Digital library
Textbooks, references and open learning resources.
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Elementary Abstract Algebra: Examples and Applications
Justin Hill; Chris Thron · Justin Hill and Chris Thron · 2019
This book is not intended for budding mathematicians. It was created for a math program in which most of the students in upper-level math classes are planning to become secondary school teachers. For such students, conventional abstract algebra texts are practically incomprehensible, both in style and in content. Faced with this situation, we decided to create a book that our students could actually read for themselves. In this way we have been able to dedicate class time to problem-solving and personal interaction rather than rehashing the same material in lecture format.
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Precalculus
David Collingwood; K. Prince; Matthew Conroy · A.T. Still University · 2016
Prior to 1990, the performance of a student in precalculus at the University of Washington was not a predictor of success in calculus. For this reason, the mathematics department set out to create a new course with a specific set of goals in mind: A review of the essential mathematics needed to succeed in calculus. An emphasis on problem solving, the idea being to gain both experience and confidence in working with a particular set of mathematical tools. This text was created to achieve these goals and the 2004-05 academic year marks the eleventh year in which it has been used. Several thousand students have successfully passed through the course. This book is full of worked out examples. We use the the notation “Soluion.” to indicate where the reasoning for a problem begins; the symbol ?? is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you find a topic treated earlier in the course. It is also a good rough outline when it comes time to study for the final examination. The book also includes an index at the end. Finally, there is an appendix at the end of the text with ”answers” to most of the problems in the text. It should be emphasized these are ”answers” as opposed to ”solutions”. Any homework problems you may be asked to turn in will require you include all your work; in other words, a detailed solution. Simply writing down the answer from the back of the text would never be sufficient; the answers are intended to be a guide to help insure you are on the right track.
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Multivariable Calculus
Don Shimamoto · Don Shimamoto · 2019
This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and finally the general case of vector-valued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required.
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APEX PreCalculus
Amy Chapman; Meagan Herald; Jessica Libertini · APEX Calculus · 2017
This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.
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College Algebra & Trigonometry
Richard Beveridge · Richard W. Beveridge · 2018
This College Algebra text will cover a combination of classical algebra and analytic geometry, with an introduction to the transcendental exponential and logarithmic functions. If mathematics is the language of science, then algebra is the grammar of that language. Like grammar, algebra provides a structure to mathematical notation, in addition to its uses in problem solving and its ability to change the appearance of an expression without changing the value.
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Statistical Thinking for the 21st Century
Russell Poldrack · Russell Poldrack · 2018
Statistical thinking is a way of understanding a complex world by describing it in relatively simple terms that nonetheless capture essential aspects of its structure, and that also provide us some idea of how uncertain we are about our knowledge. The foundations of statistical thinking come primarily from mathematics and statistics, but also from computer science, psychology, and other fields of study.
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You're Smarter Than You Think: Statistics
Safaa Dabagh · Safaa Dabagh · 2026
You're Smarter Than You Think: Statistics is a free, openly licensed introduction to statistics written for community college students and designed from the ground up for neurodivergent and anxious learners. Every section follows the same six-step rhythm (Read This First, Let's Talk About It, Now We Name It, Watch It Work, Your Turn, Check Your Voice), and every chapter opens with a Math Skills warm-up so a missing arithmetic step never derails a big idea. The book is organized around the student learning outcomes shared by community college statistics courses: describing data, estimating with confidence, and testing claims. It covers data and sampling, graphs, center and spread, probability, distributions, the Central Limit Theorem, confidence intervals, hypothesis testing, two-sample tests, ANOVA, chi-square, and regression. Four free Technology Companions (R and RStudio, jamovi, StatCrunch, and the TI-84) carry every method into whatever software a course uses, each keyed chapter by chapter and packaged with ready-made datasets. Graphs, printable work space, answer keys, per-part formula sheets, and a cumulative final-exam prep are included throughout.
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Python for Introductory Statistics
Simon Aman · City Colleges of Chicago · 2021
The purpose of this material is to provide an overview of the free programming language, Python, and a few of its software libraries that are most useful for improving Introductory Statistics students' learning and for providing an alternative statistical software package for those who perform statistical data analysis and plotting. This material, along with the companion workbook and a free web-based Python platform, could easily replace the use of other software packages and calculators in an Introductory Statistics course. Part I, Sections 1 to 4, covers the basics of the Python programming language. Part II, Sections 5 to 13, focuses on Python for introductory statistics, and Part III, Section 14, covers selected advanced statistics topics in Python. Additionally, there are demo video links accompanying key steps for further instruction. No prior programming knowledge is required or assumed.
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Representation Theory
Jan Grabowski · Open Book Publishers · 2025
This volume offers a fresh and modern introduction to one of abstract algebra’s key topics. Guiding readers through the transition between structure theory and representation theory, this textbook explores how algebraic objects like groups and rings act as symmetries of other structures. Using the accessible yet powerful language of category theory, the book reimagines standard approaches to topics such as modules and algebras in a way that unlocks modern treatments of more advanced topics such as quiver representations and even representations of Hopf algebras and categories. Aimed at undergraduate students with prior exposure to linear algebra and basic group theory, the book introduces categories early and uses them throughout, providing a cohesive framework that mirrors current mathematical research. Though technically sophisticated, it also includes examples and exercises designed to develop intuition and understanding. Grabowski’s inclusion of computational tools such as SageMath offers a valuable and traditionally underdeveloped bridge between abstract theory and hands-on exploration. This is a uniquely valuable guide for students ready to stretch their understanding of the subject’s conceptual depth and evolving frontiers.
