Mathematics Commons^™

Steam Inspired By Insight, Diana Vizcarra

The Transdisciplinary STEAM+ Journal

Innovators of the 21st century might come from unexpected places. Visual impairment is no barrier when technology and creativity intersect. The world needs blind innovators! The blind input data without visual association and download blueprints of their surroundings to format a mental database. They categorize patterns, textures, and conditions to perceive their location in space. They are able to capture the beauty of the world through poetry and predict future trends through past experience – all without visual access to the physical world they inhabit.

This writing was possible because of collaboration with Angie Menjivar.

The Efficacy Of Mathematics Education, Eric Geimer

The Transdisciplinary STEAM+ Journal

Evidence supports the notion that mathematics education in the United States is inadequate. There is also evidence that mathematics education deficiencies extend internationally. The worldwide mathematics education deficit appears large enough that improving student performance in this educational problem area could yield great economic benefit. To improve the efficacy of mathematics education, education’s root problems must first be understood. Often supposed educational root problems are considered and contrasted against potential deficiencies of mathematics methodologies and curricula that are based on mainstream educational philosophies. The educational philosophies utilized to form early-grade mathematics methodologies and related curricula are judged to be the …

Session B-2: Build Student Engagement, Mental Math, And Reasoning With "Math Talks", Sendhil Revuluri

Professional Learning Day

"Math talks" are quick routines that you can implement in your classroom within days. They can raise engagement, build efficient, accurate, and flexible mental math strategies, and help students construct arguments and critique reasoning. We will engage in math talks, analyzing how they can be enacted in the classroom and designed for specific goals or respond to specific misconceptions. Participants will learn about math talks that support understanding of number, algebra, and other domains.

Session B-1: Geometry In Art & Architecture, Julie Dowling

Professional Learning Day

Math is all around us! Discover how to implement geometry lessons using art and architecture that the students see around them every day.

Session A-2: Cycloids!, Ruth Dover

Professional Learning Day

This session includes a hands-on exploration to see graphs of different types of cycloids. Participants will use trigonometry to create the parametric equations for the graphs. This topic lends itself nicely to projects for pre-calculus students. Software will be shown to help see more examples and patterns.

Coverage And Detection In Wireless Sensor Networks., Mrinal Nandi Dr.

Doctoral Theses

A Wireless Sensor Networks (WSNs), which are two or three dimensional systems, usually consist of a large number of small sensors equipped with some processing circuit, and a wireless transceiver. The sensors have small size, low battery capacity, non-renewable power supply, small processing power, limited buffer capacity and low-power radio. They may measure distance, direction, speed, humidity, wind speed, soil makeup, temperature, chemicals, light, and various other parameters. The sensors are autonomous devices with integrated sensing, processing, and communication capabilities.In this thesis, we consider ‘coverage problem’ and ‘detection problem’ in Wireless Sensor Networks (WSNs) in grid as well as in …

Representations Associated To The Group Matrix, Joseph Aaron Keller

Theses and Dissertations

For a finite group G = {g_0 = 1, g_1,. . ., g_{n-1}} , we can associate independent variables x_0, x_1, . . ., x_{n-1} where x_i = x_{g_i}. There is a natural action of Aut(G) on C[x_0, . . . ,x_{n-})]. Let C_1, . . . , C_r be the conjugacy classes of G. If C = {g_{i_1}, g_{i_2}, . . . , g_{i_u }} is a conjugacy class, then let x(C) = x_{i_1} + x_{i_2} + . . . + x_{i_u}. Let ρG be the representation of Aut(G) on C[x_0, . . . , x_(n-1)]/〈x(C_1), . . . …

The Dual Gromov-Hausdorff Propinquity, Frédéric Latrémolière

Mathematics Preprint Series

Motivated by the quest for an analogue of the Gromov-Hausdorff distance in noncommutative geometry which is well-behaved with respect to C*- algebraic structures, we propose a complete metric on the class of Leibniz quantum compact metric spaces, named the dual Gromov-Hausdorff propinquity, which resolves several important issues raised by recent research in noncommutative metric geometry: our new metric makes *-isomorphism a necessary condition for distance zero, is well-adapted to Leibniz seminorms, and — very importantly — is complete, unlike the quantum propinquity which we introduced earlier. Thus our new metric provides a new tool for noncommutative metric geometry which offers …

The Nature And Nurture Of Intuition, Thomas Q. Sibley

Forum Lectures

Are people just innately good at mathematics or not? My teaching experience suggests mathematical ability is not just fate: Students develop their mathematical abilities by doing mathematics. In particular we discuss geometric intuition, its connection with geometric reasoning and the possibility of developing them, using examples to get the listeners actively thinking about their own geometric thinking.

Combinatorial Approach To Computation Of Jones Polynomial Of A Torus Link, N. Nemirovskaya

Journal of Undergraduate Research

First of all I would like to thank the Office of Research and Creative Activities for choosing me as one of the recipients of the Research and Creative Activities scholarship. This scholarship allowed me to spend more time working on the proposed project.

