Mathematics Commons^™

Calculus Application To Topographic Mapping, Veronica Zapata

Undergraduate Journal of Mathematical Modeling: One + Two

The goal of the paper is to find the volume of water in a ditch. An example image of ditch is given in Appendix C. The first act that before any calculation can be performed is to record the field work. Once at the property the ditch must be identified. Three points of elevations per section should be measured by the surveyor; one point is at the center of the ditch (the lowest point) and the two ones are at the ends (the highest points). The sections are detailed in Appendix A. Using the elevation points from the property, we …

Calculating The Electromotive Force Through A Loop, Esteban Leal

Undergraduate Journal of Mathematical Modeling: One + Two

This is a short article which utilizes the equations of Faraday’s law, Ampere’s law, and Ohm’s law. We manipulate the formulas to solve a practical application in which the electromotive force must be calculated. With the successful calculation of the electromotive force, we can use this technique in larger applications.

Calculating Water Wavelength Using Dispersion Relation And Approximation, Chantelle Lee

Undergraduate Journal of Mathematical Modeling: One + Two

The dispersion relation equation is used to directly compute wave number and wave length to compliment water wave pressure sensor readings. Waves are measured to help coastal engineering to better mitigate coastal infrastructures. Various given wave periods and water depths are used to show how the dispersion relation equation could compute wave length. Also, shallow and deep-water approximations are formulated from the dispersion relation equation and the results are compared.

Integrating The Equation Of Hydrostatics For Groundwater Under Non-Isothermal Conditions, Megan A. Levine

Undergraduate Journal of Mathematical Modeling: One + Two

Groundwater is an important area of study for several scientific fields and is relevant to many problems in our everyday life. One way the study of groundwater has become different in this age of technology is through modeling. Modeling is used in numerous fields to visualize complex problems and view inaccessible areas, such as under the Earth. An essential part of groundwater modeling is to know water pressure at any depth underground. The difficulty in calculating this is that there are several variables that affect water pressure, all of which are affected by one another and all are calculated by …

An Uncommon Textbook: Review Of Common Sense Mathematics By Ethan Bolker And Maura Mast, Bernard Madison

Numeracy

Ethan D. Bolker and Maura B. Mast. 2016. Common Sense Mathematics.(Washington DC.: Mathematics Association of America) ISBN-13: 978-1-93951-210-9.

Common Sense Mathematics is an integrative quantitative reasoning (QR) textbook that is built around scores of exercises derived from authentic circumstances from public media and other public sources. The exercises elicit responses from students requiring extensive communication and analyses and distinguish the book from ones typically encountered in a mathematics or science course. Responses to exercises often require one-half page or more of writing and can occupy considerable class time in discussion. The book has material for a one- or two-semester …

The Second Decade Of Numeracy: Entering The Seas Of Literacy, H. L. Vacher

Numeracy

This multipurpose editorial explores and tries to count the many types of literacy that are referred to by name in Wikipedia and Numeracy. Wikipedia’s Category:Literacy page identifies 44 kinds of literacy that are the subject of articles, ranging from numeracy and graphicacy to braille literacy and diaspora literacy. In addition, searching Google finds more than 30 adjective-literacy or noun-literacy collocations, including quantitative literacy, adult literacy, and document literacy, that do not have Wikipedia pages of their own but are mentioned on other Wikipedia pages. The sum puts this modest literacy count in line with the more than 70 bodies …

Three Formative Questions In The Quantitative Literacy Movement, Dorothy Wallace

Numeracy

In this essay we remember early discussions attempting to answer three questions that played a formative role in our understanding of and approach to numeracy, quantitative literacy, and quantitative reasoning: (1) What is numeracy? (2) Should the QL movement promote any specific kind of pedagogy? (3) What organizational structure will best support QL?

As the QL movement has progressed, these three questions continue to be difficult to answer. As a result, they have been useful formative guides for institutions and organizations seeking to improve the quantitative reasoning of students. Now that the quantitative literacy movement has a firmer standing in …

The Sons Report (1989-1994, Mathematical Association Of America): The Way It Was, Linda R. Sons

Numeracy

Recollections and commentary by Linda R. Sons on a 1994 national report entitled Quantitative Reasoning for College Graduates: A Complement to the Standards. Professor Sons chaired the committee which wrote the report and championed its use.

