Applied Mathematics Commons^™

Ten Mathematicians Who Recognized God’S Hand In Their Work, Dale L. Mcintyre

ACMS Conference Proceedings 2015

Scottish philosopher David Hume (1711-1776) once observed that

“Whoever is moved by faith to assent to [the Christian religion], is conscious of a continued miracle in his own person, which subverts all the principles of his understanding, and gives him a determination to believe what is most contrary to custom and experience.” [Hume]

Evidently Humes cynical pronouncement did not apply to Euler, Cauchy, Cantor, and other profound thinkers who believed God had commissioned and equipped them to glorify Him in their pursuit of truth through mathematics And based on their extraordinary achievements the principles of their understanding do not appear …

Home Primes And Foreign Primes, Nicholas Zoller

ACMS Conference Proceedings 2015

Home primes and foreign primes are produced by a simple recipe that blends prime factorizations with recursion. The home prime of a positive integer n is formed by concatenating the prime factors of n in non-decreasing order. If the resulting integer is prime, then we have found the home prime of n. If not, then we repeat the process as many times as needed to obtain a prime. For instance, 35 = 5·7. After concatenation, we have 57 = 3·19, which is followed by 319 = 11·29, which is followed by 1129, which is prime. Thus, the home prime …

Physical Activity In A Theory Of Computing Class, Nancy Lynn Tinkham

ACMS Conference Proceedings 2015

Physical activity breaks, sometimes called brain breaks, are beginning to gain attention among K-12 teachers as a way to keep their students alert and engaged in the classroom. In the Fall 2014 semester, faced with the task of teaching an introductory course in Theory of Computing in a once-a-week, 2 1/2-hour format, I decided to try incorporating physical activity into my own classroom. Time is precious in the college classroom, so any physical activities have to be directly related to the course material. I will describe some physically active exercises that I used in the classroom to teach students about …

Preparing Students To Read A Calculus Textbook, Douglas Phillippy

ACMS Conference Proceedings 2015

Consider the exercise of reading the textbook before class. While most educators agree that this practice leads to better learning, too often students enrolled in a calculus class do not find pre-class reading a valuable use of their time, and their commitment to doing so fades. Why is this? As instructors, we hope that these students will be well-versed in the fundamental concepts of the subject by the time they prepare for their final exam, but as they progress through the course and encounter new concepts, they may not be ready for the technical language of the standard calculus textbook. …

Pressure And Impulse In Student Learning: What I Learned From Teaching Physics, Kim Jongerius

ACMS Conference Proceedings 2015

In the fall of 2014, a one-semester gap between the departure of one physics professor and the arrival of the next afforded me the opportunity(?) to teach a first-semester, calculus-based physics class. The thirty-year gap between the last (of three) physics courses I had taken myself and this course I was to teach, combined with a two-week notice prior to the start of the semester, placed me in the interesting position of learning alongside my students. Wading through an unfamiliar text, trying to understand publisher-produced lecture slides, learning from and getting frustrated with online homework, entering review sessions fearful of …

Paper Abstracts (2015), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2015

Twentieth Conference of the Association of Christians in the Mathematical Sciences

Introduction (2015), Thomas Price, Derek Schuurman, Kevin Vander Meulen

ACMS Conference Proceedings 2015

Twentieth Conference of the Association of Christians in the Mathematical Sciences

Table Of Contents (2015), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2015

Twentieth Conference of the Association of Christians in the Mathematical Sciences

Proceedings Of The Twentieth Conference Of The Association Of Christians In The Mathematical Sciences, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2015

The proceedings of the twentieth conference of the Associate of Christians in the Mathematical Sciences held at Redeemer University College from May 27-30, 2015.

Entropy Vs. Energy Waveform Processing: A Comparison Based On The Heat Equation, Michael S. Hughes, John E. Mccarthy, Paul J. Bruillard, Jon N. Marsh, Samuel A. Wickline

Mathematics Faculty Research

Virtually all modern imaging devices collect electromagnetic or acoustic waves and use the energy carried by these waves to determine pixel values to create what is basically an “energy” picture. However, waves also carry “information,” as quantified by some form of entropy, and this may also be used to produce an “information” image. Numerous published studies have demonstrated the advantages of entropy, or “information imaging”, over conventional methods. The most sensitive information measure appears to be the joint entropy of the collected wave and a reference signal. The sensitivity of repeated experimental observations of a slowly-changing quantity may be defined …

Applications Of Latin Hypercube Sampling Scheme And Partial Rank Correlation Coefficient Analysis To Mathematical Models On Wound Healing, Hannah M. Pennington

