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. …

A Spiral Workbook For Discrete Mathematics 2nd Edition, Harris Kwong

Milne Open Textbooks

This updated text covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is …

Pappus Of Alexandria, Book Iii Of The Mathematical Collection, Pappus Of Alexandria, John B. Little

Holy Cross Bookshelf

John B. Little is the translator.

This is a translation of Book III of the Mathematical Collection by Pappus of Alexandria (ca. 290 - 350 CE) from the original Greek to English, following the edition of Friedrich Hultsch. While other books of the Mathematical Collection have been translated into English and short quotations from Book III have appeared in a number of places (see the Introduction), to my knowledge, no complete English translation of Book III has been published. Pappus was very influential as a sort of conduit between knowledge preserved from ancient Greek mathematics and European mathematicians in the …

El Desarrollo Del Pensamiento Matemático Básico Del Nivel Medio Superior Con Khan Academy, En El Centro De Estudios Tecnológicos Del Mar No. 19, Frontera, Tabasco [Presentación En Congreso], Cristo Leon, Daniel Méndez De La Cruz, Patricia Del Carmen Gerónimo Ramos, Josué Ojeda Montejo

STEM for Success Resources

Este estudio profundiza en la aplicación de la plataforma Khan Academy para mejorar el Pensamiento Matemático en estudiantes de primer semestre del CETMar No. 19 de Frontera, Tabasco, como respuesta a los desafiantes resultados en matemáticas del PLANEA Media Superior 2022. Analiza el rendimiento previo y actual, integra tecnologías educativas en la currícula, y evalúa el impacto de estas estrategias en el aprovechamiento académico, proporcionando un plan de acción replicable para instituciones de educación media superior enfrentadas a retos similares. Destacando términos clave como "Pensamiento Matemático", "Rendimiento Académico", "Khan Academy", y "Tecnologías de la Información en Educación",

Is Math Real? How Simple Questions Lead Us To Mathematics' Deepest Truths, Eugenia Cheng

Dalrymple Lecture Series

Where does math come from: from rules in a textbook? From logic and deduction? Not quite. In this talk Eugenia Cheng will argue that math comes from human curiosity - most importantly, from asking questions. Many people are discouraged from asking these questions in school, thinking they’re too simple to be taken seriously, or being told that their questions are stupid. But often, these simple-sounding questions lead to wondrous mathematical revelations. Dr Cheng will take us on a journey of discovery starting with questions like "Why does 2x3 = 3x2?" and "What's the point of maths?", leading us into research-level …

Pappus Of Alexandria, Book Viii Of The Mathematical Collection, Pappus Of Alexandria, John B. Little

Holy Cross Bookshelf

John B. Little is the translator.

This is a Greek-to-English translation of one section or chapter of a larger ancient Greek work called the Mathematical Collectionby Pappus of Alexandria (ca. 290 - 350 CE). Specifically, this is “Book VIII”' of that work. To date and to the translator’s knowledge, no complete English translation of Book VIII has been published.

Pappus was very influential as a bridge between the knowledge that had been preserved from ancient mathematics and European mathematicians in the Renaissance. This specific part of Pappus' work deals with applications of geometry to questions in mechanics.

The format …

Differential Calculus: From Practice To Theory, Eugene Boman, Robert Rogers

Milne Open Textbooks

Differential Calculus: From Practice to Theory covers all of the topics in a typical first course in differential calculus. Initially it focuses on using calculus as a problem solving tool (in conjunction with analytic geometry and trigonometry) by exploiting an informal understanding of differentials (infinitesimals). As much as possible large, interesting, and important historical problems (the motion of falling bodies and trajectories, the shape of hanging chains, the Witch of Agnesi) are used to develop key ideas. Only after skill with the computational tools of calculus has been developed is the question of rigor seriously broached. At that point, the …

Abstract Algebra: An Inquiry-Based Approach, Second Edition, Supplemental Material, Jonathan K. Hodge, Steven Schlicker, Ted Sundstrom

Open Textbooks

This text is a supplement to Abstract Algebra: An Inquiry-Based Approach, Second Edition. It includes applications of algebra to RSA encryption, check digits, the games of NIM and the 15 Puzzle, and the determination of groups of small order. In addition, reference material that could be useful for some students appears in the appendices, such as background material on functions, methods of proof (including the equivalencies of the Well-Ordering Principle and different versions of mathematical induction), and complex roots of unity. The appendices also contain a complete proof that polynomial rings are rings, a proof of the Fundamental Theorem of …

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. …

Area Activity, Admin Stem For Success

STEM for Success Showcase

Lesson plan to teach students about area including an activity plan, activity description, activity video, and additional activity materials

A Mode Sum Regularization Prescription In Quantum Field Theory In Curved Spacetimes In Higher Dimensions And For Charged Scalar Fields, Eoin Scanlon

Academic Posters Collection

Semi-classical gravity combines classical treatment of the gravitational field with quantum mechanical treatment of matter fields. A significant challenge however is the divergence contained within the stress-energy tensor when solving the semi-classical Einstein equations. This work extends to higher dimensions an extremely efficient method for renormalizing the stress-energy tensor of a quantum scalar field in spherically-symmetric black hole spacetimes, thereby removing the divergences. The method applies to a scalar field with arbitrary field parameters. The utility of the method is demonstrated by computing the renormalized stress-energy tensor for a scalar field in the Schwarzschild black hole spacetime for odd dimensions.

