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Mathematics

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Articles 1 - 30 of 929

Full-Text Articles in Physical Sciences and Mathematics

Elementary Set Theory, Richard P. Millspaugh Sep 2018

Elementary Set Theory, Richard P. Millspaugh

Open Educational Resources

This text is appropriate for a course that introduces undergraduates to proofs. The material includes elementary symbolic logic, logical arguments, basic set theory, functions and relations, the real number system, and an introduction to cardinality. The text is intended to be readable for sophomore and better freshmen majoring in mathematics.


Optimizing Maternal And Tenure Clocks: A Mathematical Proof, Tara T. Craig Jul 2018

Optimizing Maternal And Tenure Clocks: A Mathematical Proof, Tara T. Craig

Journal of Humanistic Mathematics

This essay shares my journey to solving the problem of timing, specifically as it applies to having a child on my journey towards a career as a mathematician in academia. I share some of the challenges I faced during pregnancy and the first few years of motherhood, which coincided with my first few years as an assistant professor of mathematics.


College Dropout To College Professor, Deborah L. Gochenaur, Rose I. Verbos Jul 2018

College Dropout To College Professor, Deborah L. Gochenaur, Rose I. Verbos

Journal of Humanistic Mathematics

Being a college dropout wasn’t something to be proud of; it just happened. Life doesn’t always turn out the way we want or expect. Yet, it is often how we deal with defeat that defines us – figuring out when to lick our wounds and when to come back fighting. It took a few years to redefine my dream, start a family, and seem to move forward, but the ache for more was always in the back of my mind. Could I succeed at something at which I had already failed? Going back to school at a community college ...


Rational Points On Surfaces And In Life, Amanda Knecht Jul 2018

Rational Points On Surfaces And In Life, Amanda Knecht

Journal of Humanistic Mathematics

This essay collects together examples of instances where I should have advocated for myself more as a mother and examples of how I have advocated for my children. Theses stories come from a mathematician who gave birth to two children while on the tenure track in an older department with only one tenured woman.


Beautiful Madness: Math And Motherhood --- Can You Have It All?, Abigail Wacher Jul 2018

Beautiful Madness: Math And Motherhood --- Can You Have It All?, Abigail Wacher

Journal of Humanistic Mathematics

I am a tenure-track assistant professor, and I have a beautiful three-year old boy and a husband who I love. My life today is within epsilon of the future I imagined while I was in university and contemplating a career in mathematics. Getting here, however, took longer than I thought. Along the way I often felt I was under pressure to choose between my career and having a family. I never made this choice and, although my pregnancy and my son did interfere with my career, I would not have it any other way. This is the story of how ...


Don't Ask The Baby To Do Calculus: Thoughts From An Early-Career Math Mama, Caitlin Krul Jul 2018

Don't Ask The Baby To Do Calculus: Thoughts From An Early-Career Math Mama, Caitlin Krul

Journal of Humanistic Mathematics

I very recently became a math mama. In my desperate search for patterns and structure in those first few weeks, my husband told me, "She's only three weeks old; we can't expect her to be doing calculus homework." I suppose he was right. I am working towards tenure and finding a new balance between teaching and family, all while trying to not lose sight of who I am. My personal challenges range from the logistics of being a nursing mother in a shared office to feelings of being seen as less adequate in my job if I present ...


So, Your Mom Wants To Be A Mathematician, Edie Stevens Jul 2018

So, Your Mom Wants To Be A Mathematician, Edie Stevens

Journal of Humanistic Mathematics

Despite all the stereotypes about them, mothers possess a skill set that makes them outstanding potential mathematicians. Most are organized, detail oriented, driven, determined, effective communicators; they are able to break down any concept or task into its principal components, and they can be logical and persuasive even when addressing the most formidable and unwilling audience. In short, no matter how messy, difficult, or tedious the task at hand, moms excel at getting the job done. This is my affirming story of how I left my engineering career to raise a family and returned to academia to pursue a doctoral ...


