring in c variables with an action given by the Eisenbud operators. We provide an upper bound on the degrees of the generators of this graded module in terms of the regularities of two associated coherent sheaves. In the codimension two case, our bound recovers a bound of Avramov and Buchweitz in terms of the Betti numbers of M. We also provide a description of the differential graded ...

Review Of The Joy Of X: A Guided Tour Of Math, From One To Infinity By Steven Strogatz, 2014 University of South Florida

#### Review Of The Joy Of X: A Guided Tour Of Math, From One To Infinity By Steven Strogatz, Michael T. Catalano

*Numeracy*

Strogatz, Steven. *The Joy of x: A Guided Tour of Math, from One to Infinity, *(New York, NY, Houghton Mifflin Harcourt, 2012). 316 pp. ISBN 978-0-547-51765-0

The *Joy of x: A Guided Tour of Math, from One to Infinity*, by Steven Strogatz, is an engaging and example-filled argument for mathematics as a valuable and enjoyable activity. The thirty chapters are divided into six parts, entitled Numbers, Relationships, Shapes, Change, Data, and Frontiers. The discussion ranges from intuitive explanations of basic concepts such as place value, the four arithmetic operations, percentage increase and decrease, and solving equations, to “higher” levels of ...

How Does One Design Or Evaluate A Course In Quantitative Reasoning?, 2014 University of South Florida

#### How Does One Design Or Evaluate A Course In Quantitative Reasoning?, Bernard L. Madison

*Numeracy*

In the absence of generally accepted content standards and with little evidence on the learning for long-term retrieval and transfer, how does one design or evaluate a course in quantitative reasoning (QR)? This is a report on one way to do so. The subject QR course, which has college algebra as a prerequisite and has been taught for 8 years, is being modified slightly to be offered as an alternative to college algebra. One modification is adding a significant formal writing component. As the modification occurs, the current course and the modified one are judged according to six sets of ...

What Is Higher Mathematics? Why Is It So Hard To Interpret? What Can Be Done?, 2014 University of North Florida

#### What Is Higher Mathematics? Why Is It So Hard To Interpret? What Can Be Done?, John Tabak

*Journal of Interpretation*

Courses and seminars in higher mathematics are some of the most challenging assignments faced by academic interpreters. Difficulties interpreting higher mathematics can adversely impact the academic and professional aspirations of deaf mathematics students and professionals. This paper discusses the nature of higher mathematics with the goal of identifying what distinguishes higher mathematics from other subjects; it then reviews the history of attempts to sign/interpret higher mathematics with particular attention to current challenges associated with expressing higher mathematics in sign. The final part of the paper discusses strategies for more effectively expressing higher mathematics in American Sign Language.

Automorphisms Of Cornoa Algebras, And Group Cohomology, 2014 Boise State University

#### Automorphisms Of Cornoa Algebras, And Group Cohomology, Samuel Coskey, Ilijas Farah

*Mathematics Faculty Publications and Presentations*

In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded operators on a separable complex Hilbert space, modulo the compact operators.) In this paper we establish that the analogous conclusion holds for a broad family of quotient algebras. Specifically, we will show that assuming the Continuum Hypothesis, if *A* is a separable algebra which is either simple or stable, then the corona of *A* has nontrivial automorphisms. We also discuss a connection with cohomology theory, namely, that our proof can be viewed ...

Corrigendum To: Operator Monotone Functions And Löwner Functions Of Several Variables, 2014 Washington University in St. Louis

#### Corrigendum To: Operator Monotone Functions And Löwner Functions Of Several Variables, Jim Agler, John E. Mccarthy, Nicholas J. Young

*Faculty Publications*

We fix a gap in the proof of Theorem 7.24 in *Ann. of Math.* **176** (2012), 1783–1826.

Vertex-Transitive Polyhedra In Three-Space, 2014 Northeastern University

#### Vertex-Transitive Polyhedra In Three-Space, Undine Leopold

*Mathematics Dissertations*

Vertex-transitive polyhedra of positive genus are natural generalizations of the well-known convex uniform polyhedra. Examples of non-spherical vertex-transitive polyhedra were first examined by Grünbaum and Shephard in a 1984 survey article on *Polyhedra with transitivity properties*. Besides two infinite families of toroidal vertex-transitive polyhedra, only five examples of genus 𝔤 ≥ 2 were given. To this day it is unclear whether all such polyhedra of genus two and higher have been found. Recent progress has been made by Gévay, Schulte, and Wills (to appear in *Advances in Geometry*), not only in providing the newest example (there are now seven), but in ...

