Applied Mathematics Commons^™

Modeling Phloem Temperatures Relative To Mountain Pine Beetle Phenology, Matthew Jared Lewis

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

We explore a variety of methods to estimate phloem temperatures from ambient air temperatures suitable for the mountain pine beetle, Dendroctonus ponderosae. A model's ability to induce the same phenology generated from observed phloem temperatures measures its effectiveness rather than a simple reconstruction of phloem temperatures. From a model's phenology results we are able to ascertain whether the model produces a similar amount of developmental energy exhibited by observed phloem temperatures.

Three models performed best: Newton, Newton South and Matching. The Newton model uses Newton's Law of Cooling to effectively estimate northern aspect phloem temperatures. The Newton South model …

Improved Algorithms For Ear-Clipping Triangulation, Bartosz Kajak

UNLV Theses, Dissertations, Professional Papers, and Capstones

We consider the problem of improving ear-slicing algorithm for triangulating a simple polygon. We propose two variations of ear-slicing technique for generating “good-quality” triangulation. The first approach is based on searching for the best triangle along the boundary. The second approach considers polygon partitioning on a pre-process before applying the ear-slicing. Experimental investigation reveals that both approaches yield better quality triangulation than the standard ear-slicing method.

Operation Comics: The Story Continues, Bruce Kessler, Tressa Tullis

Mathematics Faculty Publications

This talk was given, with Tressa Tullis as the main presenter and Bruce Kessler as a minor co-presenter, at the 2011 Bridges Conference in Coimbre, Portugal, on the current developments on our Operation Comics project with Cumberland Trace Elementary.

Operation Comics: The Story Continues, Bruce Kessler, Janet Tassell, Tressa Tullis

Mathematics Faculty Publications

During the 2008-2009 academic year, the author K. wrote three issues of Operation Comics, a comic book with embedded mathematics content appropriate for 4th through 6th grade students. Several printed comics were placed in Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky, US. The author Ta. was enlisted to measure the impact of the comics on the attitudes and motivation of the students using the comics. A preliminary report was given by K. at the 2009 Bridges Banff Conference, and the written report appeared in the proceedings. Since then, data has been collected on the …

Modeling And Control For Heave Dynamics Of A Flexible Wing Micro Aerial Vehicle Distributed Parameter System, Lisa M. Kuhn

Doctoral Dissertations

In recent years, much research has been motivated by the idea of biologically-inspired flight. It is a conjecture of the United States Air Force that incorporating characteristics of biological flight into air vehicles will significantly improve the maneuverability and performance of modern aircraft. Although there are studies which involve the aerodynamics, structural dynamics, modeling, and control of flexible wing micro aerial vehicles (MAVs), issues of control and vehicular modeling as a whole are largely unexplored. Modeling with such dynamics lends itself to systems of partial differential equations (PDEs) with nonlinearities, and limited control theory is available for such systems.

In …

A Numerical Method For Studying Thermal Deformation In 3d Double-Layered Thin Films With Imperfect Interfacial Thermal Contact Exposed To Ultrashort-Pulsed Lasers, Runzhou Liu

Doctoral Dissertations

Micro heat transfer induced by Ultrashort-pulsed lasers is an important research topic in mechanical engineering and material science. In order to apply ultrashort-pulsed lasers successfully, studying the thermal deformation in double-layered thin films with imperfect thermal interfacial contact induced by ultrashort-pulsed lasers is important for preventing thermal damage. For the ultrashort-pulsed laser, the thermal damage is different from that caused by the long-pulsed lasers, and ultrafast cracks occur after heating.

This dissertation presents a new finite difference method for investigating the thermal deformation in a 3D gold-chromium thin film with imperfect interfacial thermal contact exposed to ultrashort-pulsed lasers. The method …

Applications Of Variational Analysis To A Generalized Heron Problem, Boris S. Mordukhovich, Nguyen Mau Nam, Juan Salinas Jr

Mathematics Research Reports

This paper is a continuation of our ongoing efforts to solve a number of geometric problems and their extensions by using advanced tools of variational analysis and generalized differentiation. Here we propose and study, from both qualitative and numerical viewpoints, the following optimal location problem as well as its further extensions: on a given nonempty subset of a Banach space, find a point such that the sum of the distances from it to n given nonempty subsets of this space is minimal. This is a generalized version of the classical Heron problem: on a given straight line, find a point …

Smooth And Peaked Solitons Of The Camassa-Holm Equation And Applications, Darryl Holm, Rossen Ivanov

Articles

The relations between smooth and peaked soliton solutions are reviewed for the Camassa- Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH equation in action-angle variables is expressed for solitons by using the scattering data for its associated isospectral eigenvalue problem, rephrased as a Riemann- Hilbert problem. The momentum map from the action-angle scattering variables T^∗(T^N) to the flow momentum (X^∗) provides the Eulerian representation of the N-soliton solution of CH in terms of the scattering data and squared eigenfunctions of its isospectral eigenvalue problem. The …

Lesson’S Learned: A Journey In Computational Science, Ryan Botts, Lori Carter

ACMS Conference Proceedings 2011

Inspired by work on building a computational science program and student questions about modeling, we aim to discuss some of our experiences with computational science. We will first clarify what computational science is, why it is a legitimate science, why it is worth our students’ time and what makes it a challenging field. We will also discuss how computer scientists, mathematicians and laboratory scientists each have something different to contribute to the field.