Mahurin Honors College Capstone Experience/Thesis Projects

Latin hypercube sampling and Partial Rank Correlation Coefficient procedure (LHS/PRCC) can be used in combination to perform a sensitivity analysis that assesses a model over a global parameter space. Through this analysis, the uncertainty of the parameters and therefore the variability of the model output in response to this uncertainty can be observed. Latin hypercube sampling divides the parameter space into equiprobable regions and sample without replacement, producing a global, unbiased selection of parameter values. For montonic, non-linear relationships, the correlation between the outputs and parameters can be understood by performing a Partial Rank Correlation Coefficient procedure. This sensitivity analysis …

Book Review: How To Bake Pi: An Edible Exploration Of The Mathematics Of Mathematics, Darren B. Glass

Math Faculty Publications

If you think about it, mathematics is really just one big analogy. For one example, the very concept of the number three is an drawing an analogy between a pile with three rocks, a collection of three books, and a plate with three carrots on it. For another, the idea of a group is drawing an analogy between adding real numbers, multiplying matrices, and many other mathematical structures. So much of what we do as mathematicians involves abstracting concrete things, and what is abstraction other than a big analogy? [excerpt]

Standing On The Shoulders Of The Giants: Why Constructive Mathematics, Probability Theory, Interval Mathematics, And Fuzzy Mathematics Are Important, Vladik Kreinovich

Departmental Technical Reports (CS)

Recent death of Ray Moore, one of the fathers of interval mathematics, inspired these thoughts on why interval computations -- and several other related areas of study -- are important, and what we can learn from the successes of these areas' founders and promoters.

Application Of A Numerical Method And Optimal Control Theory To A Partial Differential Equation Model For A Bacterial Infection In A Chronic Wound, Stephen Guffey

Masters Theses & Specialist Projects

In this work, we study the application both of optimal control techniques and a numerical method to a system of partial differential equations arising from a problem in wound healing. Optimal control theory is a generalization of calculus of variations, as well as the method of Lagrange Multipliers. Both of these techniques have seen prevalent use in the modern theories of Physics, Economics, as well as in the study of Partial Differential Equations. The numerical method we consider is the method of lines, a prominent method for solving partial differential equations. This method uses finite difference schemes to discretize the …

The Implications Of Self-Driving Cars On Insurance, Amanda Lobello

Honors Projects in Mathematics

Self-driving cars, also known as autonomous vehicles, are being researched and tested by automakers, technology industry leaders, and other institutions. Lawmakers and politicians are discussing the legislation that will affect the fate of such technology. Primary benefits include safety, mobility, free time, less traffic, and green effects. However, there are also obstacles to the implementation of self-driving vehicles including consumer acceptance, legal liability, and cost. With the potential shift in responsibility from driver to automaker, rating factors for insurance may change, weighing more heavily on the model of the car as a factor. The fate of auto insurance is in …

Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, Meltem Uyanik

Masters Theses & Specialist Projects

This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental …

Boundary Problems For One And Two Dimensional Random Walks, Miky Wright

Masters Theses & Specialist Projects

This thesis provides a study of various boundary problems for one and two dimensional random walks. We first consider a one-dimensional random walk that starts at integer-valued height k > 0, with a lower boundary being the x-axis, and on each step moving downward with probability q being greater than or equal to the probability of going upward p. We derive the variance and the standard deviation of the number of steps T needed for the height to reach 0 from k, by first deriving the moment generating function of T. We then study two types of two-dimensional random walks with …

Modeling Enrollment At A Regional University Using A Discrete-Time Markov Chain, Zachary T. Helbert

Undergraduate Honors Theses

A discrete time Markov Chain is used to model enrollment at a regional university. A preliminary analysis is conducted on the data set in order to determine the classes for the Markov chain model. The semester, yearly, and long term results of the model are examined thoroughly. A sensitivity analysis of the probability matrix entries is then conducted to determine the overall greatest influence on graduation rates.

Mathematics In Forensic Firearm Examination, Erin N. Zalewski

Renée Crown University Honors Thesis Projects - All

Forensic Science encompasses many disciplines that employ the scientific method to examine, analyze, and interpret physical evidence in the courtroom. The discipline of Forensic Firearm Examination involves the examination and comparison of ballistic evidence components to determine if they came from the same source. In other words, firearm examiners are tasked with determining whether spent cartridge cases or bullets were fired through the same gun. Examination of ballistic evidence can involve the employment of automated matching systems, comparison microscopy, and mathematical analysis. The comparison microscope is the tool of the firearm examiner and allows for the simultaneous view of ballistic …

Geometry Of Hilbert Space Frames, Stephen Sorokanich Iii

Renée Crown University Honors Thesis Projects - All

In applied linear algebra, the term frame is used to refer to a redundant or linearly dependent coordinate system. The concept was introduced in the study of Fourier series and is pertinent in signal processing, where the reconstruction property for finite frames allows for redundant transmission of data to guard against losses due to noise. We give a brief introduction to the theory of finite frames in Section 1, including the major results that allow for the easy construction and description of frames. The subsequent sections relate to the theoretical importance of frames. As a natural extension of the definition …