Applied Mathematics Commons^™

Lagrange's Interpolation, Chinese Remainder, And Linear Equations, Jesús Jiménez

ACMS Conference Proceedings 2019

Consider a finite set of points {(x1, y1), (x2, y2), . . . , (xk , yk )} in R2. The Lagrange’s interpolation problem is to find a polynomial p(x) of degree k − 1 satisfying p(xi) = yi for 1 ≤ i ≤ k. We will recall the solution to Lagrange’s interpolation problems as an instance of the Chinese Remainder Theorem. Next, we will show that a similar approach can be used to construct solutions to a system of linear equations.

Addressing Challenges In Creating Math Presentations, David Schweitzer

ACMS Conference Proceedings 2019

When it comes to composing presentation slides with extensive mathematical content, each of the slide creation platforms has at least one significant drawback. Whether it is Beamer and its steep learning curve, PowerPoint and its relative inefficiency with math, Google Slides and its complete lack of math capabilities, or some other platform, no one tool single-handedly offers an ideal solution. Additionally, if users desire creative flexibility, such as the ability to easily change fonts or colors, the platforms’ respective limitations can become even more pronounced. In a project that has been well suited for undergraduate research, the presenter and his …

Overcoming Stereotypes Through A Liberal Arts Math Course, Jessica Hamm

ACMS Conference Proceedings 2019

"I'm just not a math person.” We’ve heard this comment countless times from our students. It is a mentality that both paralyzes and strangely comforts them. In this talk I will describe how I use my liberal arts Joy of Mathematics course to help students address and overcome stereotypes. In particular, I will discuss a specific assignment as well as share some student comments and perspectives on how this course helped change their viewpoint on more than just math.

Maximum Elements Of Ordered Sets And Anselm's Ontological Argument, Doug Ward

ACMS Conference Proceedings 2019

I will present a simple theorem concerning maximal elements of a set T endowed with an ordering “>” that is antisymmetric, i.e., if A and B are elements of T , we cannot have both A > B and B > A. A special case of this theorem is a simple version of the ontological argument, one of the classical proofs for the existence of God.

Numerical Range Of Toeplitz Matrices Over Finite Fields, Derek Thompson, Maddison Guillaume Baker, Amish Mishra

ACMS Conference Proceedings 2019

We characterize the kth numerical range of all n×n Toeplitz matrices with a constant main diagonal and another single, non-zero diagonal, where the matrices are over the field Zp[i], with p a prime congruent to 3 mod 4. We find that, for k ∈ Z∗, the kth numerical range is always equal to Zp[i] with the exception of the scaled identity. We also use similar techniques to discover a general connection between the 0th numerical range and the kth numerical range. Lastly, we conclude with a conjecture regarding the general numerical range of all triangular Toeplitz matrices.

Is Mathematical Truth Time Dependent? Comments From A Paper By Judith Grabiner, Richard Stout

ACMS Conference Proceedings 2019

Judith Grabiner, a renowned historian of mathematics, has written many papers related to signifi- cant changes in the content and nature of analysis, from the 17th through the 19th century. In her paper “Is Mathematical Truth Time Dependent?” Professor Grabiner gives several reasons for the changing nature and requirements in rigor that occurred over this period of two hundred years. In this talk I will briefly summarize her conclusions, particularly in light of how they might influence a Christian perspective on mathematics.

Models, Values, And Disasters, Michael H. Veatch

ACMS Conference Proceedings 2019

Decision-support models have values embedded in them and are subjective to varying degrees. Philosophical and ethical perspectives on operations research models are used to describe this subjectivity. Approaches to model building are then suggested that take into account subjectivity and values. For the decisions to reflect the right values, the model must align with the decision-maker’s values. I argue that it is appropriate and important for Christians applying mathematical models to be keenly aware of decision-maker’s values and seek to reflect them in the model. Disaster response planning is presented as an example where incorporating values is challenging. The responding …

Factors That Motivate Students To Learn Mathematics, Dave Klanderman, Sarah Klanderman, Benjamin Gliesmann, Josh Wilkerson, Patrick Eggleton

ACMS Conference Proceedings 2019

What motivates some students to want to learn mathematics while others do not share similar motivation? Are these factors intrinsic, extrinsic, or a combination of both? To answer these questions, we adapted a survey originally developed by Tapia (1996) and later shortened by Lim and Chapman (2015). We administered the survey in multiple middle schools, a high school, and multiple colleges and universities. We obtained over 100 completed surveys for each of these educational levels. This presentation offers an analysis of these data, including descriptive statistics and confidence intervals for each educational level. For the college and university sample, we …

Thinking Beautifully About Mathematics: A View Of Mathematics As The Science Of Measurable Orders, James M. Turner

