Digital library
Textbooks, references and open learning resources.
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Statistics for Ecologists: A Frequentist and Bayesian Treatment of Modern Regression Models
John Fieberg · University of Minnesota Libraries Publishing · 2024
Ecological data pose many challenges to statistical inference. Most data come from observational studies rather than designed experiments; observational units are frequently sampled repeatedly over time, resulting in multiple, non-independent measurements; response data are often binary (e.g., presence-absence data) or non-negative integers (e.g., counts), and therefore, the data do not fit the standard assumptions of linear regression (Normality, independence, and constant variance). This book will familiarize readers with modern statistical methods that address these complexities using both frequentist and Bayesian frameworks.
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Counting Rocks! An Introduction to Combinatorics
Henry Adams; Kelly Emmrich; Maria Gillespie; Shannon Golden · Henry Adams, Rachel Pries, and Maria Gillespie · 2023
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. The major topics in this text are counting problems (Chapters 1-4), proof techniques (Chapter 5), recurrence relations and generating functions (Chapters 6-7), and graph theory (Chapters 8-12). The material and the problems we include are standard for an undergraduate combinatorics course. In this text, one of our goals was to describe the mathematical structures underlying problems in combinatorics. For example, we separate the description of sequences, permutations, sets and multisets in Chapter 3. In addition to the videos, we would like to highlight some other features of this book. Most chapters contain an investigation section, where students are led through a series of deeper problems on a topic. In several sections, we show students how to use the free online computing software SAGE in order to solve problems; this is especially useful for the problems on recurrence relations. We have included many helpful figures throughout the text, and we end each chapter (and many of the sections) with a list of exercises of varying difficulty.
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Linear Transformations on Vector Spaces
Scott Kaschner; Amber Russell · PALNI · 2023
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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Introduction to Probability
John Baxter · John R. Baxter · 2026
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
Josh Franco · Open Political Science (OPoliSci) · 2021
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. This workbook provides a tour of the Stata software, an introduction to cross-sectional, time series, and panel data, and an introduction to a variety of models. I review models where the outcome is linear, binary, ordinal, categorical, and count. Additionally, I have an interpretation chapter on survival models. Each “Models” chapter has a similar organizational structure: about, estimated time, what is the model, how are models run in Stata, how do we interpret the model results, and a real-world example of model results in a Creative Commons licensed, peer-reviewed journal article. Additionally, mini-assignment instructions and a rubric are included so students can practice their interpretation skills.
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Classical Numerical Methods in Scientific Computing
Jos van Kan; Guus Segal; Fred Vermolen; Hans Kraaijevanger · TU Delft Open · 2023
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
Jos van Kan; Guus Segal; Fred Vermolen · TU Delft Open · 2023
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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Foundations of Biomedical Science: Quantitative Literacy: Theory and Problems
Julian Pakay · La Trobe University · 2023
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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An Intuitive, Interactive, Introduction to Biostatistics
Caitlin Ward; Collin Nolte · University of Iowa · 2023
"An Intuitive, Interactive Introduction to Biostatistics" is an introductory statistics textbook oriented towards towards undergraduate students in the health sciences. While covering the breadth of material typically presented in a first semester statistics course, including introductions to probability and distributions, study design, CLT, hypothesis testing, and inference, IIIB distinguishes itself with its focus on cultivating student intuition through the use of guided questions and interactive simulation-based applets. Written in R, this open-source text has been created with customizability in mind, offering instructors maximal flexibility in arranging and modifying the content.
