Mathematics Commons^™

Preface, Eva Thanheiser, Christine Browning

The Mathematics Enthusiast

Bharath Sriraman noted in his Editorial for Vol. 10, nos. 1–2 that the first issue of The Mathematics Enthusiast (known then as The Montana Mathematics Enthusiast) published in April 2004 was “the result of four idealistic elementary school teachers believing in the mission of this journal and writing about their attempts to reconcile the mathematics content they were learning in a mathematics for elementary school teachers course with existing mathematics education research found in practitioners’ journals as well as standards imposed by institutions’ framing policy” (p. 2). Ten years later we return to a similar focus.

Mathematical Content Knowledge For Teaching Elementary Mathematics: A Focus On Whole-Number Concepts And Operations, Eva Thanheiser, Ian Whitacre, George Roy

The Mathematics Enthusiast

This report represents part of a recent effort to summarize the state of knowledge of prospective elementary teachers’ (PTs’) mathematics content knowledge and the development thereof. Extensive reviews of the research literature were conducted by a recent PME-­‐NA Working Group across various content areas. This report focuses on whole number and operations. Research in this area is scarce. What we do know from the literature is that PTs’ knowledge of whole number and operations is insufficient and in need of improvement. PTs reason about whole numbers and operations in ways that are tied to the standard algorithms. At the same …

Mathematical Content Knowledge For Teaching Elementary Mathematics: A Focus On Algebra, Krista Strand, Briana Mills

The Mathematics Enthusiast

As part of a recent effort to summarize research-­‐based knowledge of prospective elementary school teachers’ (PTs) mathematical content knowledge, this paper summarizes research literature on PTs’ knowledge of algebra, focusing on the range of years from 1998 through 2012. The 21 papers included in this summary focus on a broad range of topics within algebra, such as (a) producing, representing, and justifying generalizations; (b) interpreting and using algebraic symbols; (c) solving algebraic word problems; and (d) understanding functions. Looking across this body of research, three themes are identified: (1) PTs generally have strong procedural skills and can make mathematically sound …

Mathematical Content Knowledge For Teaching Elementary Mathematics: A Focus On Geometry And Measurement, Christine Browning, Alden J. Edson, Patrick Kimani, Fatma Aslan-Tutak

The Mathematics Enthusiast

This paper summarizes the extant peer-­‐reviewed research on PTs’ understanding of geometry and measurement, focusing on a wide variety of topics within these content domains. When looking across the 26 studies reviewed, findings span a variety of content topics, providing little depth in either the geometry or measurement content domain. However, collective findings do indicate PTs’ overall conceptions in geometry and measurement to be limited and weak, with PTs relying on memorized procedural processes. Some evidence indicates that cognitive development, along with spatial visualization skills, plays a greater role in learning geometry than memory skills. In addition, the van Hiele …

Approaches For Generating 2d Shapes, Pratik Shankar Hada

UNLV Theses, Dissertations, Professional Papers, and Capstones

Constructing a two dimensional shape from given a set of point sites is a well known problem in computation geometry. We present a critical review of the existing algorithms for constructing polygonal shapes. We present a new approach calledinward dentingfor constructing simple polygons. We then extend the proposed approach for modeling polygons with holes. This is the

first known algorithm for modeling holes in the interior of 2d shapes. We also present experimental investigations of the quality of the solutions generated by the proposed algorithms.

For this we implemented the proposed algorithms in Java programming language. The prototype program can …

Numerical Simulations Of Traffic Flow Models, Puneet Lakhanpal

UNLV Theses, Dissertations, Professional Papers, and Capstones

Traffic flow has been considered to be a continuum flow of a compressible liquid having a certain density profile and an associated velocity, depending upon density, position and time. Several one-equation and two-equation macroscopic continuum flow models have been developed which utilize the fluid dynamics continuity equation and help us find analytical solutions with simplified initial and boundary conditions. In this thesis, the one-equation Lighthill Witham and Richards (LWR) model combined with the Greenshield's model, is used for finding analytical and numerical solutions for four problems: Linear Advection, Red Traffic Light turning into Green, Stationary Shock and Shock Moving towards …

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.

Antimagic-Type Labelings, Sogol Jahanbekam

Faculty Publications

No abstract provided.

