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Articles 1 - 30 of 30
Full-Text Articles in Mathematics
Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia
Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia
Department of Math & Statistics Faculty Publications
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
The Effects Of Standards-Based Grading On Student Performance In Algebra 2, Rachel Beth Rosales
The Effects Of Standards-Based Grading On Student Performance In Algebra 2, Rachel Beth Rosales
Dissertations
The use of standards-based grading in American public schools is increasing, offering students, parents, and teachers a new way of measuring and communicating about student achievement and performance. Parents indicate an appreciation for this method of grading, and students at the elementary grades (K-6) have improved standardized test scores in reading and math as a result of its implementation. This study seeks to determine whether standards-based grading has the same effect on students at the high school level (grades 9-12) by comparing end-of-course test scores and posttest scores of Algebra 2 students enrolled in a standards-based graded classroom with to …
The Kronecker-Weber Theorem: An Exposition, Amber Verser
The Kronecker-Weber Theorem: An Exposition, Amber Verser
Lawrence University Honors Projects
This paper is an investigation of the mathematics necessary to understand the Kronecker-Weber Theorem. Following an article by Greenberg, published in The American Mathematical Monthly in 1974, the presented proof does not use class field theory, as the most traditional treatments of the theorem do, but rather returns to more basic mathematics, like the original proofs of the theorem. This paper seeks to present the necessary mathematical background to understand the proof for a reader with a solid undergraduate background in abstract algebra. Its goal is to make what is usually an advanced topic in the study of algebraic number …
On Closed Subsets Of Non-Commutative Association Schemes Of Rank 6, Jose Vera
On Closed Subsets Of Non-Commutative Association Schemes Of Rank 6, Jose Vera
Theses and Dissertations - UTB/UTPA
The notion of an association scheme is a generalization of the concept of a group. In fact, the so-called thin association schemes correspond in a well-understood way to groups. In this thesis, we look at the structure of non-commutative association schemes of rank 6. We will show that a non-normal closed subset of a noncommutative association scheme of rank 6, must have rank 2. The so-called Coxeter schemes of rank 6 which we present in Section 4 provide examples of association schemes of rank 6 with non-normal closed subsets of rank 2. It is shown that normal closed subsets of …
Book Review: Encyclopedia Of Mathematics And Society, Gizem Karaali
Book Review: Encyclopedia Of Mathematics And Society, Gizem Karaali
Pomona Faculty Publications and Research
The Encyclopedia of Mathematics and Society is an impressive achievement of collective effort and serious thought, an amazing collection of delightful, unexpected essays, a sourcebook for students and teachers alike. The experience of reading the EMS was, for this encyclopedia enthusiast, enlightening and enjoyable.
If any librarians out there are still wondering, let me be clear: I strongly recommend this encyclopedia. For individuals, the expense might well be an initial turn-off; keeping in mind that the hard copy books come with online access to the same content might alleviate some of the pain.
As for me? I expect to enjoy …
Mathematics Libguide, Sandra Barclay
Mathematics Libguide, Sandra Barclay
Sandra Barclay
Welcome to the Horace W. Sturgis Library and the Mathematics Libguide at Kennesaw State University! To get started with your math research, this is the place to go. We hope you will find this information helpful. Please let us know what other resources you could use.
Σary, Minnesota State University Moorhead, Mathematics Department
Σary, Minnesota State University Moorhead, Mathematics Department
Math Department Newsletters
No abstract provided.
Generalized Ordered Whist Tournaments For 6n+1 Players, Elyssa Cipriano
Generalized Ordered Whist Tournaments For 6n+1 Players, Elyssa Cipriano
Honors Projects
In this project, we worked to see if it would be possible to extend the idea of an ordered whist tournament to a generalized whist tournament on 6n or 6n + 1 players. We focused on tournaments where the players are divided into n games of size 6 each consisting of two teams of size 3. We aimed to balance the 3 occasions where the players meet as opponents.
Compressed Sensing For Multiple Input-Multiple Output Radar Imaging, Juan F. Lopez Jr.
Compressed Sensing For Multiple Input-Multiple Output Radar Imaging, Juan F. Lopez Jr.