On Contradiction, Piper Harron Jul 2018

On Contradiction, Piper Harron

Journal of Humanistic Mathematics

Parenting, across species, is a clumsy, all-consuming, and often exasperating endeavor. Yet in many parts of the human world, we somehow expect to contain and control this part of ourselves. We idealize the separation of work and family. This seems to be especially true in mathematics where many of us hold space in our minds for the Devoted Genius Mathematician who has no other responsibilities but to their own passions, and no obstacles beyond the difficulties of their own pursuits. The unavoidable fact is that life with children is full of absurdities and contradictions. Unless we're willing to embrace ...


Motherhood And Teaching: Radical Care, Ksenija Simic-Muller Jul 2018

Motherhood And Teaching: Radical Care, Ksenija Simic-Muller

Journal of Humanistic Mathematics

This essay is a personal reflection on how I leverage my positioning as a caregiver in my roles of a mathematician, teacher, and mother, to advance a vision for a more just and equitable society. I argue that care at home and in the classroom takes similar forms, and can be liberating instead of oppressive


From Ecstasy To Agony And Back: Mathematics, Motherhood, And Postpartum Depression, Azadeh Rafizadeh Jul 2018

From Ecstasy To Agony And Back: Mathematics, Motherhood, And Postpartum Depression, Azadeh Rafizadeh

Journal of Humanistic Mathematics

In this essay I address some challenges I had to overcome as a non-tenured mathematician mother married to another mathematician. While some of these challenges, such as lack of sleep, were predictable, many were not. For example, I was not aware that just getting pregnant would be a difficulty. Also, I did not know how paralyzing postpartum depression could be. Looking back on these experiences after a few years, I have a new perspective. I share my experiences, feelings about them, and some of the ways I figured out to overcome the hardships I experienced.


The Multiple Identities Of A Mathematics Professor Mom, Margaret J. Mohr-Schroeder Jul 2018

The Multiple Identities Of A Mathematics Professor Mom, Margaret J. Mohr-Schroeder

Journal of Humanistic Mathematics

In this essay, i dive into the multiple identities of a Mathematics Professor Mom and how we interchange those identities as we work to achieve harmony (not balance!) in our lives.


Calculating Intersections: The Crossroads Of Mathematics And Literature In The Lives Of Mother And Daughter, Della Dumbaugh, Hannah Fenster Jul 2018

Calculating Intersections: The Crossroads Of Mathematics And Literature In The Lives Of Mother And Daughter, Della Dumbaugh, Hannah Fenster

Journal of Humanistic Mathematics

This article tells the stories of how we, Della (mom, mathematician) and Hannah (daughter, writing instructor and bookseller), arrived in our professional settings through the lens of mother and daughter. For us, the intersections of literature and mathematics inspired many of our pivotal moments.


The Situatedness Of Mathematics In Motherhood And Academia, Jennifer Schenk Sacco, Jill Shahverdian Jul 2018

The Situatedness Of Mathematics In Motherhood And Academia, Jennifer Schenk Sacco, Jill Shahverdian

Journal of Humanistic Mathematics

The authors, a mathematician and a political scientist, examine mathematics, motherhood, and academia, and argue that feminist epistemology is necessary to explain the intersection. Relying on the principles of feminist epistemology laid out by philosophers Naomi Scheman and Marianne Janack, the authors consider how work, the concept of time, teaching, arts and crafts, and decision-making all reveal the situatedness of knowing and using mathematics.


Founders, Feminists, And A Fascist -- Some Notable Women In The Missouri Section Of The Maa, Leon M. Hall Jun 2018

Founders, Feminists, And A Fascist -- Some Notable Women In The Missouri Section Of The Maa, Leon M. Hall

Leon M. Hall

In the history of the Missouri Section of the MAA, some of the more interesting people who influenced the growth and development of the section through the years were and are women. In this chapter, we discuss the contributions of a few (certainly not all) of these women to the Missouri Section and mathematics as a whole, including Emily Kathryn Wyant (founder of KME), Margaret F. Willerding (who dealt with sexism in the 1940s), Maria Castellani (an official in Mussolini’s Italy before coming to America), and T. Christine Stevens (co-founder of Project NExT). Without them, and others like them ...


