Applied Mathematics Commons^™

Using Real-World Team Projects: A Pedagogical Framework, Mike Leih

ACMS Conference Proceedings 2017

The use of team projects in a program capstone course for computer science or information systems majors has been a popular method for reinforcing and assessing program learning objectives for students in their final semester. Using real-world group projects as a learning activity is an excellent pedagogical approach in helping students develop critical thinking, team work, real-world problem solving, and communication skills. However, real-world group projects also provide many challenges to both the instructor and students alike. Instructors or students must find real-world projects appropriate for the learning objectives in the course. Instructors must determine how to provide teams with …

The Set Of Zero Divisors Of A Factor Ring, Jesús Jiménez

ACMS Conference Proceedings 2017

Let A be a ring and a an ideal of A. In this paper we show how to construct factor rings A/ a and a finite set of ideals a1, a2, ... , ak, of A/a, such that: each ideal aj is contained in the set of zero divisors of A/a, the factor ring A/a is a direct sum of these ideals, and each ideal aj is a ring with unity when endowed with addition and multiplication modulo a. Explicit examples are given when A is the ring of integers, Gaussian integers or the ring of polynomials over a field.

Developing The Underutilized Mathematical Strengths Of Students, Patrick Eggleton

ACMS Conference Proceedings 2017

This session is intended for presenting the findings from a Spring 2017 research study conducted at Taylor University regarding influences that contribute to a student's disposition toward mathematics. In the foundation level mathematics course taught for non-majors at Taylor, students are asked to share a reflection on their past mathematical experiences. Analysis of these reflections shows general themes regarding the influences, both good and bad, that have contributed to how these students approach mathematics. We would like to use this information as well as related studies to help instructors of mathematics develop positive dispositions toward mathematics in their students.

Axioms: Mathematical And Spiritual: What Says The Parable?, Melvin Royer

ACMS Conference Proceedings 2017

Relational structure A is compact provided for any structure Jffi of the same signature, if every finite substructure of Jffi has a homomorphism to A then so does Jffi. The Constraint Satisfaction Problem (CSP) for A is the computational problem of determining whether finite structures have homomorphisms into A. We explore a connection between the hierarchy of logical axioms and the complexity hierarchy of CSPs: It appears that the complexity of CSP for A corresponds to the strength of the axiom "A is compact". At the top, the statement "K3 is compacts" is logically equivalent to the compactness theorem. Thus …

A Pre-Calculus Controversy: Infinitesimals And Why They Matter, Karl-Dieter Crisman

ACMS Conference Proceedings 2017

In teaching calculus, it is not uncommon to mention the controversy over the role of infinitesimals with Newton's and Leibniz' calculus, including Berkeley's objections. In a history of mathematics course, it is a required topic! But rancor over infinitesimals and their role in mathematics predates calculus- so much so that a popular new book is dedicated to this topic. In this talk, I will discuss not just the relevant controversies between Cavalieri and the Je

The Resolved And Unresolved Conjectures Of R.D. Carmichael, Brian D. Beasley

ACMS Conference Proceedings 2017

Even before heading to Princeton University to work on his doctoral degree, Robert Daniel Carmichael started influencing the path of number theory in the 20th century. From his study of Euler's totient function to his discovery of the first absolute pseudoprime, he set the stage for years of productive research. This talk will present a brief overview of Carmichael's life, including his breadth of mathematical interests and his service on behalf of the Mathematical Association of America. It will focus mainly on his two most famous conjectures- which one has been settled, and which one remains open to this day?

"Big Idea" Reflection Assignments For Learning And Valuing Mathematics, Jeremy Case, Mark Colgan

ACMS Conference Proceedings 2017

While participating in a Faculty Learning Community, we explored the "big questions" we wanted our students to take away from our mathematics courses. We called these questions the Big Ideas of the course and developed a Big Ideas Reflection Assignment, which we continue to assign at the end of each of our courses. Students are able to demonstrate understanding and application of their learning as well as their values and appreciation of mathematics. The assignment encourages students to move beyond a focus on technique and symbolic manipulations towards a broader and more holistic approach, including making connections between their learning …

Mentoring As A Statistical Educator In A Christian College, L. Marlin Eby

ACMS Conference Proceedings 2017

In this paper, I present principles based on more than thirty years of intentional mentoring as a statistical educator in a Christian college. I believe this mentoring has been enhanced due to the setting- a Christian college, and the discipline - statistics. I discuss distinctives of the Christian college setting that positively impact mentoring in any discipline with respect to the mentor, the mentee, and the pervading campus atmosphere. I focus on mentoring as a statistical educator by specifically considering the following: attracting students to the discipline of statistics, preparing students for careers using statistics, and preparing students for graduate …