Theses and Dissertations - UTB/UTPA
Multiple input - multiple output (MIMO) radar utilizes the transmission of spatially diverse waveforms from a static antenna array to gather information about the desired scene. We will demonstrate how techniques from compressed sensing can be applied to image formation in MIMO radar when in the presence of undersampling. We analyze the problem under the general theoretical framework of inverse scattering.
Actual Vs. Perceived Value Of Players Of The National Basketball Association, Stephen Righini
Actual Vs. Perceived Value Of Players Of The National Basketball Association, Stephen Righini
Honors Projects in Mathematics
Over the past few decades the media has played an increasingly large role in shaping how player effectiveness in the National Basketball Association (NBA) is perceived. Several factors have caused fans, announcers, and even NBA team management to have unintentional bias toward certain players. This study aims to utilize various formulas created by NBA statisticians, called Player Raters, to identify how efficient each NBA player actually is in comparison to the rest of the league. Data from the past 12 seasons was compiled and six Player Raters were used to place values on every NBA player since the 2000-2001 season. …
Time Series Data Mining: A Retail Application Using Sas Enterprise Miner, Daniel Hebert
Time Series Data Mining: A Retail Application Using Sas Enterprise Miner, Daniel Hebert
Honors Projects in Mathematics
Modern technologies have allowed for the amassment of data at a rate never encountered before. Organizations are now able to routinely collect and process massive volumes of data. A plethora of regularly collected information can be ordered using an appropriate time interval. The data would thus be developed into a time series. With such data, analytical techniques can be employed to collect information pertaining to historical trends and seasonality. Time series data mining methodology allows users to identify commonalities between sets of time-ordered data. This technique is supported by a variety of algorithms, notably dynamic time warping (DTW). This mathematical …
(4,8) Ordered Generalized Whist Designs - Existence Results, Nicholas Leveilee
(4,8) Ordered Generalized Whist Designs - Existence Results, Nicholas Leveilee
Honors Projects
Ordered Generalized Whist tournaments are a new design. In this
study, we establish that ordered generalized whist tournaments exist for
tournaments with 8n + 1 players, n odd, with 4 players per team.
Quantitative Approaches To Sustainability Seminars, Rachel Levy
Quantitative Approaches To Sustainability Seminars, Rachel Levy
All HMC Faculty Publications and Research
How can mathematicians contribute to education of about sustainability? Mathematicians study climate change, energy-related technologies, models of energy availability, production and consumption, and even the political and social aspects of sustainable legislation and practices. However, at this point, few courses on sustainability can be found in math department offerings. When we consider problems that our current and future students will face, energy sustainability certainly seems important. But how many of these ideas reach our classrooms?
How Mathematics Influences Our Perception Of Beauty, Leslie Muzulu
How Mathematics Influences Our Perception Of Beauty, Leslie Muzulu
Antonian Scholars Honors Program
Beauty is an important part of our lives. Consequently, it is no surprise that we are interested in our experiences and judgments of it. What makes something beautiful? The arts and nature are considered vessels of beauty, but could mathematics be as well? Can it influence our perception of what is beautiful? This paper offers insights into how mathematics influences our perception of what is beautiful. The philosophies of aesthetics and mathematics are briefly discussed, followed by a consideration of how the presence of such mathematical structures as proportion, symmetry and perspective can significantly influence our perception of beauty in …
Trig-Star, James M. Anderson
Trig-Star, James M. Anderson
Interdisciplinary STEM Teaching & Learning Conference (2012-2019)
A TRIG-STAR is a mathematics student who has demonstrated in competition that he or she is the most skilled among classmates in the practical application of trigonometry. The competition for the honor is a timed exercise which is the solving of a trigonometry problem that incorporates the use of right triangle formulas, circle formulas, the law of sines, and the law of cosines. The contest helps to promote careers in surveying and mapping to students at the High Schools across the country. The award is sponsored by the National Society of Professional Surveyors and cosponsored locally. State winners also have …
Integrating Manipulatives To Improve Fraction Concepts, Rachel Dunn
Integrating Manipulatives To Improve Fraction Concepts, Rachel Dunn
Interdisciplinary STEM Teaching & Learning Conference (2012-2019)
Many students are overwhelmed by mathematics because the language is too difficult, the teaching strategies are insufficient or they have lost motivation. With a recent emphasis on meeting the Common Core expectations, using manipulatives to eliminate misconceptions in the mathematical classroom has become even more prevalent. I explored the misconceptions that many students struggle with and provided possible methods of eliminating them at all levels for learning. During this investigation, I studied the effect of manipulatives on students’ understanding of fraction concepts and the students’ conceptions of the unit of reference when working with fraction word problems. I learned that …
Brown, James Monroe, 1800-1886 (Sc 806), Manuscripts & Folklife Archives
Brown, James Monroe, 1800-1886 (Sc 806), Manuscripts & Folklife Archives
MSS Finding Aids
Finding aid only for Manuscripts Small Collection 806. Ciphering book, 1822-1827 (40 p.), of James M. Brown, Butler County, Kentucky, which also contains a few pages of account entries and other various notations, (806a). Photocopy of ciphering book is also included. Also letter, 1989, from donor relating family data.
