Existence And Rapid Convergence Results For Nonlinear Caputo Nabla Fractional Difference Equations,
2017
Sun Yat-sen University
Existence And Rapid Convergence Results For Nonlinear Caputo Nabla Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson
Department of Mathematics: Faculty Publications
This paper is concerned with finding properties of solutions to initial value problems for nonlinear Caputo nabla fractional difference equations. We obtain existence and rapid convergence results for such equations by use of Schauder’s fixed point theorem and the generalized quasi-linearization method, respectively. A numerical example is given to illustrate one of our rapid convergence results.
Weak Synchronization In Excitatory – Inhibitory Neuronal Networks,
2017
Brigham Young University
Weak Synchronization In Excitatory – Inhibitory Neuronal Networks, Joel Eliason, Benjamin Webb
Journal of Undergraduate Research
One ubiquitously observed dynamic phenomenon in the nervous system is that of weak synchronization or clustering, a behavior in which a large group of neurons in a population will all fire synchronously and then fall out of synchronization. When isolated to neurons that only form short-range connections, this behavior is typically referred to as “neuronal avalanches”, and is thought to be particularly important for robustness of information transmission as well as sensitivity to inputs. Given these potential computational benefits, avalanches have been a focus of theoretical biologists for the past 20 years. In particular, my project focused on the conditions, …
A Management Maturity Model (Mmm) For Project-Based Organisational Performance Assessment,
2017
Bond University
A Management Maturity Model (Mmm) For Project-Based Organisational Performance Assessment, Craig Langston, Amir Ghanbaripour
Amir Ghanbaripour
Common sense suggests that organisations are more likely to deliver successful projects if they have systems in place that reflect a mature project environment based on a culture of continuous improvement. This paper develops and discusses a Management Maturity Model (MMM) to assess the maturity of project management organisations through a customisable, systematic, strategic and practical methodology inspired from the seminal work of Darwin, Deming, Drucker and Daniel. The model presented is relevant to organisations, such as construction and engineering companies, that prefer to use the Project Management Body of Knowledge (PMBOK™ Guide) published by the Project Management Institute (PMI), …
Traveling Wave Solutions To Kawahara And Related Equations,
2017
Embry-Riddle Aeronautical University
Traveling Wave Solutions To Kawahara And Related Equations, S.C. Mancas
Publications
Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Korteweg-de Vries (KdV) equation are found by using an elliptic function method which is more general than the tanh-method. The method works by assuming that a polynomial ansatz satisfies a Weierstrass equation, and has two advantages: first, it reduces the number of terms in the ansatz by an order of two, and second, it uses Weierstrass functions which satisfy an elliptic equation for the dependent variable instead of the hyperbolic tangent functions which only satisfy the Riccati equation with constant coefficients. When the polynomial ansatz in the traveling wave …
The Resolved And Unresolved Conjectures Of R.D. Carmichael,
2017
Presbyterian College
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,
2017
Taylor University
"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 …
Using Real-World Team Projects: A Pedagogical Framework,
2017
Point Loma Nazarene University
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 …
Variations On The Calculus Sequence,
2017
Eastern University
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 …
The Topology Of Harry Potter: Exploring Higher Dimensions In Young Adult Fantasy Literature,
2017
Michigan State University
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 …
Ten Mathematicians Who Recognized God's Hand In Their Work (Part 2),
2017
Grove City College
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 …
The Set Of Zero Divisors Of A Factor Ring,
2017
Point Loma Nazarene University
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.
The Daily Question: Building Student Trust And Interest In Undergraduate Introductory Probability And Statistics Courses,
2017
United States Naval Academy
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 …
Finding Meaning In Calculus (And Life),
2017
Messiah College
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
Axioms: Mathematical And Spiritual: What Says The Parable?,
2017
Indiana Wesleyan University
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 …
Cultivating Mathematical Affections Through Engagement In Service-Learning,
2017
Regents School of Austin
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
Blended Courses Across The Curriculum: What Works And What Does Not,
2017
Point Loma University
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 …
A Pre-Calculus Controversy: Infinitesimals And Why They Matter,
2017
Gordon College
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
Start A Math Teacher Circle: Connect K-12 Teachers With Engaging, Approachable, And Meaningful Mahtematical Problems,
2017
Dordt College
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
Reading Journals: Preview Assignments That Promote Student Engagement, Productive Struggle, And Ultimate Success In Undergraduate Mathematics Courses,
2017
Lenoir-Rhyne University
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 …
Mentoring As A Statistical Educator In A Christian College,
2017
Messiah College
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 …