ACMS Conference Proceedings 2019

At Calvin College, First Year Students are required to take a section of our Discovering the Christian Mind course during our January term. For the past 3 years, I have taught a section of this course titled Thinking Beautiful ly about Mathematics. In it, I explored, with the students, various areas of mathematics, as well as how mathematicians have explored them, while addressing such questions as “Is mathematics invented or discovered?” and “Why is mathematics unreasonably effective?” Ultimately, we look to identify ways and characterizations for how beauty displays itself in mathematics and how and it what ways beauty is …

Marin Mersenne: Minim Monk And Messenger; Monotheism, Mathematics, And Music, Karl-Dieter Crisman

ACMS Conference Proceedings 2019

If you have taught a number theory course or even watched the mathematical news, you know that occasionally a new (and enormous) “Mersenne prime” is discovered. Those who have introduced students to the prehistory of calculus may know of a certain Marin Mersenne as the interlocutor who drew Fermat and Descartes (and others) out to discuss their methods of tangents (and more). But who was Mersenne, and what did he actually do? This presentation will give an overview of his times, his role in the history of science, and his own writings. We’ll especially look into why a monk from …

Analyzing The Impact Of Active Learning In General Education Mathematics Courses, Amanda Harsy, Marie Meyer, Michael Smith, Brittany Stephenson

ACMS Conference Proceedings 2019

This talk shares the preliminary results of a study that explores the general perceptions and attitudes of students in general education mathematics courses taught using primarily active learning- based methods (like group work, projects, and discovery learning), and compares them with those enrolled in a general education mathematics course taught in a more traditional and lecture-based method. We present an analysis of survey data collected throughout the semester, which explores the disposition and mindset of students, their mathematical confidence and anxiety, and perceptions of pedagogical methods used for the teaching of mathematics. We also explored how these perceptions and dispositions …

Computer Science: Creating In A Fallen World, Russell Tuck

ACMS Conference Proceedings 2019

When God created people in his image, he gave us the gift of sub-creation. One of the great joys of Computer Science is exercising that gift to create tools : software and computer systems that serve people and solve problems. Like all God’s gifts, he charges us to exercise the gift of sub-creation wisely and for good. While there are many obvious implications and challenges, being good stewardship of users’ time and reducing discrimination are particularly relevant and perhaps less obvious examples. Although computer scientists exercise the gift of sub-creation, we do so as fallen people in a fallen world. …

A Unifying Project For A Tex/Cas Course, Andrew Simoson

ACMS Conference Proceedings 2019

We describe a CAS and TEX usage course for mathematics majors. As a unifying project, each student selects two primes p and q with pq < 100, explores mathematical pq ideas, and generates associated graphs, figures, tables for a final TEX paper. We summarize several pq explorations: stu- dents render page pq from Schwartz’s picture book about primes, You Can Count on Monsters, via Mathematica and TEX’s picture environment; students generate fractal images of pq; and students discover the primes of the ring Z r√pql.

Introduction (2019), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2019

No abstract provided.

Paper Abstracts (2019), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2019

No abstract provided.

Table Of Contents (2019), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2019

No abstract provided.

Association Of Christians In The Mathematical Sciences Proceedings 2019, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2019

The conference proceedings of the Association of Christians in the Mathematical Sciences biannual conference, May 29-June 1, 2019 at Indiana Wesleyan University.

Schedule (2019), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2019

No abstract provided.

Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene

CODEE Journal

The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem highlights …

Sir Models: Differential Equations That Support The Common Good, Lorelei Koss

CODEE Journal

This article surveys how SIR models have been extended beyond investigations of biologically infectious diseases to other topics that contribute to social inequality and environmental concerns. We present models that have been used to study sustainable agriculture, drug and alcohol use, the spread of violent ideologies on the internet, criminal activity, and health issues such as bulimia and obesity.

An Interpolation Process On The Roots Of Ultraspherical Polynomials, R. Srivastava, Yamini Singh

Applications and Applied Mathematics: An International Journal (AAM)

The paper is devoted to studying a Pál-type interpolation problem on the roots of Ultraspherical polynomials of degree n-1 with parameter k+1 on the closed interval -1 to 1. The aim of this paper is to find a unique interpolatory polynomial of degree at most m equal to 2n+2k+1 satisfying the interpolatory conditions that is, function values of the polynomial of degree m at the zeros of the function values of the ultraspherical polynomials and the first derivative values of the polynomial of degree m at the zeros of the first derivative values of the ultraspherical polynomials.We will use the …

Calculus Of The Impossible: Review Of The Improbability Principle (2014) By David Hand And The Logic Of Miracles (2018) By Lásló Mérő, Samuel L. Tunstall

Numeracy

David J. Hand. 2014. The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day (New York, NY: Scientific American/Farrar, Straus and Giroux) 288 pp. ISBN: 978-0374175344.