A Bayesian Secondary Analysis In An Asthma Study, Samuel P. Wilcock, Vernon M. Chinchilli, Stephen P. Peters

ACMS Conference Proceedings 2011

A recent study published in the New England Journal of Medicine by the Asthma Clinical Research Network (ACRN) compared three different treatments for their effectiveness in treating adults with uncontrolled asthma. This paper will describe the study design and its results, then detail the beginnings of a secondary analysis using Bayesian methods to estimate the parameters of interest. The methods will be explained, and the preliminary estimates given and contextualized. The paper will conclude with a discussion of the next steps and the goals for further analysis of the data in this study.

What We Can Learn From Process Theology: Integrating Faith And Mathematics, Josh Wilkerson

ACMS Conference Proceedings 2011

In the inaugural issue of The Journal of the Association of Christians in the Mathematical Sciences, James Bradley, the founding editor, suggests fourteen areas that need to be addressed by Christian mathematicians who are series about integrating their faith and their work. One of those areas is the topic of this paper. Bradly frames the question: “Some thinkers (perhaps influenced by process theology) have asserted the idea that God’s creation is not a finished work but that he creates new mathematical objects through mathematicians. Is this idea theologically sound? Is it helpful for our understanding of mathematics?” I copy …

Google And The Mathematics Of Web Search, Michael Rempe

ACMS Conference Proceedings 2011

This article examines the algorithms used by Google to rank search engine results, called PageRank.

Calculus Communication Circle, Judith Palagallo

ACMS Conference Proceedings 2011

Calculus Communication Circle is a network for the professional development of Advanced Placement Calculus teachers. In Northeast Ohio the Circle provides a forum where teachers meet to share ideas about mathematics and the teaching of calculus. This article describes the creation of the Circle and the progress it has made over its three year existence.

Using Original Historical Mathematics Texts In The Classroom, Maria Zack

ACMS Conference Proceedings 2011

Incorporating information from the history of mathematics into undergraduate mathematics courses is an effective way to help students make connections between the mathematics they are learning and their general education courses. It also helps students to see mathematics as living subject that has changed over time. One way to introduce historical topics into a variety of classes is through the use of original mathematical texts. This paper describes how non-experts can make use of original texts and provides sources for identifying candidate texts.

The Mathematics Of Cubic Sudoku, Nicholas Zoller

ACMS Conference Proceedings 2011

In the last decade the Sudoku puzzle has fixed itself in America’s puzzle consciousness. Sudoku puzzles share space with crossword puzzles and word finds in newspaper puzzle sections, and several books have been written for the Sudoku playing community. Mathematicians are among the most dedicated Sudoku players. Although some are content with simply solving puzzle after puzzle, others have used tools from combinatorics and algebra to study its important properties.

We investigate a variant of Sudoku called Cubic Sudoku, as well as Cubic Sudoku’s simpler relative, Cubic Shidoku. We successfully count the number of Cubic Shidoku puzzles in two different …

Math History Study Abroad Program: Learning Math History In A Cultural Context, Donna Pierce

ACMS Conference Proceedings 2011

In January 2011 fifteen Whitworth University mathematics students and I, their professor, traveled through Europe to study the history of mathematics. The goal was to gain an understanding of how mathematical ideas have developed over time; how social, cultural and historical factors have influenced the development of mathematics and conversely, how mathematics contributed to society and human culture. Over a course of three weeks we traveled to three countries and over a half dozen cities, viewing the tools, papers and workbooks or these mathematicians, seeing their engineering and artistic creations, and learning from local experts as they guided us through …

Thinking Philosophically About Mathematics, Robert L. Brabenec

ACMS Conference Proceedings 2011

In my early years as a teacher of mathematics, the history of mathematics was seldom mentioned in the classroom. It was viewed as an unworthy topic that would detract from the presentation of mathematics itself. This opinion has dramatically changed over the years, and the history of mathematics is now embraced and used by many mathematicians in their teaching and even research. We might choose to ask a related question. How much philosophy is necessary or helpful for a mathematics teacher to know, and to use in his or her teaching? We see a growing interest in the philosophy of …

The Need For A Graphics Programming Course, Nathan Gossett

ACMS Conference Proceedings 2011

A discussion of the benefits of offering a course on programming Computer Graphics in an undergraduate Computer Science curriculum. A sample course outline is provided, as well as a discussion of ways to conduct lectures, labs and a list of suggested assignments. A discussion of “dos and don’t s will also be presented, including a list of required prerequisite courses and skills that students would need in order for the course to be a success.

