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Counting Rocks! An Introduction to Combinatorics

Contributors: Adams, Emmrich, Gillespie, Golden, and Pries

Publisher: Henry Adams, Rachel Pries, and Maria Gillespie

License: CC BY

This textbook, Counting Rocks!, is the written component of an interactive introduction to combinatorics at the undergradaute level. Throughout the text, we link to videos where we describe the material and provide examples; see the Youtube playlist on the Colorado State University (CSU) Mathematics YouTube channel.

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Un Análisis Científico del Ruido Ambiental y Laboral en Sectores Urbanos

Contributors: Astudillo-Martínez, Andrade-Bravo, García-Valdez, and Almenaba-Guerrero

Publisher: Editorial Grupo AEA

License: CC BY-NC-SA

¿Cuál es el nivel de ruido existente Av. Av. 3 de Julio y sus intersecciones entre la calle Ambato y la Y del Indio Colorado de la ciudad de Santo Domingo?, el presente trabajo de investigación tiene como objetivo principal conocer el nivel de ruido existente en este sector de la ciudad, con el fin de determinar el alcance de su afectación y sobre todo sus fuentes, se realizó la evaluación correspondiente de acuerdo con la normativa TULSMA. y Decreto Ejecutivo N° 2393, aplicando la investigación de campo se midió la presencia de ruido ambiental y ocupacional, se requirió del uso de dosímetros calibrados y certificados para obtener información precisa. En esta investigación se estudió estas importantes intersecciones, siendo que, en cuanto a normativa ambiental sobrepasa el nivel tolerable con un diferencial de 10 decibeles en promedio, mientras que en referencia del ruido laboral esta intersección está por debajo de los niveles permisibles con al menos 9 decibeles en promedio, las posibles enfermedades subyacentes más comunes encontradas fueron el estrés, los dolores de cabeza que afectaban principalmente a la población comerciante permanente, y la actividad que mayor emisión de ruido produjo fue el tránsito vehicular, del mismo modo se identificó que el día que se produjo mayor contaminación acústica fue el sábado entre las 11:30 am hasta la 13:00 pm.

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Introduction to Probability

Contributor: Baxter

Publisher: John R. Baxter

License: CC BY-SA

This is an introduction to probability theory, designed for self-study. It covers the same topics as the one-semester introductory courses which I taught at the University of Minnesota, with some extra discussion for reading on your own. The reasons which underlie the rules of probability are emphasized. Probability theory is certainly useful. But how does it feel to study it? Well, like other areas of mathematics, probability theory contains elegant concepts, and it gives you a chance to exercise your ingenuity, which is often fun. But in addition, randomness and probability are part of our experience in the real world, present everywhere and yet still somewhat mysterious. This gives the subject of probability a special interest.

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Polimetrics: A Stata Companion to Introduction to Political Science Research Methods - 1st Edition

Contributor: Franco

Publisher: Open Political Science (OPoliSci)

License: CC BY-NC

Polimetrics: A Stata Companion, authored by Dr. Josh Franco, is an Open Education Resource workbook licensed CC BY-NC and designed as a Stata companion to Introduction to Political Science Research Methods.

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Classical Numerical Methods in Scientific Computing

Contributors: van Kan, Segal, and Vermolen

Publisher: TU Delft Open

License: CC BY

Partial differential equations are paramount in mathematical modelling with applications in engineering and science. The book starts with a crash course on partial differential equations in order to familiarize the reader with fundamental properties such as existence, uniqueness and possibly existing maximum principles. The main topic of the book entails the description of classical numerical methods that are used to approximate the solution of partial differential equations. The focus is on discretization methods such as the finite difference, finite volume and finite element method. The manuscript also makes a short excursion to the solution of large sets of (non)linear algebraic equations that result after application of discretization method to partial differential equations. The book treats the construction of such discretization methods, as well as some error analysis, where it is noted that the error analysis for the finite element method is merely descriptive, rather than rigorous from a mathematical point of view. The last chapters focus on time integration issues for classical time-dependent partial differential equations. After reading the book, the reader should be able to derive finite element methods, to implement the methods and to judge whether the obtained approximations are consistent with the solution to the partial differential equations. The reader will also obtain these skills for the other classical discretization methods. Acquiring such fundamental knowledge will allow the reader to continue studying more advanced methods like meshfree methods, discontinuous Galerkin methods and spectral methods for the approximation of solutions to partial differential equations.

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Numerical Methods in Scientific Computing

Contributors: van Kan, Segal, and Vermolen

Publisher: TU Delft Open

License: CC BY

This is a book about numerically solving partial differential equations occurring in technical and physical contexts and the authors have set themselves a more ambitious target than to just talk about the numerics. Their aim is to show the place of numerical solutions in the general modeling process and this must inevitably lead to considerations about modeling itself. Partial differential equations usually are a consequence of applying first principles to a technical or physical problem at hand. That means, that most of the time the physics also have to be taken into account especially for validation of the numerical solution obtained. This book aims especially at engineers and scientists who have ’real world’ problems. It will concern itself less with pesky mathematical detail. For the interested reader though, we have included sections on mathematical theory to provide the necessary mathematical background. Since this treatment had to be on the superficial side we have provided further reference to the literature where necessary.

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Linear Transformations on Vector Spaces

Contributors: Kaschner and Russell

Publisher: PALNI

License: CC BY

Linear Transformations on Vector Spaces serves primarily as a textbook for undergraduate Linear Algebra courses. While standard Linear Algebra books begin by focusing on solving systems of linear equations and associated procedural skills, our book begins by developing a conceptual framework for the topic using the central objects, vector spaces and linear transformations. It covers the same concepts, skills, and, applications as conventional texts in a one-semester course, but students walk away with a much richer and more useful mastery of the topics. The book is structured to facilitate the implementation of the flipped classroom. The text features a continuous narrative to illuminate the big picture of the material and is written to help students develop their textbook reading skills. Also, there are “Explorations” scattered throughout each section; these are quick first examples intended for students to complete while reading before class meetings. Additional materials include section overview homework assignments and worksheets that can be used for in-class practice.

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Introducing Mathematical Biology

Contributor: Best

Publisher: The University of Sheffield

License: CC BY

Mathematical modelling plays an increasingly important role in almost any area of life sciences, and this interactive textbook focuses on the areas of population ecology, infectious diseases, immunology and cell dynamics, gene networks and pharmacokinetics. It is aimed at anyone who is interested in learning about how to model biological systems, including undergraduate and postgraduate mathematics students who have not studied mathematical biology before, life-sciences students with an interest in modelling, and post-16 mathematics students interested in university-level material. Some mathematical knowledge is assumed, and the mathematical models used are all in the form of ordinary differential equations.

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Understanding How Geometry Works - First Edition

Contributor: Johnston

Publisher: MERLOT

License: CC BY-NC-SA

Understanding How Geometry Works, a conceptual overview for educators is designed for students who are prospective elementary and middle school level teachers.

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Foundations of Biomedical Science: Quantitative Literacy: Theory and Problems

Contributor: Pakay

Publisher: La Trobe eBureau

License: CC BY-NC-SA

Foundations of Biomedical Science: Quantitative Literacy Theory and Problems is designed to help students develop the fundamental mathematical and quantitative literacy required to navigate and interpret evidence-based Biomedical data. This will provide students with the skills and confidence to habitually question any quantitative data they come across and to use these skills to make informed judgements regarding their veracity.

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