Finitely Presented Groups For The Undergraduate Algebra Student, Davis Shurbert
Finitely Presented Groups For The Undergraduate Algebra Student, Davis Shurbert
Summer Research
The concept of a finitely presented group is a topic which students do not normally see until graduate school. Through contributions to the open source computer algebra system Sage, I was able to accomplish my goal of making finitely presented groups more accessible to undergraduate students. Implementing this goal required a series of smaller tasks, all building together to expand the original framework regarding this type of group representation. I began my research by creating a catalogue of named groups easily accessible to the user as finitely presented group objects, along with a method to convert from a permutation group …
On A Theorem Of Livsic, William T. Ross, Alexandru Aleman, R. T. W. Martin
On A Theorem Of Livsic, William T. Ross, Alexandru Aleman, R. T. W. Martin
Department of Math & Statistics Faculty Publications
The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators such as Schrodinger operators in mathematical physics. Examples of simple symmetric operators include multiplication operators on various spaces of analytic functions such as model subspaces of Hardy spaces, deBranges-Rovnyak spaces and Herglotz spaces, ordinary differential operators (including Schrodinger operators from quantum mechanics), Toeplitz operators, and infinite Jacobi matrices.
In this paper we develop a general representation theory of simple symmetric operators with equal deficiency indices, and …
Direct And Reverse Carleson Measure For Hb Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann
Direct And Reverse Carleson Measure For Hb Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann
Department of Math & Statistics Faculty Publications
In this paper we discuss direct and reverse Carleson measures for the de Branges-Rovnyak spaces H(b), mainly when b is a non-extreme point of the unit ball of H∞.
Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia
Model Spaces: A Survey, William T. Ross, Stephan Ramon Garcia
Department of Math & Statistics Faculty Publications
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
Oddification Of The Cohomology Of Type A Springer Varieties, Heather M. Russell, Aaron D. Lauda
Oddification Of The Cohomology Of Type A Springer Varieties, Heather M. Russell, Aaron D. Lauda
Department of Math & Statistics Faculty Publications
We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q = −1. This allows us to define graded modules over the Hecke algebra at q = −1 that are ‘odd’ analogs of the cohomology of type A Springer varieties. The graded module associated to the full flag variety corresponds to the quotient of the skew polynomial ring by the left ideal of nonconstant odd symmetric functions. The top degree component of the odd cohomology of Springer varieties is identifiedwith the …
Behavior Of Solutions For Bernoulli Initial-Value Problems, Carlos Marcelo Sardan
Behavior Of Solutions For Bernoulli Initial-Value Problems, Carlos Marcelo Sardan
Theses Digitization Project
The purpose of this project is to investigate blow-up properties of solutions for specific initial-value problems that involve Bernoulli Ordinary Differential Equations (ODE's). The objective is to find conditions on the coefficients and on the initial-values that lead to unbounded growth of solutions in finite time.
Coloring Pythagorean Triples And A Problem Concerning Cyclotomic Polynomials, Daniel White
Coloring Pythagorean Triples And A Problem Concerning Cyclotomic Polynomials, Daniel White
Theses and Dissertations
One may easily show that there exist $O( \log n)$-colorings of $\{1,2, \ldots, n\}$ such that no Pythagorean triple with elements $\le n$ is monochromatic. In Chapter~\ref{CH:triples}, we investigate two analogous ideas. First, we find an asymptotic bound for the number of colors required to color $\{1,2,\ldots ,n\}$ so that every Pythagorean triple with elements $\le n$ is $3$-colored. Afterwards, we examine the case where we allow a vanishing proportion of Pythagorean triples with elements $\le n$ to fail to have this property.