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Introduction to Arithmetic Groups
Dave Morris · Deductive Press · 2015
Introduction to Arithmetic Groups
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Numerical Methods for Ordinary Differential Equations
Kees Vuik; Fred Vermolen; Martin van Gijzen · TU Delft Open · 2023
In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize the aspects that play an important role in practical problems. We confine ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation. The techniques discussed in the intro-ductory chapters, for instance interpolation, numerical quadrature and the solution to nonlinear equations, may also be used outside the context of differential equations. They have been in-cluded to make the book self-contained as far as the numerical aspects are concerned. Chapters, sections and exercises marked with a * are not part of the Delft Institutional Package. The numerical examples in this book were implemented in Matlab, but also Python or any other programming language could be used. A list of references to background knowledge and related literature can be found at the end of this book. Extra information about this course can be found at http://NMODE.ewi.tudelft.nl, among which old exams, answers to the exercises, and a link to an online education platform. We thank Matthias Moller for his thorough reading of the draft of this book and his helpful suggestions.
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COMPUTATIONAL PHYSICS: A Practical Introduction to Computational Physics and Scientific Computing (using C++)
Konstantinosn Anagnostopoulos · National Technical University of Athens · 2016
This book is an introduction to the computational methods used in physics, but also in other scientific fields. It is addressed to an audience that has already been exposed to the introductory level of college physics, usually taught during the first two years of an undergraduate program in science and engineering. It assumes no prior knowledge of numerical analysis, programming or computers and teaches whatever is necessary for the solution of the problems addressed in the text. It can be used as a textbook in introductory computational physics or scientific computing classes. The book starts with very simple problems in particle motion and ends with an in-depth discussion of advanced techniques used in Monte Carlo simulations in statistical mechanics. The level of instruction rises slowly, while discussing problems like the diffusion equation, electrostatics on the plane, quantum mechanics and random walks. All the material can be taught in two semesters, but a selection of topics can form the material of a one semester course. The book aims to provide the students with the background and the experience needed in order to advance to high performance computing projects in science and engineering. It puts emphasis on hands--on programming of numerical code but also on the production, analysis and interpretation of data. But it also tries to keep the students motivated by considering interesting applications in physics, like chaos, quantum mechanics, special relativity and the physics of phase transitions. There is a C++ and a Fortran edition for the core programming. Data analysis is performed using the powerful tools of the GNU/Linux environment. All the necessary software is open source and freely available. The book and the accompanying software are given under a Creative Commons License/GNU public License as a service to the community. It can be used freely as a whole, or any part of it, in any form, by anyone. There is no official distribution of hard copies, b
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Calculus in Context
James Callahan; David Cox; Kenneth Hoffman · Smith College Open Educational Resources: Textbooks · 1994
Designing the curriculum We believe that calculus can be for students what it was for Euler and the Bernoullis: a language and a tool for exploring the whole fabric of science. We also believe that much of the mathematical depth and vitality of calculus lies in connections to other sciences. The mathematical questions that arise are compelling in part because the answers matter to other disciplines. We began our work with a "clean slate," not by asking what parts of the traditional course to include or discard. Our starting points are thus our summary of what calculus is really about. Our curricular goals are what we aim to convey about the subject in the course. Our functional goals describe the attitudes and behaviors we hope our students will adopt in using calculus to approach scientific and mathematical questions. Starting Points Calculus is fundamentally a way of dealing with functional relationships that occur in scientific and mathematical contexts. The techniques of calculus must be subordinate to an overall view of the questions that give rise to these relationships. Technology radically enlarges the range of questions we can explore and the ways we can answer them. Computers and graphing calculators are much more than tools for teaching the traditional calculus. The concept of a dynamical system is central to science. Therefore, differential equations belong at the center of calculus, and technology makes this possible at the introductory level. The process of successive approximation is a key tool of calculus, even when the outcome of the process--the limit--cannot be explicitly given in closed form. Curricular Goals Develop calculus in the context of scientific and mathematical questions. Treat systems of differential equations as fundamental objects of study. Construct and analyze mathematical models. Use the method of successive approximations to define and solve problems. Develop geometric visualization with hand-drawn and computer graphics. Give num
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The Art of Polynomial Interpolation
Stuart Murphy · Pennsylvania State University
The inspiration for this text grew out of a simple question that emerged over a number of years of teaching math to Middle School, High School and College students. Practically speaking, what is the origin of a particular polynomial? So much time is spent analyzing, factoring, simplifying and graphing polynomials that it is easy to lose sight of the fact that polynomials have a wealth of practical uses. Exploring the techniques of interpolating data allows us to view the development and birth of a polynomial. This text is focused on laying a foundation for understanding and applying several common forms of polynomial interpolation. The principal goals of the text are: Breakdown the process of developing polynomials to demonstrate and give the student a feel for the process and meaning of developing estimates of the trend (s) a collection of data may represent. Introduce basic matrix algebra to assist students with understanding the process without getting bogged down in purely manual calculations. Some manual calculations have been included, however, to assist with understanding the concept. Assist students in building a basic foundation allowing them to add additional techniques, of which there are many, not covered in this text.