The Daily Question: Building Student Trust And Interest In Undergraduate Introductory Probability And Statistics Courses, Matthew A. Hawks

ACMS Conference Proceedings 2017

Introducing probability or statistics to disinterested undergraduate students is challenging. Adding faith in such a classroom at a secular institution only increases the complexity. We share an unobtrusive way to build trust with students, creating a medium to both naturally share your faith and have your students look forward to attending each class. The context is the United States Naval Academy, a four-year undergraduate institution with an emphasis on leader development. In addition to a calculus sequence, Humanities majors enroll in Probability with Naval Applications or Introductory Statistics. These sophomores or juniors are split between those who have no intention …

The Topology Of Harry Potter: Exploring Higher Dimensions In Young Adult Fantasy Literature, Sarah Klanderman, Alexa Schut, Dave Klanderman, William Boerman-Cornell

ACMS Conference Proceedings 2017

As one of the most beloved series in children’s literature today, the Harry Potter books excite students of all ages with the adventures of living in a magical world. Magical objects (e.g., bottom-less handbags, the Knight Bus, time turners, and moving portraits) can inspire generalizations to mathematical concepts that would be relevant in an undergraduate geometry or topology course. Intuitive explanations for some of the magical objects connect to abstract mathematical ideas. We
offer a typology with a total of five categories, including Three Dimensions in Two Dimensions, Higher Dimensions in Three Dimensions, Two and Three Dimensional Movement, Higher Dimensional …

Start A Math Teacher Circle: Connect K-12 Teachers With Engaging, Approachable, And Meaningful Mahtematical Problems, Thomas Clark, Mike Janssen, Amanda Harsy, Dave Klanderman, Mandi Maxwell, Sharon Robbert

ACMS Conference Proceedings 2017

Many K-12 math teachers are not ready to teach from a conceptual and inquiry-oriented per

Ten Mathematicians Who Recognized God's Hand In Their Work (Part 2), Dale Mcintyre

ACMS Conference Proceedings 2017

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." Evidently Hume's cynical pronouncement did not apply to Descartes, Newton, Riemann, 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 …

Introduction (2017), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2017

No abstract provided.

Paper Abstracts (2017), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2017

No abstract provided.

Conference Schedule (2017), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2017

No abstract provided.

Table Of Contents (2017), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2017

No abstract provided.

Association Of Christians In The Mathematical Sciences Proceedings 2017, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2017

The conference proceedings of the Association of Christians in the Mathematical Sciences biannual conference, May 31-June 2, 2017 at Charleson Southern University.

2017-2018 Graduate Handbook For The Master Of Arts In Educational Mathematics, Otterbein Office Of Graduate Programs

Graduate School

Graduate Handbook on the MAEM Program at Otterbein University.

Quantifying Life: A Computational Approach To Teaching Mathematics To Biology Students, Dmitry Kondrashov

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Creating Art Patterns With Math And Code, Boyan Kostadinov

Publications and Research

The goal of this talk is to showcase some visualization projects that we developed for a 3-day Code in R summer program, designed to inspire the creative side of our STEM students by engaging them with computational projects that we developed with the purpose of mixing calculus level math and code to create complex geometric patterns. One of the goals of this program was to attract more minority and female students into applied math and computer science majors.

The projects are designed to be implemented using the high-level, open-source and free computational environment R, a popular software in industry for …

Introducing Complex Systems Analysis In High School Mathematics Using System Dynamics Modeling: A Potential Game-Changer For Mathematics Instruction, Diana Marie Fisher

Dissertations and Theses

Complex systems abound on this planet, in the composition of the human body, in ecosystems, in social interaction, in political decision-making, and more. Analytical methods allowing us to better understand how these systems operate and, consequently, to have a chance to intervene and change the undesirable behavior of some of the more pernicious systems have developed and continue to be enhanced via quickly changing technology. Some of these analytical methods are accessible by pre-college students, but have not been widely used at that level of education. Jay Forrester, the founder of one of the methodologies, System Dynamics (SD), used to …

Teaching Numerical Methods In The Context Of Galaxy Mergers, Maria Kourjanskaia

Physics

Methods of teaching numerical methods to solve ordinary differential equations in the context of galaxy mergers were explored. The research published in a paper by Toomre and Toomre in 1972 describing the formation of galactic tails and bridges from close tidal interactions was adapted into a project targeting undergraduate physics students. Typically undergraduate physics students only take one Computational Physics class in which various techniques and algorithms are taught. Although it is important to study computational physics techniques, it is just as important to apply this knowledge to a problem that is representative of what computational physics researchers are investigating …

Parts Of The Whole: Teaching Quantitative Reasoning In The Predator-Prey Model, Dorothy Wallace

Numeracy

The classical predator-prey equations are in nearly every differential equations text and mathematical biology text. Usually they are presented fait accompli, leaving the student to analyze them or play with a computer program. Here we show that the process of fully understanding where these equations come from and how they are derived provides numerous opportunities to teach or reinforce quantitative reasoning skills necessary to future scientists. This example is used to invoke logic, systems thinking, causal reasoning, understanding functions of one or more variables, quantities versus rates of change, proportional reasoning, unit analysis, and comparison to data.