This paper traces the development of the 1994 MAA report Quantitative Reasoning for College Graduates: A Complement to the Standards--a report which is still surprisingly relevant. The paper highlights some major parts of the report, describing the context in which its conclusions were made. Additionally, it challenges and encourages those continuing the quest for QL in the nation by noting progress made …

Developing Mathematics Teachers’ Attention To Quantitative Reasoning In Task Design: A Modeling Approach, David Glassmeyer

Numeracy

This study examines how a models-and-modeling perspective affected teachers' attention to quantitative reasoning in task design. A Model-Eliciting Activity (MEA) was implemented with 21 teachers over four weeks, challenging teachers to design a quantitative reasoning task for their students. Teachers’ initial quantitative reasoning tasks did not incorporate quantities or quantitative relationships, two essential components of quantitative reasoning. As teachers revised their tasks through the MEA, most teachers began attending to these components. This article details how a modeling approach to teacher education provided a method to describe and support teachers to incorporate quantitative reasoning in their classroom tasks, though attending …

Lump Solutions And Riemann-Hilbert Approach To Soliton Equations, Sumayah A. Batwa

USF Tampa Graduate Theses and Dissertations

In the first part of this dissertation we introduce two matrix iso-spectral problems, a Kaup-Newell type and a generalization of the Dirac spectral problem, associated with the three-dimensional real Lie algebras sl(2;R) and so(3;R), respectively. Through zero curvature equations, we furnish two soliton hierarchies. Hamiltonian structures for the resulting hierarchies are formulated by adopting

the trace identity. In addition, we prove that each of the soliton hierarchies has a bi-Hamiltonian structure which leads to the integrability in the Liouville sense. The motivation of the first part is to construct soliton hierarchies with infinitely many commuting symmetries and conservation laws.

The …

Groups Generated By Automata Arising From Transformations Of The Boundaries Of Rooted Trees, Elsayed Ahmed

USF Tampa Graduate Theses and Dissertations

In this dissertation we study groups of automorphisms of rooted trees arising from the transformations of the boundaries of these trees. The boundary of every regular rooted tree can be endowed with various algebraic structures. The transformations of these algebraic structures under certain conditions induce endomorphisms or automorphisms of the tree itself that can be described using the language of Mealy automata. This connection can be used to study boundarytransformations using the propertiesof the induced endomorphisms, or vice versa.

We concentrate on two ways to interpret the boundary of the rooted d-regular tree. In the first approach discussed in detail …

Quantitative Literacy And Civic Virtue, William Briggs

Numeracy

Mathematics educators are occasionally called upon to justify the existence or the offering of quantitative literacy courses. This paper argues that effective quantitative literacy courses have different goals than algebra courses and are legitimate alternatives to algebra courses for non-STEM students. Furthermore, quantitative literacy courses affirm the historic relationship between citizenship and education. In today’s world of proliferating news sources, social media, and fake news, quantitative literacy has become an essential component of the long-held ideal of civic virtue.

Hamiltonian Structures And Riemann-Hilbert Problems Of Integrable Systems, Xiang Gu

USF Tampa Graduate Theses and Dissertations

We begin this dissertation by presenting a brief introduction to the theory of solitons and integrability (plus some classical methods applied in this field) in Chapter 1, mainly using the Korteweg-de Vries equation as a typical model. At the end of this Chapter a mathematical framework of notations and terminologies is established for the whole dissertation.

In Chapter 2, we first introduce two specific matrix spectral problems (with 3 potentials) associated with matrix Lie algebras $\mbox{sl}(2;\mathbb{R})$ and $\mbox{so}(3;\mathbb{R})$, respectively; and then we engender two soliton hierarchies. The computation and analysis of their Hamiltonian structures based on the trace identity affirms …

Generalizations Of Quandles And Their Cohomologies, Matthew J. Green

USF Tampa Graduate Theses and Dissertations

Quandles are distributive algebraic structures originally introduced independently by David Joyce and Sergei Matveev in 1979, motivated by the study of knots. In this dissertation, we discuss a number of generalizations of the notion of quandles. In the first part of this dissertation we discuss biquandles, in the context of augmented biquandles, a representation of biquandles in terms of actions of a set by an augmentation group. Using this representation we are able to develop a homology and cohomology theory for these structures.