Symbolic Logic, Tony Roy

Books

Textbook for symbolic logic, beginning at a level appropriate for beginning students, continuing through Godel's completeness and incompleteness theorems. The text naturally divides into two volumes, the first for reasoning in logic, the second for reasoning about it.

The first volume includes parts I and II of the text. Part I introduces the complete classical predicate calculus with equality, including both axiomatic and natural derivation systems. Part II transitions to methods for reasoning about logic, including direct reasoning from definitions and mathematical induction.

The second volume includes parts III and IV of the text. Part III develops basic results in …

Calculus I Companion, Beth Campbell Hetrick, Kimberly R. Spayd

Open Educational Resources

A course pack for supplementing Calculus 1 with algebra, geometry, trigonometry, and precalculus topics, including reading material, activities, and practice problems assembled from various OER texts.

Conceptual Mathematics In Society, Ricela Feliciano-Semidei

Books, Book Chapters, & Supplemental Materials

This textbook is a compilation of chapters with educational purposes for the course MATH 103 in Spring 2023. The first part (Chapters 1 and 2) includes logic and critical thinking. Understanding the thinking process and strategies for solving problems in an effective way will provide students with skills that will be required to succeed in all college math courses. The second part (Chapters 3 & 4) is an opportunity to develop numbers sense through strengthening conceptual understanding of fractions and algebraic thinking. This will help develop foundational mathematical knowledge for college mathematics courses. The third and fourth parts of this …

The Magic Ratio Of Circles, Admin Stem For Success

STEM for Success Showcase

The ratio of a circle's circumference to diameter

• What pi is

Use logic to sense that the diameter and circumference of a circle will always be related

Arithmetic And Geometric Series, Admin Stem For Success

STEM for Success Showcase

Math:

-Introducing the concept of arithmetic and geometric series/discussing the differences

-Multiplying, adding, dividing, subtracting, exponents

Math And The Moon Activity Plan, Admin Stem For Success

STEM for Success Showcase

No abstract provided.

Platonic Solids Activity Plan, Admin Stem For Success

STEM for Success Showcase

No abstract provided.

Basic Math Terms And Properties, Admin Stem For Success

STEM for Success Showcase

Basic Math Terms

In a math equation or sentence, the operator identifies the action taken. The equal sign shows the relationship that the expressions on the two sides are equal in value.

Feedback, Learning Outcomes And Mathematics Anxiety In A Digital Game Based Learning Approach In Mathematics Education, André Almo

Academic Posters Collection

Feedback is a crucial part of learning, and an essential element in digital game-based learning approaches, in which digital games - known as 'serious games' - are used to deliver educational content. Feedback features respond to players' actions within the game, providing them with information and guidance, as well as potentially impacting their learning, motivation and engagement. However, these features may be designed differently, since they include various distinct characteristics and dimensions. This work proposes a new taxonomy for feedback features in serious games, with an emphasis in game design aspects, in order to provide clearer descriptions and distinctions of …

Hart, Robert W., Papers, 1924-1966, Special Collections, Leonard H. Axe Library

Finding Aids

Personal documents, correspondence, and financial records of Robert W. Hart, former professor at Pittsburg State University.

Robert William Hart was born in 1896 to William and Sarah Hart and grew up in Crawford County, Kansas. In 1916 he graduated from the State Manual Training Normal School (now Pittsburg State University), and found early work as an engineer. Robert served as an ensign in the navy during World War I. He taught in the public schools in Fort Scott and Pittsburg from 1916-1918; 1921-1923. In 1920 he married Retta Statler and they had two children. In 1923 he was hired as …

Strong Homotopy Lie Algebras And Hypergraphs, Samuel J. Bevins, Marco Aldi

Undergraduate Research Posters

We study hypergraphs by attaching a nilpotent strong homotopy Lie algebra. We especially focus on hypergraph theoretic information that is encoded in the cohomology of the resulting strong homotopy Lie algebra.