Identification Of Tetrapeptides From A Mixture Based Positional Scanning Library That Can Restore Nm Full Agonist Function Of The L106p, I69t, I102s, A219v, C271y, And C271r Human Melanocortin-4 Polymorphic Receptors (Hmc4rs), Erica M. Haslach, Huisuo Huang, Marvin Dirain, Ginamarie Debevec, Phaedra Geer, Radleigh Santos, Marc Giulianotti, Clemencia Pinilla, Jon R. Appel, Skye R. Doering, Michael A. Walters, Richard A. Houghten, Carrie Haskell-Luevano

Mathematics Faculty Articles

Human obesity has been linked to genetic factors and single nucleotide polymorphisms (SNPs). Melanocortin-4 receptor (MC4R) SNPs have been associated with up to 6% frequency in morbidly obese children and adults. A potential therapy for individuals possessing such genetic modifications is the identification of molecules that can restore proper receptor signaling and function. These compounds could serve as personalized medications improving quality of life issues as well as alleviating diseases symptoms associated with obesity including type 2 diabetes. Several hMC4 SNP receptors have been pharmacologically characterized in vitro to have a decreased, or a lack of response, to endogenous agonists …

Higher Order A-Stable Schemes For The Wave Equation Using A Successive Convolution Approach, Matthew F. Causley, Andrew J. Christlieb

Mathematics Publications

In several recent works, we developed a new second order, A-stable approach to wave propagation problems based on the method of lines transpose (MOL$^T$) formulation combined with alternating direction implicit (ADI) schemes. Because our method is based on an integral solution of the ADI splitting of the MOL$^T$ formulation, we are able to easily embed non-Cartesian boundaries and include point sources with exact spatial resolution. Further, we developed an efficient $O(N)$ convolution algorithm for rapid evaluation of the solution, which makes our method competitive with explicit finite difference (e.g., finite difference time domain) solvers, in terms of both accuracy and …

A Computational Approach To Qualitative Analysis In Large Textual Datasets, Michael Evans

Dartmouth Scholarship

In this paper I introduce computational techniques to extend qualitative analysis into the study of large textual datasets. I demonstrate these techniques by using probabilistic topic modeling to analyze a broad sample of 14,952 documents published in major American newspapers from 1980 through 2012. I show how computational data mining techniques can identify and evaluate the significance of qualitatively distinct subjects of discussion across a wide range of public discourse. I also show how examining large textual datasets with computational methods can overcome methodological limitations of conventional qualitative methods, such as how to measure the impact of particular cases on …

Oscillatory Behavior Of Solutions Of Third-Order Delay And Advanced Dynamic Equations, Murat Adivar, Elvan Akin, Raegan Higgins

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we consider oscillation criteria for certain third-order delay and advanced dynamic equations on unbounded time scales. A time scale T is a nonempty closed subset of the real numbers. Examples will be given to illustrate some of the results.

Asymptotic Spectral Properties Of The Schrödinger Operator With Thue-Morse Potential, William Clark, Rachael Kline, Michaela Stone

Undergraduate External Publications

The open problem

Study the Thue-Morse trace map; in particular, find the asymptotics of the Hausdorff dimension of the spectrum as the coupling constant tends to zero or infinity.

Our research

• We studied the dynamics of the Thue-Morse trace map.

• We developed MATLAB code to help approximate the box-counting dimension, thickness, and Hausdorff measure of the Schrödinger operator with Thue-Morse potential.

• We analysed the resulting data, which confirmed conjectures about the asymptotic behavior of the fractal dimensions of the operator. Asymptotic Spectral Properties of the Schr¨odinger Operator with Thue-

Arithmetic Toric Varieties, E. Javier Elizondo, Paulo Lima-Filho, Frank Sottile, Zach Teitler

Mathematics Faculty Publications and Presentations

We study toric varieties over a field k that split in a Galois extension K / k using Galois cohomology with coefficients in the toric automorphism group. Part of this Galois cohomology fits into an exact sequence induced by the presentation of the class group of the toric variety. This perspective helps to compute the Galois cohomology, particularly for cyclic Galois groups. We use Galois cohomology to classify k-forms of projective spaces when K / k is cyclic, and we also study k-forms of surfaces.

The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre

Presentations and Publications

We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein–Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from …

The 2010 Banff Workshop On Teachers As Stakeholders In Mer, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

If You Really Want To Get Ahead, Get A Bunch Of Theories… And Data To Test Them, Alan H. Schoenfeld

The Mathematics Enthusiast

This paper addresses questions of mathematics teachers’ professional development. My goal is not to provide “answers,” although I have worked for some years to enhance teachers’ capacity to create rich learning environments for their students. Rather, my goal is to problematize the issue, to ask: How do we frame questions of professional development in ways that are theoretically grounded? What theories do you need to know, in order do a good job of professional development? In the light of this kind of theoretical framing, I will discuss two related attempts at supporting teachers in their work.

The Teachers Institute Approach To Professional Development, Roger Howe

The Mathematics Enthusiast

The Yale New Haven Teachers Institute (YNHTI) provides a distinctive, perhaps nearly unique, approach to professional development. It originated in the 1978 as an outreach activity of Yale University to the New Haven Public Schools. For 20 years, it operated almost exclusively in New Haven. In 1998, under the leadership of its founder, James Vivian, YNHTI conducted a National Demonstration Project, and since 2004 has promoted a National Initiative, to spread the Teachers Institute model to other cities, with a focus on school districts with low income demographics. Currently there is a League of Teachers Institutes with Institutes operating in …