We then introduce an n-ary generalization of the notion of quandles. We discuss a number of properties …

Developing A Model To Predict Prevalence Of Compulsive Behavior In Individuals With Ocd, Lindsay D. Fields

USF Tampa Graduate Theses and Dissertations

The most common method of diagnosing Obsessive-Compulsive Disorder is the Yale-Brown Obsessive Compulsive Scale, which measures the severity of symptoms without regard to compulsions. However, this scale is limited to only considering the quantifiable time and energy lost to compulsions. Conversely, current systems of brain imaging arrest mobility and thus make it virtually impossible to observe compulsions at all, focusing instead on neurological responses to external stimuli. There is little research which merges both approaches, to consider the neuro-physiological effects of obsessions as well as the physical response through compulsions. As such, this research is focused on developing a model …

A Hybrid Dynamic Modeling Of Time-To-Event Processes And Applications, Emmanuel A. Appiah

USF Tampa Graduate Theses and Dissertations

In the survival and reliability data analysis, parametric and nonparametric methods are used to estimate the hazard/risk rate and survival functions. A parametric approach is based on the assumption that the underlying survival distribution belongs to some specific family of closed form distributions (normal, Weibull, exponential, etc.). On the other hand, a nonparametric approach is centered around the best-fitting member of a class of survival distribution functions. Moreover, the Kaplan-Meier and Nelson-Aalen type nonparametric approach do not assume either distribution class or closed-form distributions. Historically, well-known time-to-event processes are death of living specie in populations and failure of component in …

Orthogonal Polynomials With Respect To The Measure Supported Over The Whole Complex Plane, Meng Yang

USF Tampa Graduate Theses and Dissertations

In chapter 1, we present some background knowledge about random matrices, Coulomb gas, orthogonal polynomials, asymptotics of planar orthogonal polynomials and the Riemann-Hilbert problem. In chapter 2, we consider the monic orthogonal polynomials, $\{P_{n,N}(z)\}_{n=0,1,\cdots},$ that satisfy the orthogonality condition,

\begin{equation}\nonumber \int_\mathbb{C}P_{n,N}(z)\overline{P_{m,N}(z)}e^{-N Q(z)}dA(z)=h_{n,N}\delta_{nm} \quad(n,m=0,1,2,\cdots), \end{equation}

where $h_{n,N}$ is a (positive) norming constant and the external potential is given by

$$Q(z)=|z|^2+ \frac{2c}{N}\log \frac{1}{|z-a|},\quad c>-1,\quad a>0.$$

The orthogonal polynomial is related to the interacting Coulomb particles with charge $+1$ for each, in the presence of an extra particle with charge $+c$ at $a.$ For $N$ large and a fixed ``c'' this …

Non-Equilibrium Phase Transitions In Interacting Diffusions, Wael Al-Sawai

USF Tampa Graduate Theses and Dissertations

The theory of thermodynamic phase transitions has played a central role both in theoretical physics and in dynamical systems for several decades. One of its fundamental results is the classification of various physical models into equivalence classes with respect to the scaling behavior of solutions near the critical manifold. From that point of view, systems characterized by the same set of critical exponents are equivalent, regardless of how different the original physical models might be. For non-equilibrium phase transitions, the current theoretical framework is much less developed. In particular, an equivalent classification criterion is not available, thus requiring a specific …

Review Of Painting By Numbers By Jason Makansi, Thomas J. Pfaff

Numeracy

Makansi, Jason. 2016. Painting By Numbers: How to Sharpen Your BS Detector and Smoke Out the "Experts." (Tucson, AZ: Layla Dog Press, 2016). 196 pp. ISBN 978-0-9984259-0-0.

In Painting by Numbers Jason Makansi adds another book to the quantitative literacy bookshelf, with a book focusing on models. The book offers twelve commandments to aid the reader in assess quantitative models. The second section of the book offers examples to apply the models. Increasing quantitative literacy is crucial and generally, the more books the better. Unfortunately, this book is too superficial, often misses key ideas, and can easily lead a person …

Life, The Universe, And Numeracy: Review Of A Numerate Life By John Allen Paulos (2015), Kira H. Hamman

Numeracy

John Allen Paulos. 2015. A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours (Buffalo, NY: Prometheus Books) 200 pp. ISBN: 978-1633881181

John Allen Paulos, author of Innumeracy and many other books addressing quantitative literacy and numeracy in society, tackles autobiography in this quirky "anti-memoir."

A Few Reflections On A Numerate Life, John Allen Paulos

Numeracy

John Allen Paulos. 2015. A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours (Amherst, NY: Prometheus Books). 200 pp. ISBN 978-1633881181.

This piece briefly introduces and excerpts A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours, written by John Allen Paulos and published by Prometheus Books. The book shares observations on life—many biographical—from the perspective of a numerate mathematician. The excerpt uses basic statistical reasoning to explore why we should expect that being odd is a most normal experience.

