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Full-Text Articles in Mathematics

Does Content Matter In An Introduction-To-Proof Course?, Milos Savic Jul 2017

Does Content Matter In An Introduction-To-Proof Course?, Milos Savic

Journal of Humanistic Mathematics

Introduction-to-proof courses are becoming more prevalent in mathematics departments as more recognize the need to support students while they transition from courses focused on computation (such as calculus) to proof-intensive courses (such as real analysis). In such introduction courses, there are some common proving techniques to teach (induction, contradiction, and contraposition to name a few), but the content varies from institution to institution. This note adds to the discussion on content in such courses by analyzing two prior studies, one using a coding scheme designed to illuminate step-by-step justifications in a proof, and the other focused on interviews with course …

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On Commensurability And Symmetry, David Pierce Jul 2017

On Commensurability And Symmetry, David Pierce

Journal of Humanistic Mathematics

Commensurability and symmetry have diverged from a common Greek origin. We review the history of this divergence. In mathematics, symmetry is now a kind of measure that is different from size, though analogous to it. Size being given by numbers, the concept of numbers and their equality comes into play. For Euclid, two magnitudes were symmetric when they had a common measure; also, numbers were magnitudes, commonly represented as bounded straight lines, for which equality was congruence. When Billingsley translated Euclid into English in the sixteenth century, he used the word "commensurable" for Euclid's symmetric magnitudes; but the word had …

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The Biblical Value Of Pi In Light Of Traditional Judaism, Morris Engelson Jul 2017

The Biblical Value Of Pi In Light Of Traditional Judaism, Morris Engelson

Journal of Humanistic Mathematics

There are numerous attempts at a solution to the puzzle as to why the Biblical value of pi, as demonstrated by the measurements of King Solomon's pool, is exactly 3 and not a better approximation. This article shows that virtually all such published solutions are deficient because volume-based factors are ignored. Issues respecting the volume of this pool are explained, and some possible solutions of the puzzle are presented.

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Perchance To Dream: Art, Mathematics, And Shakespeare, Randall E. Cone Jul 2017

Perchance To Dream: Art, Mathematics, And Shakespeare, Randall E. Cone

Journal of Humanistic Mathematics

Visual representation of textual works has often aided in the understanding of sophisticated concepts. In the Digital Age this is particularly true, given the advent of natural language processing, the ubiquity of general programming languages, and the maturation of digital visualization. In this article, we eschew the traditional disciplinary boundaries to view and analyze Shakespeare’s works in various ways. Our point of departure is Hamlet, where we first examine the play as a unity — both graphically and analytically. We then focus on Act III, Scene 1, where we analyze one of the most famous passages in English Literature: …

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Front Matter Jul 2017

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

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Calculus Reform: Increasing Stem Retention And Post-Requisite Course Success While Closing The Retention Gap For Women And Underrepresented Minority Students, Doug Bullock, Janet Callahan, Jocelyn B. S. Cullers Jun 2017

Calculus Reform: Increasing Stem Retention And Post-Requisite Course Success While Closing The Retention Gap For Women And Underrepresented Minority Students, Doug Bullock, Janet Callahan, Jocelyn B. S. Cullers

Mathematics Faculty Publications and Presentations

Boise State University (BSU) implemented an across-the-board reform of calculus instruction during the 2014 calendar year. The details of the reform, described elsewhere (Bullock, 2015), (Bullock 2016), involve both pedagogical and curricular reform. Gains from the project have included a jump in Calculus I pass rate, greater student engagement, greater instructor satisfaction, a shift toward active learning pedagogies, and the emergence of a strong collaborative teaching community. This paper examines the effects of the reform on student retention. Since the curricular reform involved pruning some content and altering course outcomes, which could conceivably have negative downstream impacts, we report on …

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Finding Meaning In Calculus (And Life), Doug Phillippy Jun 2017

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

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Cultivating Mathematical Affections Through Engagement In Service-Learning, Josh Wilkerson Jun 2017

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

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Reading Journals: Preview Assignments That Promote Student Engagement, Productive Struggle, And Ultimate Success In Undergraduate Mathematics Courses, Sarah Nelson Jun 2017

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 …

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Blended Courses Across The Curriculum: What Works And What Does Not, Ryan Botts, Lori Carter, Catherine Crockett Jun 2017

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 …

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Variations On The Calculus Sequence, Christopher Micklewright Jun 2017

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 …

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Using Real-World Team Projects: A Pedagogical Framework, Mike Leih Jun 2017

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 …

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The Set Of Zero Divisors Of A Factor Ring, Jesús Jiménez Jun 2017

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.

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Developing The Underutilized Mathematical Strengths Of Students, Patrick Eggleton Jun 2017

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.

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Axioms: Mathematical And Spiritual: What Says The Parable?, Melvin Royer Jun 2017

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 …

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A Pre-Calculus Controversy: Infinitesimals And Why They Matter, Karl-Dieter Crisman Jun 2017

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

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The Resolved And Unresolved Conjectures Of R.D. Carmichael, Brian D. Beasley Jun 2017

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?

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"Big Idea" Reflection Assignments For Learning And Valuing Mathematics, Jeremy Case, Mark Colgan Jun 2017

"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 …

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Mentoring As A Statistical Educator In A Christian College, L. Marlin Eby Jun 2017

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 …

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The Daily Question: Building Student Trust And Interest In Undergraduate Introductory Probability And Statistics Courses, Matthew A. Hawks Jun 2017

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 …

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The Topology Of Harry Potter: Exploring Higher Dimensions In Young Adult Fantasy Literature, Sarah Klanderman, Alexa Schut, Dave Klanderman, William Boerman-Cornell Jun 2017

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 …

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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 Jun 2017

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

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Ten Mathematicians Who Recognized God's Hand In Their Work (Part 2), Dale Mcintyre Jun 2017

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 …

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

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

ACMS Conference Proceedings 2017

No abstract provided.

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

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

ACMS Conference Proceedings 2017

No abstract provided.

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

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

ACMS Conference Proceedings 2017

No abstract provided.

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

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

ACMS Conference Proceedings 2017

No abstract provided.

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

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.

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Revolution In Ideology: Crafting A Holistic Scientific Dialectic, Nathan Neill May 2017

Revolution In Ideology: Crafting A Holistic Scientific Dialectic, Nathan Neill

Dialogue & Nexus

Ideology drives scientific research far more than is acknowledged. Since science itself is conducted by individuals, each scientist has a biased conception of themselves and their surroundings relative to the rest of the universe, even if it is never explicated. This sense of relation to the greater universe is what defines the ideology of the individual. It is this sense of relation and self that creates the individual, who goes on to investigate the natural world by the scientific method. In this paper I will examine extant scientific ideology, particularly in Western science, and propose changes that could be helpful.

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Six Septembers: Mathematics For The Humanist, Patrick Juola, Stephen Ramsay Apr 2017

Six Septembers: Mathematics For The Humanist, Patrick Juola, Stephen Ramsay

Zea E-Books Collection

Scholars of all stripes are turning their attention to materials that represent enormous opportunities for the future of humanistic inquiry. The purpose of this book is to impart the concepts that underlie the mathematics they are likely to encounter and to unfold the notation in a way that removes that particular barrier completely. This book is a primer for developing the skills to enable humanist scholars to address complicated technical material with confidence. This book, to put it plainly, is concerned with the things that the author of a technical article knows, but isn’t saying. Like any field, mathematics operates …

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