Lásló Mérő. 2018. The Logic of Miracles: Making Sense of Rare, Really Rare, and Impossibly Rare Events (New Haven, CT: Yale University Press) 288 pp. ISBN: 978-0300224153.

David Hand and Lásló Mérő both grapple with the occurrence of seemingly impossible events in these two popular science books. In this comparative review, I describe the two books, and explain why I prefer Hand's treatment of the impossible.

A Numerical Method For Functional Hammerstein Integro-Differential Equations, L. Saeedi, A. Tari

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a numerical method is presented to solve functional Hammerstein integro-differential equations. The presented method combines the successive approximations method with trapezoidal quadrature rule and natural cubic spline interpolation to solve the mentioned equations. The existence and uniqueness of the problem is also investigated. The convergence and numerical stability of the problem are proved, and finally, the accuracy of the method is verified by presenting some numerical computations.

Diagnostic Effects Of An Early Mastery Activity In College Algebra And Precalculus, Nathan Wakefield, Joe Champion, Jessalyn Bolkema, Douglas Dailey

Department of Mathematics: Faculty Publications

The purpose of this study was to investigate implementation of an early intervention mastery activity during the first two weeks of college algebra and precalculus courses at a large U.S. public university. Statistical modeling of (N = 935) students’ performance in the courses, including a logistic regression model of pass/fail course achievement with students’ high school rank, ACT Mathematics scores, and performance on the intervention as explanatory variables, suggested significant independent differences in course performance across performance levels on the early mastery activity. An evaluation of diagnostic validity for the model yielded a 19% false negative rate (predicted to …

Parts Of The Whole: Why I Teach This Subject This Way, Dorothy Wallace

Numeracy

The importance of mathematics to biology is illustrated by search data from Google Scholar. I argue that a pedagogical approach based on student research projects is likely to improve retention and foster critical thinking about mathematical modeling, as well as reinforce quantitative reasoning and the appreciation of calculus as a tool. The usual features of a course (e.g., the instructor, assessment, text, etc.) are shown to have very different purposes in a research-based course.

Finding Meaning In Calculus (And Life), Doug Phillippy

ACMS Conference Proceedings 2017

A 2015 publication of the Mathematical Association of America (Insights and Recommendations from the MAA National Study of College Calculus) noted that "students taking college calculus exhibited a reduction in positive attitude toward mathematics, which can affect their career aspira

Cultivating Mathematical Affections Through Engagement In Service-Learning, Josh Wilkerson

ACMS Conference Proceedings 2017

Why should students value mathematics? While extensive research exists on developing the cognitive ability of students, very little research has examined how to cultivate the affections of students for mathematics. The phrase "mathematical affections" is a play on the affective domain of learning as well as on the general notion of care towards something. Mathematical affections are more than a respect for the utility of the subject; the term is much broader and includes aesthetic features as well as habits of mind and attitude. This paper will analyze the findings from a research project exploring the impact of service

Reading Journals: Preview Assignments That Promote Student Engagement, Productive Struggle, And Ultimate Success In Undergraduate Mathematics Courses, Sarah Nelson

ACMS Conference Proceedings 2017

We spend lots of time searching for the best textbook for students. We want our students to have a reliable and useful resource to reference, as needed. We even ask them to read over certain material before classes. Often, however, we fail to guide our students in how to read the text productively. Incorporating reading journals into your classes is an excellent way to simultaneously develop your students' ability to read mathematical text and capitalize on what the students already have to offer. In this presentation, we will look at how reading journals motivate students in a variety of mathematics …

Blended Courses Across The Curriculum: What Works And What Does Not, Ryan Botts, Lori Carter, Catherine Crockett

ACMS Conference Proceedings 2017

Recent hype around online and blended courses touts the benefits of immediate student feedback, flexible pace, adaptive learning, and better utility of classroom space. Here we aim to summarize the results of a 3-year pilot study using blended courses across the quantitative science curriculum (Mathematics, Statistics and Computer Science), in both upper and lower division, major and GE courses. We present findings on student attitudes towards this format, most helpful course components, time on task, progress on learning outcomes and faculty perspectives. This summary can be used to inform best practices in hybrid design, implementation and faculty expectations in the …

Variations On The Calculus Sequence, Christopher Micklewright

ACMS Conference Proceedings 2017

Many institutions have embraced a standard format for the Calculus sequence, comprising three four-credit courses covering a fairly consistent set of topics. While there is much to recommend this approach, it still leaves some fantastic concepts rushed or untouched, and it can be argued that it demands too much of students with weaker backgrounds. As such, some schools have experimented with variations on the standard format. In this talk, I will present the model that my institution currently uses, exploring the strengths and weaknesses of our particular approach. I will also suggest ideas, developed in conversation with other ACMS members …