Graceful Colorings And Connection In Graphs, Alexis D. Byers Jun 2018

Graceful Colorings And Connection In Graphs, Alexis D. Byers

Dissertations

For a graph G of size m, a graceful labeling of G is an injective function f : V (G)

{0, 1, . . . , m} that gives rise to a bijective function f 1 : E(G) {1, 2, . . . , m} defined by f 1(uv) = |f (u) f (v)|. A graph is graceful if it has a graceful labeling. Over the years, a number of variations of graceful labelings have been introduced, some of which have been described in terms of colorings.

A proper (vertex) coloring of a graph G is an assignment of colors to the vertices of G such that adjacent vertices ...


Introduction To Financial Mathematics Course, Sonia M F Garcia May 2018

Introduction To Financial Mathematics Course, Sonia M F Garcia

Mathematica Militaris

The teaching of financial mathematics at the university level has become more common in the past decade. It is crucial that young officers of our military system be aware of its intricacies in order to present themselves before the world with a more rounded and broader literacy.


Know Your Customer: Driving Calculus Course Design Through Data, Andrew Plucker May 2018

Know Your Customer: Driving Calculus Course Design Through Data, Andrew Plucker

Mathematica Militaris

Research suggests that students struggle with calculus on various levels. Student and instructor feedback is a necessary cycle to restructure and improve course curriculum. The aim of this paper is to discuss and illustrate how solicited feedback and administrative data can be coupled together to drive decisions about course design.


Mathematical Modelling Of English Coulee: Tanks In Series, Matthew Picklo May 2018

Mathematical Modelling Of English Coulee: Tanks In Series, Matthew Picklo

Essential Studies UNDergraduate Showcase

In the scope of the College of Arts and Science project: “Coulee Cleanway: Modelling and Analysis of the English Coulee Physiochemical Environment, UND Campus, Grand Forks”, a mathematical model attempting to describe the transportation of dissolved species within the English Coulee was developed based on “Tanks in Series”. By dividing the channel into discrete regions, a governing system of equations derived from conservation of mass equations and well-mixed assumptions is used to describe the spatial and temporal changes in concentration. The resulting system of differential equations was solved by a Runge-Kutta 4 numerical method, which allowed for the addition of ...


The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas Apr 2018

The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas

Honors Projects

In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time ...


Transforming Students Through Geometric Transformations, Sierra Galicia Apr 2018

Transforming Students Through Geometric Transformations, Sierra Galicia

Honors Theses AY 17/18

It is a common saying among teachers that the hardest grades to teach are middle school. Beginning January 3rd, 2018, I was placed in an eighth-grade mathematics classroom for student teaching with the mindset that I was going to tackle this challenge head-on. I started the experience enthusiastic and ready to teach my students with exciting and engaging lessons. Unfortunately, I soon found that many students have low self-esteem, low self-confidence and they lack the necessary perseverance needed to complete challenging assignments and to be successful in math. It quickly became apparent why people say middle school is the hardest ...


The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila Apr 2018

The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila

Sandy Avila

No abstract provided.


Simulations And Queuing Theory: The Effects Of Randomly Bypassing Security, Emily Ortmann Apr 2018

Simulations And Queuing Theory: The Effects Of Randomly Bypassing Security, Emily Ortmann

Masters Theses & Doctoral Dissertations

We discuss queueing theory in the setting of airport security and customs. By developing queueing simulations based on mathematical models, we explore a variety of questions related to optimal queue design with respect to efficiency, feasibility, priority, and other prescribed/variable constraints.


Simulations And Queueing Theory: The Effects Of Priority And Vip Thresholds, Laura Schuck Apr 2018

Simulations And Queueing Theory: The Effects Of Priority And Vip Thresholds, Laura Schuck

Masters Theses & Doctoral Dissertations

Everyone has experienced waiting in lines, whether it is at the airport, the grocery store, or somewhere in-between. By developing queueing simulations based on mathematical models of airport security and customs, we explore a variety of questions related to optimal queue design with respect to efficiency, feasibility, priority, and other prescribed/variable constraints.


Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle Apr 2018

Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle

Masters Theses & Specialist Projects

The Bernoulli distribution is a basic, well-studied distribution in probability. In this thesis, we will consider repeated Bernoulli trials in order to study runs of identical outcomes. More formally, for t ∈ N, we let Xt ∼ Bernoulli(p), where p is the probability of success, q = 1 − p is the probability of failure, and all Xt are independent. Then Xt gives the outcome of the tth trial, which is 1 for success or 0 for failure. For n, m ∈ N, we define Tn to be the number of trials needed to first observe n consecutive successes (where the nth ...


Under The Influence, Leonardo Cavicchio Apr 2018

Under The Influence, Leonardo Cavicchio

Honors Projects in Mathematics

The purpose of this Honors Capstone entitled Under the Influence is to assess the validity of claims concerning the possible influence of roommates on one another, concerning alcohol on college campuses. This will be done by examining data collected in a prior study conducted over a two-year period. This analysis will focus on how alcohol consumption changes in correlation with the personality factors of roommates over an extended period of time. This secondary analysis of de-identified data will focus on primary and secondary subquestions. The primary question that will be addressed with the data set collected from the University of ...


Underachievement In Mathematics In The Early Childhood Classroom, Amy E. Lieberman Apr 2018

Underachievement In Mathematics In The Early Childhood Classroom, Amy E. Lieberman

Education: Student Scholarship & Creative Works

No abstract provided.


The Impact Of Khan Academy Math Remediation On Ninth Grade Student Achievement, Sandra Kelly Apr 2018

The Impact Of Khan Academy Math Remediation On Ninth Grade Student Achievement, Sandra Kelly

Doctoral Dissertations and Projects

The purpose of this quasi-experimental study was to determine if using Khan Academy as math remediation for fifteen minutes per day during a ninth grade Math I class would significantly affect student math achievement as measured by the North Carolina READY Math I End-of-Course Assessment. This quantitative study conducted at two rural high schools in West Virginia used remediation theory to make a comparison against a control population with the independent variable being grade level instruction only or grade level instruction plus math remediation using Khan Academy. The participants in the study included 131 ninth grade high school students taking ...


Archimedes In The Classroom, Rachel Towne Apr 2018

Archimedes In The Classroom, Rachel Towne

Masters Essays

Eureka! Eureka! What better way to excite and engage students than to bring Archimedes into the classroom? Archimedes is widely regarded as the greatest mathematician of antiquity. Very little is known about Archimedes’ personal life. Archimedes was born in Syracuse, Sicily around 287 B.C., and he was the son of an astronomer. He probably studied in Alexandria, Egypt under followers of Euclid. Today we know Archimedes as a brilliant mathematician and scientist, he spent much of his career inventing war machines. Despite orders not to harm Archimedes, his life was cut short in 212 B.C. when the Romans ...


Modeling Multimodal Failure Effects Of Complex Systems Using Polyweibull Distribution, Daniel A. Timme Mar 2018

Modeling Multimodal Failure Effects Of Complex Systems Using Polyweibull Distribution, Daniel A. Timme

Theses and Dissertations

The Department of Defense (DoD) enlists multiple complex systems across each of their departments. Between the aging systems going through an overhaul and emerging new systems, quality assurance to complete the mission and secure the nation‘s objectives is an absolute necessity. The U.S. Air Force‘s increased interest in Remotely Piloted Aircraft (RPA) and the Space Warfighting domain are current examples of complex systems that must maintain high reliability and sustainability in order to complete missions moving forward. DoD systems continue to grow in complexity with an increasing number of components and parts in more complex arrangements. Bathtub-shaped ...


I'Ve Got Your Number: A Multiple Choice Guessing Game, Ryan Cushman, Adam J. Hammett Feb 2018

I'Ve Got Your Number: A Multiple Choice Guessing Game, Ryan Cushman, Adam J. Hammett

Adam J. Hammett, Ph.D.

We consider the following guessing game: fix positive integers k, m, and n. Player A ("Ann") chooses a (uniformly) random integer from the set {1,2,3,...,n}, but does not reveal it to Player B ("Gus"). Gus then presents Ann with a k-option multiple choice question about which number she chose, to which Ann responds truthfully. After m such questions have been asked, Gus must attempt to guess the number chosen by Ann. Gus wins if he guesses Ann's number. The purpose of this note is to find all canonical m-question algorithms which maximize the probability of Gus ...