Digital Commons Network^™

A Brief Introduction To General Topology, Richard P. Millspaugh

Open Educational Resources

The material in this text is intended to be accessible to undergraduates who have had an introduction to elementary set theory and proof techniques. It includes sufficient material from general topology to prove the two main topological results found in a standard first semester calculus course: the Intermediate Value Theorem and the Extreme Value Theorem. This material can be found in Chapters 2 through 6 and makes up the bulk of the text. Rather than approaching these topics through use of the standard euclidean metric, it defines the standard topology on R in terms of the usual order on R. …

Apex Calculus: Und Edition (June 2023), Gregory Hartman, Department Of Mathematics, University Of North Dakota

Open Educational Resources

This text comprises a three–volume series on Calculus. The first part covers material taught in many “Calculus 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6. The second text covers material often taught in “Calculus 2”: integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 7 through 10. The third text covers topics common in “Calculus 3” or “Multivariable Calculus”: parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 11 through 15. All three are available separately for free. …

Matrix Multiplier: Cramer’S Method Calculation, Haruka Kido

Electrical Engineering Student Publications

This paper is a technical report of the C++ and LabVIEW algorithms for and the underlying mathematics of The Cramer’s Method. The systemic process of the Cramer’s Method enhances the efficiency of solving matrix multiplication problems involving systems of linear equations with sets of 3 or more added or subtracted unknown variables associated with numerical coefficients. The coefficients of the system of equations generate the numbers in the matrix to be used in the replicable and formulaic computation process.

Math Active Learning Lab: Math 107 Precalculus Notebook, Gwennie Byron, Department Of Mathematics, University Of North Dakota

Open Educational Resources

This course notebook has been designed for students of Math 107 (Precalculus) 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.

Math Active Learning Lab: Math 98 Notebook, Gwennie Byron, Michele Iiams, Department Of Mathematics, University Of North Dakota

Open Educational Resources

This course notebook has been designed for students of Math 98 (Intermediate Algebra) 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.

Math Active Learning Lab: Math 103 College Algebra Notebook, Gwennie Byron, Department Of Mathematics, University Of North Dakota

Open Educational Resources

This course notebook has been designed for students of Math 103 (College Algebra) 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.

Modeling The Spread Of Disease, James Hollister

Essential Studies UNDergraduate Showcase

Mathematically modeling the spread of disease in a population is a focus among epidemiologists. Using an SIR model (susceptible, infected, and recovered), we can create a system of differential equations to help better understand how a disease spreads in a simple environment. However, if we are to create a more realistic environment, computer simulations may be necessary. We can use the results from these simulations to try and find ways to eradicate the disease as efficiently as possible. In this poster, we will present the SIR model, present a system of differential equations that describe the movement of disease in …

Equations Of Motion In A Rotating Noninertial Reference Frame, Nicholas L. Sponsel

Essential Studies UNDergraduate Showcase

Measurement is an essential part of empirical research. As such, understanding whether the frame of reference in which a measurement occurs is inertial is essential for accurate data. As a rotating sphere, Earth is a non-inertial frame of reference and gives rise to fictitious forces. These forces are derived through vector algebra and further solved through matrix differential equations. The final solution for how velocity evolves over time results in sinusoidal functions with a period of 24 hours for Earth. To test the equations further, rational scenarios are proposed for different locations on the surface of Earth involving different initial …

A New Trend In Human Reproduction - Women In The Usa, Abby Rokke

Essential Studies UNDergraduate Showcase

The control a woman is allowed to have over her own reproductive system has been a recent popular topic of debate. Since the 1950's, women have made up over half of the total United States population. With women making up the majority of the country's citizens, it would be quite the contradiction for them to not have the right to make decisions about their own bodies. Over the last two decades many contraceptive and medical advances have assisted in a woman's ability to make her own choice. An interesting trend in childbearing has occurred from this new wave of technologies. …

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.

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.

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 …

Gödel’S Incompleteness Theorem, Emma Buntrock

Essential Studies UNDergraduate Showcase

In 1931 Gödel released his Incompleteness Theorem. His theorem was the opposite of what other mathematicians at the time wanted, but it was very influential to realize there is no perfectly complete formal systems. The incompleteness theorem is based of the idea that in a consistent system there are pieces that can not be proved or disproved, causing for incompleteness. The second part of that idea is that such a system can not prove that itself is consistent, which also makes it incomplete. I will verify theses proofs using a series of logic problems that show how a system is …

Improving The Problem With Problem Solving, Cole Thibert

Essential Studies UNDergraduate Showcase

As a prospective math educator who will be teaching in the near future, I was concerned with the idea of preparing my future students for college math courses. I decided to research the effects of teaching students how to appropriately use problem solving strategies in math. My research led me towards looking at the benefits of students becoming better problem solvers and how teachers can implement problem solving into their daily lessons.

When this implementation is successful, students can become more independent with their learning, they are able to work and persevere through challenging problems, and they have a greater …

The Most Important Statistics In Football, Jacob Holmen

Essential Studies UNDergraduate Showcase

This research is based on the Five Factors that were devised by Bill Connelly of SBNation. The Five Factors of football include Explosiveness, Efficiency, Field Position, Finishing Drives, and Turnovers. Each factor is composed of associated statistics that when put together make up the most important statistics in football. This research includes the analysis of all 857 FBS (the highest level of NCAA Division I football) games from the 2016 season. Data was analyzed through the use of an Excel spreadsheet. Five different statistics were looked at, each associated with one of the Five Factors. The statistics include Yards per …

Analytics And Baseball's New Generation, John Roche

Essential Studies UNDergraduate Showcase

Major League Baseball has been a catalyst for making decisions in sports and competition from a purely mathematical viewpoint. We have seen teams utilize unique on-field player alignments and roster-building strategies based on statistical observations and applications of math. This project examines the advantages Sabermetrics and analytics present within the sport. Untapped statistical categories that could further the success of teams in the future is also briefly discussed.

Apex Calculus: Und Edition, Gregory Hartman, Department Of Mathematics, University Of North Dakota

Open Educational Resources

This text comprises a three–volume series on Calculus. The first part covers material taught in many “Calculus 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6. The second text covers material often taught in “Calculus 2”: integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 7 through 10. The third text covers topics common in “Calculus 3” or “Multivariable Calculus”: parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 11 through 15. All three are available separately for free. …

Mathematics, Woodrow Mcbride

UND Departmental Histories

This departmental history was written on the occasion of the UND Centennial in 1983.

Calculation Of Galois Groups, Daniel Schnackenberg

Theses and Dissertations

In the 19th Century Galois developed a method for determining whether an equation is solvable. It relied on the close relationship between fields and their automorphism group. This paper is a survey of the techniques of Galois theory. After presenting the main results of elementary Galois theory and some useful facts about factorization, I develop the important methods of calculating the Galois group and give a proof of the Chebotarev density theorem.