Deconstructing The Welch Equation Using P-Adic Methods, Abigail Mann, Adelyn Yeoh

Mathematical Sciences Technical Reports (MSTR)

The Welch map x -> g^x-1+c is similar to the discrete exponential map x -> g^x, which is used in many cryptographic applications including the ElGamal signature scheme. This paper analyzes the number of solutions to the Welch equation: g^x-1+c = x (mod p^e) where p is a prime, and looks at other patterns of the equation that could possibly exploited in a similar cryptographic system. Since the equation is modulo p^e, where p is a prime number, p-adic methods of analysis are used in counting the number of solutions modulo p …

Deconstructing The Welch Equation Using P-Adic Methods, Abigail Mann, Adelyn Yeoh

Rose-Hulman Undergraduate Research Publications

The Welch map x -> g^x-1+c is similar to the discrete exponential map x -> g^x, which is used in many cryptographic applications including the ElGamal signature scheme. This paper analyzes the number of solutions to the Welch equation: g^x-1+c = x (mod p^e) where p is a prime, and looks at other patterns of the equation that could possibly exploited in a similar cryptographic system. Since the equation is modulo p^e, where p is a prime number, p-adic methods of analysis are used in counting the number of solutions modulo p …

Hoijer '15 Studies Correlations Between Mathematics And Music, Danielle Kamp

News and Events (Discontinued Series)

No abstract provided.

Simmons' Research Aims To Improve Function For Online Security, Danielle Kamp

News and Events (Discontinued Series)

No abstract provided.

Near Oracle Performance And Block Analysis Of Signal Space Greedy Methods, Raja Giryes, Deanna Needell

CMC Faculty Publications and Research

Compressive sampling (CoSa) is a new methodology which demonstrates that sparse signals can be recovered from a small number of linear measurements. Greedy algorithms like CoSaMP have been designed for this recovery, and variants of these methods have been adapted to the case where sparsity is with respect to some arbitrary dictionary rather than an orthonormal basis. In this work we present an analysis of the so-called Signal Space CoSaMP method when the measurements are corrupted with mean-zero white Gaussian noise. We establish near-oracle performance for recovery of signals sparse in some arbitrary dictionary. In addition, we analyze the block …

Transposing Noninvertible Polynomials, Nathan Cordner

Library Research Grants

In the class of invertible polynomials, the notion of dual polynomials W and W^T, as well as dual groups G and G^T is well-understood. In this paper we investigate finding dual pairs W and W^T for noninvertible polynomials. We find that in many instances, our intuition that stems from invertible polynomials does not extend to the noninvertible case.

Modelling Stock Returns In 'Volatility-In-Mean' Framework Under Up And Down Market Movements, Srikanta Kundu Dr.

Doctoral Theses

The first chapter of this thesis begins with a brief review of the existing literature on empirical studies on stock returns, especially those in the context of the relationship between risk and return, at both univariate and multivariate levels. In the next section, studies on the relationship between stock return and monetary policy are reviewed. The motivation of this work is discussed in Section 1.4. Finally, the format of the thesis is given in Section 1.5.A Brief Review of the Literature on Risk-Return Relationship-Both Univariate and Multivariate Cases. In this section, we first present a brief review of this literature …

The Physicist's Basement, Nora Culik

Journal of Humanistic Mathematics

No abstract provided.

The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried

Journal of Humanistic Mathematics

Teachers and students of mathematics often view history of mathematics as just mathematics as they know it, but in another form. This view is based on a misunderstanding of the nature of history of mathematics and the kind of knowledge it attempts to acquire. Unfortunately, it can also lead to a deep sense of disappointment with the history of mathematics itself, and, ultimately, a misunderstanding of the historical nature of mathematics. This kind of misunderstanding and the disappointment following from it--both raised to the level of resentment--run through the paper "A Critique of the Modern Consensus in the Historiography of …

A Critique Of The Modern Consensus In The Historiography Of Mathematics, Viktor Blåsjö

Journal of Humanistic Mathematics

The history of mathematics is nowadays practiced primarily by professional historians rather than mathematicians, as was the norm a few decades ago. There is a strong consensus among these historians that the old-fashioned style of history is “obsolete,” and that “the gains in historical understanding are incomparably greater” in the more “historically sensitive” works of today. I maintain that this self-congratulatory attitude is ill-founded, and that the alleged superiority of modern historiographical standards ultimately rests on a dubious redefinition of the purpose of history rather than intrinsic merit.

How Do I Love Thee? Let Me Count The Ways For Syllabic Variation In Certain Poetic Forms, Mike Pinter

Journal of Humanistic Mathematics

The Dekaaz poetic form, similar to haiku with its constrained syllable counts per line, invites a connection between poetry and mathematics. Determining the number of possible Dekaaz variations leads to some interesting counting observations. We discuss two different ways to count the number of possible Dekaaz variations, one using a binary framework and the other approaching the count as an occupancy problem. The counting methods described are generalized to also count variations of other poetic forms with syllable counts specified, including haiku. We include Dekaaz examples and suggest a method that can be used to randomly generate a Dekaaz variation.

Fields In Math And Farming, Susan D'Agostino

Journal of Humanistic Mathematics

A young woman’s search for a a contemplative, insightful experience leads her from farming to mathematics.