Ambientes De Inclusión Para El Desarrollo Del Pensamiento Numérico Con Población Con Síndrome De Down, Luisa Valeria Escobar Buitrago, Ingry Yuliana Torres Garzón, Juan David Firigua Bejarano

Educación

La importancia de tratar sobre una educación inclusiva es hacer que la humanidad obtenga la aceptación hacia la diversidad, donde se encuentre un mundo lleno de posibilidades reconociendo todos los tipos de población entre ella las personas con Síndrome de Down, lo cual consiste en que la educación esté centrado en el respeto y la valoración de la diversidad, haciendo un enfoque general en las necesidades que esta población tiene, desarrollando habilidades para su desenvolvimiento tanto personal como laboral en determinada sociedad, por lo tanto el objetivo principal de este trabajo es desarrollar el pensamiento numérico de los estudiantes de …

Math 57: Applied Differential Equations I, John Mayberry

Pacific Open Texts

This book is designed for the fourth semester, “capstone” course in a calculus sequence with an emphasis on modeling with linear differential equations. Students will learn to translate verbal descriptions of physical problems into differential equation models, solve and visualize solutions to differential equations using MATLAB, calculate and investigate the behavior of analytic solutions to linear differential equations, discuss how solutions to differential equations depend on parameters, and interpret solutions to differential equations in the context of applications.

Compilación De Procesos Investigativos En Educación Matemática, Martha Lidia Barreto Moreno, Yeferson Castellanos Novoa, María Alejandra Mayorga Henao, Diana Marcela Contento Sarmiento, Jesús Antonio Villarraga Palomino, Andrés Alberto Gutiérrez Morales, Juan David Firigua Bejarano, Yineth Marleidy Parra Ubaque, Lady Johanna Silva Marín

Educación

En el libro Compilación de procesos de investigación en educación matemática, consta de cuatro capítulos donde se presentan los procesos desarrollados en el marco de proyectos de investigación a nivel de pregrado y postgrado en Educación.

El primer capítulo consiste en la sistematización de la acción docente desarrollada en el marco de los Talleres Itinerantes de Alfabetización Computacional en la provincia de Sumapaz, propuesta de innovación para implementar procesos didácticos que contribuyan al desarrollo del pensamiento matemático computacional en educación básica primaria rural.

El segundo capítulo contiene el proceso investigativo que dio continuidad al trabajo realizado en la Fase1, sobre …

College Algebra Slide Decks, Bader Abukhodair, Michelle Zeng

All Open Educational Resources

This collection of slide decks is designed to be used in concert with the following Open Eduational Resources:

- OpenStax College Algebra 2e Open Texbook

- Department of Mathematics Video Playlist

- Homework questions from myOpenMath

Concepts include are: A study of equations, graphs, and inequalities for linear, quadratic, polynomial, rational, logarithmic, exponential, and absolute value functions. Transformations on graphs, complex numbers, circles, systems of inequalities, and systems of equations including matrices.

Introduction To Mathematical Analysis I - 3rd Edition, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen

PDXOpen: Open Educational Resources

Video lectures explaining problem solving strategies are available

Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. In addition, the notes include many carefully selected exercises of various levels …

The Art Of Analysis, Christopher Hammond

Open Educational Resources

Christopher Hammond, Professor of Mathematics at Connecticut College, has written an introductory textbook in real analysis. This resource is freely available for anyone to use, either individually or in a classroom setting.

The primary innovation of this text is a new perspective on teaching the theory of integration. Most introductory analysis courses focus initially on the Riemann integral, with other definitions discussed later (if at all). The paradigm being proposed is that the Riemann integral and the “generalized Riemann integral” should be considered simultaneously, not separately – in the same manner as uniform continuity and continuity. Riemann integrability is simply …

Mathematics For Biomedical Physics, Jogindra M. Wadehra

Open Textbooks

Mathematics for Biomedical Physics is an open access peer-reviewed textbook geared to introduce several mathematical topics at the rudimentary level so that students can appreciate the applications of mathematics to the interdisciplinary field of biomedical physics. Most of the topics are presented in their simplest but rigorous form so that students can easily understand the advanced form of these topics when the need arises. Several end-of-chapter problems and chapter examples relate the applications of mathematics to biomedical physics. After mastering the topics of this book, students would be ready to embark on quantitative thinking in various topics of biology and …

Propuestas Y Resultados De Investigación Transmoderna, Translocal Y Digital Desde Jóvenes Semilleristas, Xiomara Gonzalez Gaitan

Institucional

En el presente libro intitulado Propuestas y resultados de investigación transmoderna, translocal y digital desde jóvenes semilleristas, se encuentran compilados las propuestas, avances y resultados de los proyectos en curso de los Semilleros de Investigación de la Universidad de Cundinamarca, Colombia, que se presentaron en el “II encuentro de semilleros de investigación: ciencia, tecnología e innovación en la era digital” en su versión 2020. Hacemos la labor de publicar estos proyectos con la intensión de difundir el conocimiento y como muestra del esfuerzo y alcance de la labor investigativa de los semilleristas de la Universidad de Cundinamarca. Esperamos que lo …