Work In Progress: Online Resource Platform For Mathematics Education, 2014 Dublin Institute of Technology

#### Work In Progress: Online Resource Platform For Mathematics Education, Marisa Llorens, Edmund Nevin, Eileen Mageean

*Conference Papers*

Mathematics is intrinsic to engineering and as such plays an integral role in the education of engineers. New challenges are being faced in higher education particularly in the areas of student motivation, engagement and attainment. As a result mathematics is often the focus of engineering education research. Traditional methods of delivery such as lectures and tutorials need to evolve to counter these challenges with new pedagogical approaches explored including the use of new technologies. Today’s students are immersed in an increasingly technological world and are willing to adapt to new technological advances. This paper describes a study being undertaken ...

Free Energies In A General Non-Local Theory Of A Material With Memory, 2014 Dublin Institute of Technology

#### Free Energies In A General Non-Local Theory Of A Material With Memory, Giovambattista Amendola, Mauro Fabrizio, Murrough Golden

*Articles*

A general theory of non-local materials, with linear constitutive equations and memory effects, is developed within a thermodynamic framework. Several free energy and dissipation functionals are constructed and explored. These include an expression for the minimum free energy and a functional that is a free energy for important categories of memory kernels and is explicitly a functional of the minimal state. The functionals discussed have a similar general form to the corresponding expressions for simple materials. A number of new results are derived for them, most of which apply equally to both types of material. In particular, detailed formulae are ...

Playing With Permutations: Examining Mathematics In Children’S Toys, 2014 Western Oregon University

#### Playing With Permutations: Examining Mathematics In Children’S Toys, Jillian J. Johnson

*Honors Senior Theses/Projects*

In John P. Bonomo’s and Carolyn K. Cuff's paper *How Do You Stack Up?* a mathematical problem was posed. This question was regarding a common children’s toy known as a stacking ring tower. The problem the authors addressed came as a result of a common occurrence: the event that not all of the rings are placed on the tower in the “proper” order. When the rings are placed on the tower in a variation of that “proper” order, some of them will inevitably stick over the top of the tower. The problem the authors decided to tackle ...

Dynamics Of Climate Change: Explaining Glacier Retreat Mathematically, 2014 Bridgewater State University

#### Dynamics Of Climate Change: Explaining Glacier Retreat Mathematically, Robert Guillette

*Honors Program Theses and Projects*

No abstract provided.

The Mathematics Of The Card Game Set, 2014 Rhode Island College

#### The Mathematics Of The Card Game Set, Paola Y. Reyes

*Honors Projects Overview*

SET is a card game of visual perception. The goal is to be the first to see a SET from the 12 cards laid face up on the table. Each card has four attributes, which can vary as follows: 1. Shape: oval, squiggle, or diamond 2. Color: red, green, or blue 3. Number: the number of copies of each symbol can be 1, 2, or 3 4. Filling: solid, unfilled, stripped Each card has a unique combination, for a total of 34 = 81 different cards in a deck. A SET consist of three cards for which each of the four ...

Surface Reconstruction Using Differential Invariant Signatures, 2014 Macalester College

#### Surface Reconstruction Using Differential Invariant Signatures, Sophors Khut

*Mathematics, Statistics, and Computer Science Honors Projects*

This thesis addresses the problem of reassembling a broken surface. Three di- mensional curve matching is used to determine shared edges of broken pieces. In practice, these pieces may have different orientation and position in space, so edges cannot be directly compared. Instead, a differential invariant signature is used to make the comparison. A similarity score between edge signatures determines if two pieces share an edge. The Procrustes algorithm is applied to find the translations and rotations that best fit shared edges. The method is implemented in Matlab, and tested on a broken spherical surface.

