Mathematics Commons^™

Linguistic Invention In Mathematical Communication Among Practicing Elementary School Teachers, Christine Johnson, Janet Walter

Journal of Undergraduate Research

As a tutor in the BYU Math Lab, I attempted to model correct vocabulary to be consistent with the students’ textbooks and professors. However, at times it seemed as though I needed to use more creative language to effectively communicate mathematical concepts. I began to wonder if it was possible to model correct mathematical vocabulary and convey my intended meanings at the same time. As an undergraduate in the Mathematics Education program, I knew that studying mathematical communication would make me a more effective teacher.

Traveling Waves, Keith Rudd, Dr. Jeffery Humpherys

Journal of Undergraduate Research

Traveling waves are, mathematically speaking, partial differential equations which can be expresses as U(x-ct), where x is the spatial variable, t is time, and c is the speed of the wave. Traveling waves have applications in fluid dynamics, optics, and many other areas.

Foundations Of Tropical Geometry Classification Of Polynomials, Nathan Manwaring, Dr. Tyler Jarvis

Journal of Undergraduate Research

Tropical Mathematics is a relatively new field of mathematics that is getting a lot of attention recently. It is applicable in the field of Combinatorics as well as Phylogenetics, and more uses are being found each day. Our goal was to find a way to classify Tropical Polynomials so that they may be better understood and ultimately bridge the gap between different applications and discoveries in Tropical Mathematics.

Finding A Galois Representation Corresponding To A Hecke Eigenclass, Meghan De Witt, Dr. Darrin Doud

Journal of Undergraduate Research

My project was to finish a thirteen year old unsolved problem that provided an important computational example of a conjecture in the field of Algebraic Number Theory.

Exploring The Open-Response Task As A Tool For Assessing The Understanding Of Fifth- Grade Students In The Content Area Of Fractions, Heather Bahlmann, Janet G. Walter

Journal of Undergraduate Research

Inferring student understanding is at the heart of improvement in mathematics learning and teaching. Assessment provides valuable information which can be used to “promote growth, modify programs, recognize student accomplishments, and improve instruction” (NCTM, 1995, p.27). It is imperative that the methods for assessing student understanding be constantly explored and evaluated. Ou decision to research the open-response task as an assessment tool results from our perspective that students make sense of mathematics by exercising personal agency. Personal agency is the freedom and responsibility to choose to act (Walter & Gerson, 2006). Open-response tasks allow students to exercise personal agency, hence …

Two-Part Reconstruction In Compressed Sensing, Yanting Ma, Dror Baron, Deanna Needell

CMC Faculty Publications and Research

Two-part reconstruction is a framework for signal recovery in compressed sensing (CS), in which the advantages of two different algorithms are combined. Our framework allow s to accelerate the reconstruction procedure without compromising the reconstruction quality. To illustrate the efficacy of ou r two-part approach, we extend the author’s previous Sudocodes algorithm and make it robust to measurement noise. In a 1- bit CS setting, promising numerical results indicate that our algorithm offers both a reduction in run-time and improvement in reconstruction quality

The Effect Of A Long-Term Professional Development Course In Standards-Based Mathematics On The Attitudes And Practices Of Inservice Teachers, Destiny Turner, Dr. Candice Ridlon

Journal of Undergraduate Research

In 2000, the National Council of Teachers of Mathematics (NCTM) developed a set of principles and standards to guide mathematics teaching in grades K-12. These principles outline pedagogy that encourages students to discover and understand math on a conceptual level. These monumental standards are widely recognized, but unfortunately, are not as widely implemented in actual classrooms. Most often, this problem is addressed through short-term professional development workshops.

Review: Unitary Equivalence To Truncated Toeplitz Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Factorization Of Tropical Polynomials, Nathan Grigg, Dr. Tyler Jarvis

Journal of Undergraduate Research

Tropical algebra, also called “min-plus” or “max-plus” algebra, is a relatively new topic in mathematics that has recently caught the interest of algebraic geometers, computer scientists, combinatorists, and other mathematicians. According to Andreas Gathmann , tropical algebra was pioneered by mathematician and computer scientist Imre Simon in the 1980s but did not receive widespread attention until a few years ago. Interestingly, the title “tropical algebra” is nothing more than a reference to Simon’s home country—Brazil.

Non-Linear Ray Tracing Visualizing The Impossible, Jared Duke, Dr. Matthew Anderson

Journal of Undergraduate Research

Ray tracing is a common technique for computational, photo-realistic simulation of the “real world.” However, most current approaches assume light propagation is linear: that is, light always travels in a straight line. Our aim was to create a ray tracing program that would handle the “bending” of light waves at relativistic speeds or by gravitational forces. This could in turn be used to assist scientists in understanding the numerical results from their research and to help others understand and visualize such complex natural phenomenon.