Math Course For Liberal Arts Majors: A Pilot With Embedded Remediation, Eileen B. Perez, Hansun To, Mary Fowler, Linda Larrivee

Numeracy

This study was designed to determine if embedded remediation is significant in accelerating the pathway to completion of a college-level math course for students needing remediation. The project studied the impact on student success in a quantitative literacy course at a Massachusetts four-year state university with remedial material embedded. The course satisfies the university’s general education math requirement for students with liberal arts majors who are not required to complete college algebra or calculus-based courses. The paper begins with a presentation of the issues with remedial mathematics and its impact on students’ graduation and persistence. Next, the paper covers the …

Model Function Of Women’S 1500m World Record Improvement Over Time, Annie Allmark

Undergraduate Journal of Mathematical Modeling: One + Two

We give an example of simple modeling of the known sport results that can be used for athletes’ self-improvement and estimation of future achievements.

This project compares the women’s 1500-meter world record times to the time elapsed between when they were run. The function of time which describes this comparison is found through graphing the data and interpreting the graphs. Then the obtained model function is compared to the real time data. The conclusions drawn from the result include that the calculated function of time lacks in accuracy as time elapsed increases, but the model could be used to estimate …

Polycrystalline Silicon Solar Module Power Max, Jaynil Patel

Undergraduate Journal of Mathematical Modeling: One + Two

In recent years solar energy has started to make its impact in the sunshine state. The solar panels are made up of photovoltaic cells, which convert the sun’s rays into electricity. One of the ways to improve solar panel efficiency is to increase the power output of a solar collector. The maximum power is calculated by determining the maximum power for voltage and the current. This is done by adding the maximum values for the equation for power and then using differentiation. After the maximum values are found for each hour of the day from sunset to noon, each individual …

Tsunami Waves, Samantha Pennino

Undergraduate Journal of Mathematical Modeling: One + Two

Predicting the travel time of tsunami waves is imperative to the safety and well-being of possibly affected communities since tsunami waves can happen incredibly fast. So, knowing how long an area is until a tsunami approaches dramatically helps with mitigation strategies. As an example we calculate the travel time of a tsunami wave to Somalia and Sri-Lanka that flowed an earthquake in 2004 in the Indian ocean off the coast of Sumatra. This is done by using the velocity from the shallow wave equation of the waves and piecewise integration.

Optimization Of A Water Gas Shift Reaction, Ali Albuloushi

Undergraduate Journal of Mathematical Modeling: One + Two

The optimum flow rate of steam (H₂0) to the reactor for the purpose of producing hydrogen gas for sale is determined.

Trend Analysis And Completion Prediction Of The Section Project, Ronald Jones

Undergraduate Journal of Mathematical Modeling: One + Two

Creating an accurate prediction of the completion timeline of a software development project is complicated and error prone. Developers will gain a natural intuition as to how long a task should take then. However, this prediction can end up being wrong in many cases due to many factors. This paper will attempt to determine a formula which allows a more accurate prediction to be created.

Creating an accurate prediction of the completion timeline of a software development project is complicated and error prone. Developers will gain a natural intuition as to how long a task should take then. However, this …

Minimizing Container Weight, Ibrahim Alomran

Undergraduate Journal of Mathematical Modeling: One + Two

Increased globalization has resulted in increased competition in the shipping industry. Since large carriers control over 70% of the total shipping industry, small carriers are left with only 30% of the market share to compete for. Ultimately, profit margins for small carriers have become very minimal. There is, therefore, need to develop a strategy that will aid in optimizing the profits of carriers. The goal of this paper is to develop a model that will help determine the minimum weight for a particular container design. The validity of the model is important in the sense that minimum container weight will …

Elapsed Time Of Vehicle Acceleration, Jensen Mctighe

Undergraduate Journal of Mathematical Modeling: One + Two

Newton’s Second Law states that force is equal to the mass of an object multiplied by its acceleration. More specifically, force is the mass times the instantaneous change in velocity over time of an object. By rearranging this equation, it can be determined that the time elapsed of the acceleration of an object is equal to the integral of the inverse value of the force relative to change in velocity (dv). In the context of real world application, this method can be used to calculate the time taken for a vehicle to accelerate from its minimum to maximum speed, given …

Design Of Nozzle For High-Powered Solid Rocket Propellant, Jackson Stephenson

Undergraduate Journal of Mathematical Modeling: One + Two

This paper presents a preliminary nozzle design for a high-altitude rocket to be built by SOAR, the Society of Aeronautics and Rocketry. The equations and methods used for analysis came from professional sources via text or informational videos. The equations in focus will look at the temperature/pressure/area-Mach relationships for isentropic flow, pressure expansions in selected materials, and finding other characteristic properties using safe chemical property assumptions using CEARUN. The equations were used under the assumption of an isentropic flow under sea level conditions. If the design and the projected results look promising, they will be implemented soon for machining and …