Unrelated, in 1908, Schur raised the question of the irreducibility over $\Q$ of polynomials of the form …
Factoring The Duplication Map On Elliptic Curves For Use In Rank Computations, Tracy Layden
Factoring The Duplication Map On Elliptic Curves For Use In Rank Computations, Tracy Layden
Scripps Senior Theses
This thesis examines the rank of elliptic curves. We first examine the correspondences between projective space and affine space, and use the projective point at infinity to establish the group law on elliptic curves. We prove a section of Mordell’s Theorem to establish that the abelian group of rational points on an elliptic curve is finitely generated. We then use homomorphisms established in our proof to find a formula for the rank, and then provide examples of computations.
Selected Research In Covering Systems Of The Integers And The Factorization Of Polynomials, Joshua Harrington
Selected Research In Covering Systems Of The Integers And The Factorization Of Polynomials, Joshua Harrington
Theses and Dissertations
In 1960, Sierpi\'{n}ski proved that there exist infinitely many odd positive integers $k$ such that $k\cdot 2^n+1$ is composite for all positive integers $n$. Such integers are known as Sierpi\'{n}ski numbers. Letting $f(x)=ax^r+bx+c\in\mathbb{Z}[x]$, Chapter 2 of this document explores the existence of integers $k$ such that $f(k)2^n+d$ is composite for all positive integers $n$. Chapter 3 then looks into a polynomial variation of a similar question. In particular, Chapter~\ref{CH:FH} addresses the question, for what integers $d$ does there exist a polynomial $f(x)\in\mathbb{Z}[x]$ with $f(1)\neq -d$ such that $f(x)x^n+d$ is reducible for all positive integers $n$. The last two chapters of …
Undergraduate And Graduate Teaching Assistants' Perceptions Of Their Responsibilities - Factors That Help Or Hinder, Alena Moon, Hyunyi Jung, Farshid Marbouti, Kelsey Joy Rodgers, Heidi A. Diefes-Dux
Undergraduate And Graduate Teaching Assistants' Perceptions Of Their Responsibilities - Factors That Help Or Hinder, Alena Moon, Hyunyi Jung, Farshid Marbouti, Kelsey Joy Rodgers, Heidi A. Diefes-Dux
Mathematics, Statistics and Computer Science Faculty Research and Publications
Effective teaching assistants (TAs) are crucial for effective student learning. This is especially true in science, technology, engineering, and mathematics (STEM) programs, where TAs are enabling large programs to transition to more student-centered learning environments. To ensure that TAs are able to support these types of learning environments, their perspectives of training, their abilities, and other work related aspects must be understood. In this paper a survey that was created based on interviews conducted with eight TAs is discussed. The survey has four primary categories of content that are critical for understanding TAs' perspectives: (1) background, (2) motivation, (3) training, …
Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients, Morgan Cole
Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients, Morgan Cole
Theses and Dissertations
Consider a polynomial f(x) having non-negative integer coefficients with f(b) prime for some integer b greater than or equal to 2. We will investigate the size of the coefficients of the polynomial and establish a largest such bound on the coefficients that would imply that f(x) is irreducible. A result of Filaseta and Gross has established sharp bounds on the coefficients of such a polynomial in the case that b = 10. We will expand these results for b in {8, 9, ..., 20}.
Information Literacy In The Discipline, Mellon Grant For Math 405 Partnership With A. Shallue, Crystal Boyce, Andrew Shallue
Information Literacy In The Discipline, Mellon Grant For Math 405 Partnership With A. Shallue, Crystal Boyce, Andrew Shallue
Crystal Boyce
The goal of the assignment was to familiarize students with what it means to learn mathematics outside of a classroom environment. This is connected to the main goal of the course, which is to develop skills in proof writing and in technical presentations.
Information Literacy In The Discipline, Mellon Grant For Math 310 Partnership With D. Roberts, Crystal Boyce, Daniel Roberts
Information Literacy In The Discipline, Mellon Grant For Math 310 Partnership With D. Roberts, Crystal Boyce, Daniel Roberts
Crystal Boyce
As of now, MATH 310 has neither a required writing component nor an assignment that deals with information literacy. We are proposing the implementation of a new assignment that would incorporate both of these components. This assignment would have multiple stages spread over approximately a one-month time period.