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 …
Developing The Underutilized Mathematical Strengths Of Students,
2017
Taylor University
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.
Elimination For Systems Of Algebraic Differential Equations,
2017
The Graduate Center, City University of New York
Elimination For Systems Of Algebraic Differential Equations, Richard Gustavson
Dissertations, Theses, and Capstone Projects
We develop new upper bounds for several effective differential elimination techniques for systems of algebraic ordinary and partial differential equations. Differential elimination, also known as decoupling, is the process of eliminating a fixed subset of unknown functions from a system of differential equations in order to obtain differential algebraic consequences of the original system that do not depend on that fixed subset of unknowns. A special case of differential elimination, which we study extensively, is the question of consistency, that is, if the given system of differential equations has a solution. We first look solely at the ``algebraic data" of …
Choice Of Choice: Paradoxical Results Surrounding Of The Axiom Of Choice,
2017
Union College - Schenectady, NY
Choice Of Choice: Paradoxical Results Surrounding Of The Axiom Of Choice, Connor Hurley
Honors Theses
When people think of mathematics they think "right or wrong," "empirically correct" or "empirically incorrect." Formalized logically valid arguments are one important step to achieving this definitive answer; however, what about the underlying assumptions to the argument? In the early 20th century, mathematicians set out to formalize these assumptions, which in mathematics are known as axioms. The most common of these axiomatic systems was the Zermelo-Fraenkel axioms. The standard axioms in this system were accepted by mathematicians as obvious, and deemed by some to be sufficiently powerful to prove all the intuitive theorems already known to mathematicians. However, this system …
Elliptic Curve Cryptology,
2017
Union College - Schenectady, NY
Elliptic Curve Cryptology, Francis Rocco
Honors Theses
In today's digital age of conducting large portions of daily life over the Internet, privacy in communication is challenged extremely frequently and confidential information has become a valuable commodity. Even with the use of commonly employed encryption practices, private information is often revealed to attackers. This issue motivates the discussion of cryptology, the study of confidential transmissions over insecure channels, which is divided into two branches of cryptography and cryptanalysis. In this paper, we will first develop a foundation to understand cryptography and send confidential transmissions among mutual parties. Next, we will provide an expository analysis of elliptic curves and …
Application Of Kudryashov Method For The Ito Equations,
2017
University of Guilan
Application Of Kudryashov Method For The Ito Equations, Mozhgan Akbari
Applications and Applied Mathematics: An International Journal (AAM)
In this present work, the Kudryashov method is used to construct exact solutions of the (1+1)- dimensional and the (1+2)-dimensional form of the generalized Ito integro-differential equation. The Kudryashov method is a powerful method for obtaining exact solutions of nonlinear evolution equations. This method can be applied to non-integrable equations as well as integrable ones.
A Novel Approach For Solving Volterra Integral Equations Involving Local Fractional Operator,
2017
University of Thi-Qar
A Novel Approach For Solving Volterra Integral Equations Involving Local Fractional Operator, Hassan K. Jassim
Applications and Applied Mathematics: An International Journal (AAM)
The paper presents an approximation method called local fractional variational iteration method (LFVIM) for solving the linear and nonlinear Volterra integral equations of the second kind with local fractional derivative operators. Some illustrative examples are discussed to demonstrate the efficiency and the accuracy of the proposed method. Furthermore, this method does not require spatial discretization or restrictive assumptions and therefore reduces the numerical computation significantly. The results reveal that the local fractional variational iteration method is very effective and convenient to solve linear and nonlinear integral equations within local fractional derivative operators.
Thermal Stress Analysis In A Functionally Graded Hollow Elliptic-Cylinder Subjected To Uniform Temperature Distribution,
2017
RTM Nagpur University
Thermal Stress Analysis In A Functionally Graded Hollow Elliptic-Cylinder Subjected To Uniform Temperature Distribution, V. R. Manthena, N. K. Lamba, G. D. Kedar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, an analytical method of a thermoelastic problem for a medium with functionally graded material properties is developed in a theoretical manner for the elliptic-cylindrical coordinate system under the assumption that the material properties except for Poisson’s ratio and density are assumed to vary arbitrarily with the exponential law in the radial direction. An attempt has been made to reconsider the fundamental system of equations for functionally graded solids in a two-dimensional state under thermal and mechanical loads. The general solution of displacement formulation is obtained by the introduction of appropriate transformation and carried out the analysis by …