Hurdle Models And Age Effects In The Major League Baseball Draft, 2014 Macalester College

#### Hurdle Models And Age Effects In The Major League Baseball Draft, Justin Sims

*Mathematics, Statistics, and Computer Science Honors Projects*

Major League Baseball (MLB) franchises expend an abundance of resources on scouting in preparation for the June Amateur Draft. In addition to the classic "tools" assessed, another factor considered is age: younger players may get selected over older players of equal ability because of anticipated development, whereas college players may get selected over high school players due to a shortened latency before reaching the majors. Additionally, Little League rules in effect until 2006 operated on an August 1-July 31 year, meaning that, in their youth, players born on August 1 were the eldest relative to their cohort. We examine the ...

Parallel Design Patterns And Program Performance, 2014 Macalester College

#### Parallel Design Patterns And Program Performance, Yu Zhao

*Mathematics, Statistics, and Computer Science Honors Projects*

With the rapid advancement of parallel and distributed computing (PDC), three types of hardware and their corresponding software (hardware-software pairs) are becoming more and more popular: Distributed Memory Systems with the Message Passing Interface (MPI) library, Shared Memory Systems with the OpenMP library and Co-processor Systems with a general purpose parallel computing library. Alongside the development of both hardware and software aspects of PDC, the process of designing parallel programs has also improved significantly over the years. A consequence of this is that researchers have been able to describe many parallel design patterns, which are recurring solutions to well-known problems ...

Traditional Lecture Versus An Activity Approach For Teaching Statistics: A Comparison Of Outcomes, 2014 Utah State University

#### Traditional Lecture Versus An Activity Approach For Teaching Statistics: A Comparison Of Outcomes, Jennifer L. Loveland

*All Graduate Theses and Dissertations*

Many educational researchers have proposed teaching statistics with less lecture and more active learning methods. However, there are only a few comparative studies that have taught one section of statistics with lectures and one section with activity-based methods; of those studies, the results are contradictory. To address the need for more research on the actual effectiveness of active learning methods in introductory statistics, this research study was undertaken.

An introductory, university level course was divided into two sections. One section was taught entirely with traditional lecture. The other section was taught using active learning methods and a minimal amount of ...

High Cognitive Test Item Development And Implementation, 2014 Utah State University

#### High Cognitive Test Item Development And Implementation, Ashley Salisbury

*All Graduate Plan B and other Reports*

In secondary math classrooms there has been a movement toward discovery and problem solving based instruction. This type of instruction requires teachers to teach on what is often considered a higher level of cognition and allows students to discover more ideas and concepts on their own as opposed to traditional lecture style. Teachers with well thought-out examples, questions, and activities provide students with tools to solve problems on their own requiring students to make mathematical discoveries and connections. These skills not only benefit students in their math class but are analytical skills students can use throughout their lives.

With this ...

A Numerical Model For Nonadiabatic Transitions In Molecules, 2014 East Tennessee State University

#### A Numerical Model For Nonadiabatic Transitions In Molecules, Devanshu Agrawal

*Undergraduate Honors Theses*

In molecules, electronic state transitions can occur via quantum coupling of the states. If the coupling is due to the kinetic energy of the molecular nuclei, then electronic transitions are best represented in the adiabatic frame. If the coupling is instead facilitated through the potential energy of the nuclei, then electronic transitions are better represented in the diabatic frame. In our study, we modeled these latter transitions, called ``nonadiabatic transitions.'' For one nuclear degree of freedom, we modeled the de-excitation of a diatomic molecule. For two nuclear degrees of freedom, we modeled the de-excitation of an ethane-like molecule undergoing cis-trans ...

Results On Edge-Colored Graphs And Pancyclicity, 2014 University of Nebraska - Lincoln

#### Results On Edge-Colored Graphs And Pancyclicity, James Carraher

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

This thesis focuses on determining when a graph with additional structure contains certain subgraphs, particularly circuits, cycles, or trees. The specific problems and presented results include a blend of many fundamental graph theory concepts such as edge-coloring, routing problems, decomposition problems, and containing cycles of various lengths. The three primary chapters in this thesis address the problems of finding eulerian circuits with additional restrictions, decomposing the edge-colored complete graph K_n into rainbow spanning trees, and showing a 4-connected claw-free and N(3,2,1)-free graph is pancyclic.

Adviser: Stephen G. Hartke