Assessing Cognitive Construction In Learning Statistics As Applied Through Mathematics Education, Aubrey Baxter, Dr. Hope Gerson

Journal of Undergraduate Research

Paul Fields in the statistics department was my first mentor. Together we tried to develop a new pedagogy for teaching statistics. This interested me because I may teach advanced placement statistics after I graduate from the Mathematics Education program. A position then came available to me as a research assistant for Dr. Hope Gerson. It was a better opportunity because it is in my field of study and it allowed me work with statistics and apply calculus. Together with Dr. Walter, Dr. Gerson taught an Honors Calculus 1 class for two semesters and an Honors Calculus 2 class for one …

Calculus Excel At Byu: Increasing Student Potential For Success, Karla Jeanese Hendricks, Dr. Michael Dorff

Journal of Undergraduate Research

Success in calculus can have significant implications both within an intended field of study and throughout academic pursuits. Of the 34 science, technology, engineering, and mathematics (STEM) majors at BYU, 25 of them require calculus for graduation and 20 of them require it as a prerequisite for other courses. A study at Bryant University in Rhode Island examined mathematics SAT scores, verbal SAT scores, percentile rank in high school graduating class, percentage score on a college mathematics placement exam, and calculus grades of actuarial students; it was found that the calculus grades were the “single best predictor of a student’s …

Why Rozenzweig-Style Midrashic Approach Makes Rational Sense: A Logical (Spinoza-Like) Explanation Of A Seemingly Non-Logical Approach, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A 20 century German Jewish philosopher Franz Rosenzweig promoted a new approach to knowledge, an approach in which in addition to logical reasoning, coming up with stories with imagined additional details is also important. This approach is known as midrashic since it is similar to the use of similar stories -- known as midrashes -- in Judaism. While stories can make the material interesting, traditionally, such stories are not viewed as a serious part of scientific discovery. In this paper, we show that this seemingly non-logical approach can actually be explained in logical terms and thus, makes perfect rational sense.

Why In Mayan Mathematics, Zero And Infinity Are The Same: A Possible Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In Mayan mathematics, zero is supposed to be, in some sense, equal to infinity. At first glance, while this statement may have a deep philosophical meaning, it does not seem to make much mathematical sense. In this paper, we show, that this statement may be made mathematically reasonable. Specifically, on a real line, it is often useful to consider both −∞ and +∞ as a single infinity. When we deal with very small and very large numbers, it makes sense to use floating point representation, i.e., in effect, consider logarithms of the original values. In terms of logarithms, the original …

A Construction That Produces Wallis-Type Formulas, Joshua M. Fitzhugh, David L. Farnsworth

Articles

Generalizations of the geometric construction that repeatedly attaches rectangles to a square, originally given by Myer- son, are presented. The initial square is replaced with a rectangle, and also the dimensionality of the construction is increased. By selecting values for the various parameters, such as the lengths of the sides of the original rectangle or rectangular box in dimensions more than two and their relationships to the size of the attached rectangles or rectangular boxes, some interesting formulas are found. Examples are Wallis-type infinite-product formulas for the areas of p-circles with p > 1.

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 …

Can The Differentiated Math Classroom Be A Reality?, Carl Jeff Morris

Mathematics Graduate Theses

Imagine a math classroom that looked more like a Google workplace where collaboration, teamwork, and innovation are the centerpieces. Instead of just students sitting in rows passively learning about the nature of mathematics, picture a classroom of students in small circle discussing mathematics. This could range from groups working together on a problem solving strategy for a newly learned concept, students helping students using technology as an aid, another small group receiving intervention from the teacher, or individual students making or viewing instructional math videos. All of this according to research focused on classroom differentiation; specifically in middle school and …

The Generalized Sub-Fractional Brownian Motion, Aissa Sghir

Communications on Stochastic Analysis

No abstract provided.

Bayesian Decision Theoretic Approach To Directional Multiple Hypotheses Problems, Naveen K. Bansal, Klaus J. Miescke

Mathematics, Statistics and Computer Science Faculty Research and Publications

A multiple hypothesis problem with directional alternatives is considered in a decision theoretic framework. Skewness in the alternatives is considered, and it is shown that this skewness permits the Bayes rules to possess certain advantages when one direction of the alternatives is more important or more probable than the other direction. Bayes rules subject to constraints on certain directional false discovery rates are obtained, and their performances are compared with a traditional FDR rule through simulation. We also analyzed a gene expression data using our methodology, and compare the results to that of a FDR method.

Stein's Method For Brownian Approximations, L Coutin, L Decreusefond

Communications on Stochastic Analysis

No abstract provided.