Bringing Undergraduate Research Into The Classroom, Stephen Lovett

ACMS Conference Proceedings 2011

Mathematics graduate programs and companies that employ math majors often want to ascertain an applicant’s potential for research. However, in many undergraduate courses, assessments consist only of regular exercise sets, quizzes, and in-class tests. Without doing a senior research thesis or landing an official REUs, students do not regularly gain experience in or an appreciation for research. Courses in the humanities regularly require students to write in the discipline, progressively preparing them methodologically for “writing in the field.” This begs the question: could math departments do a little more to prepare our students to use mathematics beyond college?

In this …

Real Simulations And Simulated Reality, Wayne Iba

ACMS Conference Proceedings 2011

Movies such as The Matrix have stimulated popular interest in “brain in a vat” scenarios. Amidst the traditional questions of the mind, we tend to overlook an integral enabling component—the world simulation—which merits consideration in its own right. When facing the simulations in these imagined scenarios, we struggle with conceptual muddles regarding what is real and not. In this paper, I argue that simulated worlds are every bit as real as the one we inhabit. This turns out to be important when considering the possibility, as suggested by Nick Bostrom, that the world we experience as “real” is actually a …

Pk Mathematics, Jeremy Case

ACMS Conference Proceedings 2011

An examination of the historical development of mathematics and how mathematical history has changed by looking at mathematicians who were also PKs (Preacher’s Kids).

History Of Mathematics: An Exercise In Strengths, Mary Walkins

ACMS Conference Proceedings 2011

As a leader in strengths-based education, Lee University encourages each new student, since fall of 2003, to take the Gallup StrengthsFinder to determine their top 5 signature themes (out of a possible 34). At Lee, the syllabus for the History of Mathematics course calls for students to write a paper on a mathematician. In the fall of 2009, as an added dimension, students were asked to critically think about and incorporate the strengths they believe that mathematician may have. Each student was required to compare and contrast his or her strengths with those of the mathematician. This was done with …

The Study Of Mathematics: A Text From A Christian Perspective, Doug Phillippy

ACMS Conference Proceedings 2011

This paper examines the integration of the Christian faith with the teaching of mathematical texts using the author’s textbook, The Study of Mathematics: Developing a mature understanding of mathematical thought, with consideration of Christian faith and vocation.

The History Of The Area Between A Line And A Parabola, Gordon A. Swain

ACMS Conference Proceedings 2011

This is a review of various methods used by many mathematicians to determine the area of the segment bounded by a parabola and a line. We include descriptions of proofs from the Greek period (Archimedes), the Arabic period (ibn Qurra and ibn Sinan), and the 1600's in European (Galileo, Roberval, Fermat and Wallis, among others), in order to display the changing nature of mathematics.

Pascal’S Thoughts Seen In The Light Of Scripture, Loredana Ciurariu

ACMS Conference Proceedings 2011

In this paper we study Pascal’s character via his writings. There are indications that his health might have deteriorated following the experiments he had done using mercury. He talks in his Pensées about faith, grace and purity of the heart, about the peoples and the way in which God leads them, about wisdom, dreams and hopes and that which lies in the human heart. If a statistics was done concerning the most used books and verses from the Bible in Pensées, these would be: Ecclesiastes, Proverbs, Matthew, Mark, Jeremiah, Hebrews, Romans, Luke, Isaiah, Psalms. But those which occupy a central …

Two Faith Integration Projects For Freshman Majors, Nicholas J. Willis

ACMS Conference Proceedings 2011

Two projects will be presented that integrate faith and Mathematics in a freshman Introduction to Proofs class at George Fox University. The first project asks students to look at the life of a Christian Mathematician. The focus of this project is to show students that many great mathematicians also had immense faith. The second project asks students to take a close look at their own life. How do they plan to live a life of Christian faith in their chosen profession? Both projects are designed to encourage students to look at their careers in Mathematics as a vocation.

The Search For Hamilton, Eric Gossett

ACMS Conference Proceedings 2011

In July and August of 2009 my wife and I went on a four-week trip to Scotland and Ireland. We would be visiting Dublin, so I decided that we should visit the famous bridge where William Rowan Hamilton carved the equations for the quaternions. The task was not as simple as I had assumed. This paper gives some details of the search.

Where, Oh Waring? The Classic Problem And Its Extensions, Brian D. Beasley

ACMS Conference Proceedings 2011

This paper will sketch brief outlines of Edward Waring’s life and the history behind the eventual solution to his famous conjecture about expressing positive integers as the sum of kth powers. In addition, it will present some of the related questions currently being studied, such as expressing sufficiently large integers as sums of powers, sums of powers of primes, and sums of unlike powers.

Connecting Mathematics Students To Philosophy And Faith, Nathan Moyer

ACMS Conference Proceedings 2011

This paper describes a class project that helps students wrestle with the deep philosophical questions of mathematics in a relevant way. Through article readings and group discussions, various historical views of mathematical philosophy are examined and critiqued. An emphasis is placed upon students making meaningful connections between their own views of mathematics and their personal Christian faith or worldview.

Paper Abstracts (2011), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2011

Eighteenth Conference of the Association of Christians in the Mathematical Sciences