Multiple Problem-Solving Strategies Provide Insight Into Students’ Understanding Of Open-Ended Linear Programming Problems, Marla A. Sole

Publications and Research

Open-ended questions that can be solved using different strategies help students learn and integrate content, and provide teachers with greater insights into students’ unique capabilities and levels of understanding. This article provides a problem that was modified to allow for multiple approaches. Students tended to employ high-powered, complex, familiar solution strategies rather than simpler, more intuitive strategies, which suggests that students might need more experience working with informal solution methods. During the semester, by incorporating open-ended questions, I gained valuable feedback, was able to better model real-world problems, challenge students with different abilities, and strengthen students’ problem solving skills.

Characterizing Mathematics Graduate Student Teaching Assistants’ Opportunities To Learn From Teaching, Yvonne Lai, Wendy Smith, Nathan Wakefield, Erica R. Miller, Julia St. Goar, Corbin M. Groothuis, Kelsey M. Wells

Department of Mathematics: Faculty Publications

Exemplary models to inform novice instruction and the development of graduate teaching assistants (TAs) exist. What is missing from the literature is the process of how graduate students in model professional development programs make sense of and enact the experiences offered. A first step to understanding TAs’ learning to teach is to characterize how and whether they link observations of student work to hypotheses about student thinking and then connect those hypotheses to future teaching actions. A reason to be interested in these connections is that their strength and coherence determine how well TAs can learn from experiences. We found …

On The Stability Of A Pexiderized Functional Equation In Intuitionistic Fuzzy Banach Spaces, Nabin C. Kayal, Pratap Mondal, T. K. Samanta

Applications and Applied Mathematics: An International Journal (AAM)

During the last few decades several researchers have been devoted to establishing stability of different kinds of functional equations, differential equations, functional differential equations, fractional differential equations, etc. under different sufficient conditions in different spaces like Banach spaces, Banach modules, fuzzy Banach spaces etc. In this paper, we remain confined in the discussion of stability of functional equations in intuitionistic fuzzy Banach spaces. Ulam was the first person who introduced an open question concerning the stability of a group homomorphism in an international conference. Thereafter several researchers have replied and are still replying to this open question in different contexts. …

On Calculation Of Failure Probability For Structures Designed Based On Magnitudes Of Historical Event, Farzad Noubary, Reza Noubary

Applications and Applied Mathematics: An International Journal (AAM)

During their operational life, structures may be subject to various types of live load caused by events such as earthquakes, high speed winds, etc. Given the design life of a structure, the probability for a specific live load to cause a failure depends on the magnitude of the load structure it is designed to withstand (designed load). In this article, methods are developed for calculation of the failure probability for structures designed to withstand loads comparable to historical loads at the site of interest.

Art, Math, And Physics; All About For, Chris Brownell, Steve Pauls

The Transdisciplinary STEAM+ Journal

Anish Kapoor’s public sculpture “Cloud Gate” and Frame of Reference.

Secondary Mathematics Teachers’ Attitudes And Beliefs Toward Statistics: Developing An Initial Profile, Christina M. Zumbrun

Dissertations

Over the last several decades, mathematics education researchers have given increased attention to students’ and teachers’ attitudes and beliefs toward mathematics and statistics, but no work has been done that examines practicing secondary mathematics teachers’ (SMTs’) attitudes and beliefs towards statistics in light of the GAISE framework and the Common Core State Standards for Mathematics (CCSSM). This study begins to address this gap in the research by creating the Teacher Attitude and Beliefs toward Statistics Survey (TABSS), a synthesis of items taken from the Survey of Attitudes Toward Statistics (Schau, 2003), the Statistics Course Attitude Scale and newly developed items …

Designing For Mistrust, Eric Gossett

ACMS Conference Proceedings 2015

The 2014 ACM North Central Region programming contest contained a problem about a group of v bandits who want to use multiple locks to seal their treasure and distribute keys in such a way that no group of less than m bandits can open all the locks. The problem asks for an algorithm that will determine the number of locks needed for any set of parameters (v, m). I will present an analytic solution that produces a minimum number of locks, a recurrence relation solution, and a constructive algorithm that can print out a table showing the …