Mathematics Commons^™

Mean Value Theorems For Riemannian Manifolds Via The Obstacle Problem, Brian Benson, Ivan Blank, Jeremy Lecrone

Department of Math & Statistics Faculty Publications

We develop some of the basic theory for the obstacle problem on Riemannian manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide class of Riemannian manifolds and has no weights at all within the integral.

Neutrosophic Triplet Structures - Vol. 1, Florentin Smarandache, Memet Sahin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets …

A Self-Contained Course In The Mathematical Theory Of Statistics For Scientists & Engineers With An Emphasis On Predictive Regression Modeling & Financial Applications., Tim Smith

Open Access Textbooks

Preface & Acknowledgments

This textbook is designed for a higher level undergraduate, perhaps even first year graduate, course for engineering or science students who are interested to gain knowledge of using data analysis to make predictive models. While there is no statistical perquisite knowledge required to read this book, due to the fact that the study is designed for the reader to truly understand the underlying theory rather than just learn how to read computer output, it would be best read with some familiarity of elementary statistics. The book is self-contained and the only true perquisite knowledge is a solid …

Barrier Graphs And Extremal Questions On Line, Ray, Segment, And Hyperplane Sensor Networks, Kirk Anthony Boyer

Electronic Theses and Dissertations

A sensor network is typically modeled as a collection of spatially distributed objects with the same shape, generally for the purpose of surveilling or protecting areas and locations. In this dissertation we address several questions relating to sensors with linear shapes: line, line segment, and rays in the plane, and hyperplanes in higher dimensions.

First we explore ray sensor networks in the plane, whose resilience is the number of sensors that must be crossed by an agent traveling between two known locations. The coverage of such a network is described by a particular tripartite graph, the barrier graph of the …

Upper Dimension And Bases Of Zero-Divisor Graphs Of Commutative Rings, S. Pirzada, M. Aijaza, Shane Redmond

EKU Faculty and Staff Scholarship

For a commutative ring R with non-zero zero divisor set Z∗(R), the zero divisor graph of R is Γ(R) with vertex set Z∗(R), where two distinct vertices x and y are adjacent if and only if x y = 0. The upper dimension and the resolving number of a zero divisor graph Γ(R) of some rings are determined. We provide certain classes of rings which have the same upper dimension and metric dimension and give an example of a ring for which these values do not coincide. Further, we obtain some bounds for the upper dimension in zero divisor graphs …

The Encyclopedia Of Neutrosophic Researchers - Vol. 3, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: …

Cantor Sets, Cantorvals, And Their Topological Structure, Ángel Adrián Agüero

Open Access Theses & Dissertations

With interesting topological properties, the Cantor set is worth studying for itself. In other areas, topological structures arise that are in fact homeomorphic to the Cantor set. In particular, we see sets that are homeomorphic to the Cantor set which result from the subsums of particular series, as well as linear combinations of algebraic sums of Cantor sets. These also result in what has been termed a Cantorval, which we also investigate.

Towards Analytical Techniques For Systems Engineering Applications, Griselda Valdepeñas Acosta

Open Access Theses & Dissertations

One of the main objectives of systems engineering is to design, maintain, and analyze systems that help the users. To design an appropriate system for an application domain, we need to know: what are the users' desires and preferences (so that we know in what direction we should aim to change this domain), what is the current state and what is the dynamics of this application domain, and how to use all this information to select the best alternatives for the system design and maintenance. Designing a system includes selecting numerical values for many of the parameters describing the corresponding …

A Complete Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder Genannt Luehr

Doctoral Dissertations

A graph is outer-planar (OP) if it has a plane embedding in which all of the vertices lie on the boundary of the outer face. A graph is near outer-planar (NOP) if it is edgeless or has an edge whose deletion results in an outer-planar graph. An edge of a non outer-planar graph whose removal results in an outer-planar graph is a vulnerable edge. This dissertation focuses on near outer-planar (NOP) graphs. We describe the class of all such graphs in terms of a finite list of excluded graphs, in a manner similar to the well-known Kuratowski Theorem for planar …

Math Active Learning Lab: Math 93 Notebook, Michele Iiams, Gwennie Byron

Open Educational Resources

This course notebook has been designed for students of Math 93 (Algebra Prep III) at the University of North Dakota. It has been designed to help you get the most out of the ALEKS resources and your time.

• Topics in the Notebook are organized by weekly learning module.
• Space for notes from ALEKS learning pages, e-book and videos directs you to essential concepts.
• Examples and “You Try It” problems have been carefully chosen to help you focus on these essential concepts.
• Completed Notebook is an invaluable tool when studying for exams.

Σ-Ary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

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.

The source files for the text can be found at https://github.com/RPMillspaugh/SetTheory

Math Active Learning Lab: Math 92 Notebook, Michele Iiams, Gwennie Byron

Open Educational Resources

This course notebook has been designed for students of Math 92 (Algebra Prep II) at the University of North Dakota. It has been designed to help you get the most out of the ALEKS resources and your time.

• Topics in the Notebook are organized by weekly learning module.
• Space for notes from ALEKS learning pages, e-book and videos directs you to essential concepts.
• Examples and “You Try It” problems have been carefully chosen to help you focus on these essential concepts.
• Completed Notebook is an invaluable tool when studying for exams.

T-De Vries Algebra, Nawal Alznad

Electronic Theses and Dissertations

The main point of this dissertation is to introduce the action on de Vries algebra by a topological monoid and we denoted the resulting category by dVT. In order to reach our goal, we started with introducing new proofs for some well known results in the category of flows. Then, we studied the Generalized Smirnov's Theorem for flows. After we studied the new category (dVT), we were able to provide a new way to construct the Čech-stone flow compactification of a given flow. Finally, we developed the co-free T-de Vries algebra for a special case.

Surface Entropy Of Shifts Of Finite Type, Dennis Pace

Electronic Theses and Dissertations

Let χ be the class of 1-D and 2-D subshifts. This thesis defines a new function, H_S : χ x R → [0,∞] which we call the surface entropy of a shift. This definition is inspired by the topological entropy of a subshift and we compare and contrast several structural properties of surface entropy to entropy. We demonstrate that much like entropy, the finiteness of surface entropy is a conjugacy invariant and is a tool in the classification of subshifts. We develop a tiling algorithm related to continued fractions which allows us to prove a continuity result about surface …

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

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 at …

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

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

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 myself as …

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

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 that, …

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

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

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

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

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.

Limit Behavior Of Mass Critical Hartree Minimization Problems With Steep Potential Wells, Yujin Guo, Yong Luo, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

We consider minimizers of the following mass critical Hartree minimization problem: e_λ(N) ≔ inf{u∈H¹(ℝ^d),‖u‖²₂=N} E_λ(u), where d ≥ 3, λ > 0, and the Hartree energy functional E_λ(u) is defined by E_λ(u)≔∫_R^d|∇u(x)|²dx + λ∫_R^d g(x)u²(x)dx − 1/2∫_R^d∫_R^d {u²(x)u²(y)/|x−y|²} dxdy. Here the steep potential g(x) satisfies 0 = g(0) = inf_ℝ^dg(x) ≤ g(x) ≤ 1 and 1 …

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 …

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 …