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Advanced Algebra
John Redden · 2012
Intermediate Algebra is the second part of a two-part course in Algebra. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study of applications found in most disciplines. Used as a standalone textbook, it offers plenty of review as well as something new to engage the student in each chapter. Written as a blend of the traditional and graphical approaches to the subject, this textbook introduces functions early and stresses the geometry behind the algebra. While CAS independent, a standard scientific calculator will be required and further research using technology is encouraged. Intermediate Algebra clearly lays out the steps required to build the skills needed to solve a variety of equations and interpret the results. With robust and diverse exercise sets, students have the opportunity to solve plenty of practice problems. In addition to embedded video examples and other online learning resources, the importance of practice with pencil and paper is stressed. This text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. In addition, Intermediate Algebra was written from the ground up in an open and modular format, allowing the instructor to modify it and leverage their individual expertise as a means to maximize the student experience and success. The importance of Algebra cannot be overstated; it is the basis for all mathematical modeling used in all disciplines. After completing a course sequence based on Elementary and Intermediate Algebra, students will be on firm footing for success in higher-level studies at the college level.
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Basic Algebra with Applications
Ivan Zaigralin · Ivan G. Zaigralin · 2018
Basic Algebra with Applications
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Statistics for Research Students
Erich Fein; John Gilmour; Tayna Machin; Liam Hendry · University of Southern Queensland · 2022
This book aims to help you understand and navigate statistical concepts and the main types of statistical analyses essential for research students.
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Introduction to Applied Statistics for Psychology Students
Gordon Sarty · University of Saskatchewan · 2022
Introduction to Applied Statistics for Psychology Students, by Gordon E. Sarty (Professor, Department of Psychology, University of Saskatchewan) began as a textbook published in PDF format, in various editions between 2014-2017. The book was written to meet the needs of University of Saskatchewan psychology students at the undergraduate (PSY 233, PSY 234) level. In 2019-2020, funding was provided through the Gwenna Moss Centre for Teaching and Learning, along with technical assistance from the Distance Education Unit, to update and adapt this book, making it more widely available in an easy-to-use and more adaptable digital (Pressbooks) format. The update also made revisions so that the book could be published with a license appropriate for open educational resources (OER). OERs are defined as “teaching, learning, and research resources that reside in the public domain or have been released under an intellectual property license that permits their free use and re-purposing by others” (Hewlett Foundation). This textbook and other OERs like it are openly licensed using a Creative Commons license, and are offered in various digital and e-book formats free of charge. Printed editions of this book can be obtained for a nominal fee through the University of Saskatchewan bookstore.
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Intermediate Algebra
Katherine Yoshiwara · Bruce Yoshiwara · 2020
Intermediate Algebra is a textbook for students who have some acquaintance with the basic notions of variables and equations, negative numbers, and graphs, although we provide a "Toolkit" to help the reader refresh any skills that may have gotten a little rusty. In this book we journey farther into the subject, to explore a greater variety of topics including graphs and modeling, curve-fitting, variation, exponentials and logarithms, and the conic sections. We use technology to handle data and give some instructions for using a graphing calculator, but these can easily be adapted to any other graphing utility.
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Elementary Algebra
Katherine Yoshiwara · Bruce Yoshiwara · 2019
This text introduces the basic skills and ideas of algebra.