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Integral Calculus with Applications to Life Sciences
Paul Tsopméné · University of British Columbia Library · 2025
Integral Calculus with Applications to Life Sciences is an open educational resource (OER) that covers an unusually broad range of topics—including integration, infinite series, differential equations, linear algebra, probability, and statistics—rarely found in a single textbook. Each section begins with clear learning outcomes and a motivational paragraph, often tied to applications in the life sciences, helping students see the immediate relevance of what they learn. Examples are worked out in full detail. Every time a calculus or algebraic rule is applied, it is explicitly stated at the point of use. Rather than isolating algebra review in a preliminary chapter, this text integrates algebra throughout, allowing students to reinforce foundational skills while learning new material. This approach is especially supportive for students who may struggle with algebra. Practice problems with complete solutions follow each example, and most sections end with an application to biology, medicine, or related fields. The exercise sections include not only standard questions but also critical thinking problems such as finding errors in worked solutions, constructing counterexamples, and solving real-world problems. The text includes final answers for all exercises at the back. Hyperlinks allow students to jump seamlessly between exercises and final answers. By combining clarity, rigor, accessibility, and real-world relevance, one of the main goals of this OER is to help students not only to succeed in calculus but also to appreciate its power in understanding the living world.
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A Contemporary Approach to Research and Statistics in Psychology
Klaire Somoray · Council of Australian University Librarians · 2023
This book is designed as a short and introductory resource specifically aimed to help students grasp key concepts typically found in undergraduate psychology statistics subjects. It was initially developed for online and intensive programs, which are becoming increasingly popular in psychology education. The book utilises jamovi, a free and open-source statistical software. This peer reviewed book is completely free to download, use, and adapt and it is released using the CC BY-NC 4.0 licence.
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Functions, Trigonometry, and Systems of Equations
Vanessa Coffelt · Texas A&M University · 2025
This is the second edition of a Precalculus textbook designed specifically for Math 150: Functions, Trigonometry, and Systems of Equations at Texas A&M University.
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Significant Statistics
John Russell · Virginia Tech Publishing · 2025
Significant Statistics: An Introduction to Statistics is intended for students enrolled in a one-semester introduction to statistics course who are not mathematics or engineering majors. It focuses on the interpretation of statistical results, especially in real world settings, and assumes that students have an understanding of intermediate algebra. In addition to end of section practice and homework sets, examples of each topic are explained step-by-step throughout the text and followed by a 'Your Turn' problem that is designed as extra practice for students. Significant Statistics: An Introduction to Statistics was adapted from content published by OpenStax including Introductory Statistics, OpenIntro Statistics, and Introductory Statistics for the Life and Biomedical Sciences. John Morgan Russell reorganized the existing content and added new content where necessary. Instructors reviewing, adopting, or adapting this textbook: please help us understand your use by filling out this form: https://bit.ly/stat-interest.
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Statistics with JASP: First Steps for Psychology Students
Rebecca Denniss; Stanislava Naneva · University of Sheffield · 2025
New to statistics software? This guide is designed just for you. Whether you are studying psychology or any subject that involves analysing data, this easy-to-follow introduction to JASP will help you get to grips with the basics—no previous experience needed. Originally written for first-year psychology students at the University of Sheffield, it walks you through everything from entering data and adjusting settings to running t-tests, correlations, and chi-square analyses. With clear explanations, practical tips, and helpful screenshots, this guide makes learning JASP simple and stress-free.
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Quantitative Problem Solving in Natural Resources
Pete Moore · Iowa State University Digital Press · 2025
This book is a collection of resources focused on solving quantitative problems that non-mathematicians interested in biology and environmental sciences may find compelling. It is not intended as a guide to be followed through a series of skills, but rather as a resource to support the problem-solving process and help lower conceptual and computational barriers along the way.
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Learning Statistics with jamovi: A Tutorial for Beginners in Statistical Analysis
Danielle Navarro; David Foxcroft · Open Book Publishers · 2025
Based on Danielle Navarro’s widely acclaimed and prize-winning book Learning Statistics with R, this elegantly designed textbook offers undergraduate students a thorough and accessible introduction to jamovi, as well as how to get to grips with statistics and data manipulation. Lucid and easy to understand, Learning Statistics with jamovi covers the analysis of contingency tables, t-tests, correlation, regression, ANOVA and factor analysis, while also giving students a firm grounding in descriptive statistics and graphing. It includes learning aids for applying statistical principles using the jamovi interface, as well as embedded data files to accompany the book, and comprehensive chapters on probability theory, sampling and estimation, and null hypothesis testing. Freely available in open access, Learning Statistics with jamovi is an ideal introduction for undergraduate and postgraduate students of psychology, as well as behavioural and health science students and anyone who needs to understand and use statistical analysis in their work.
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Linear Algebra Done Right
Sheldon Axler · Springer · 2024
Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
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Geometry with an Introduction to Cosmic Topology
Michael Hitchman · Michael P. Hitchman · 2020
Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe. The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits. Geometry is suitable for a semester course in non-Euclidean geometry or as a guide to independent study, with over 200 exercises and several essays on topics including the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe.
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Basic Statistics Using R for Crime Analysis
Jaeyoung Choi · The Pennsylvania Alliance for Design of Open Textbooks (PA-ADOPT) · 2024
Limited access to subscription-based statistical software poses obstacles when students want to apply the skills they acquired in college. Although students may learn programs like SPSS or Stata while at the university, they often find themselves unable to continue using these programs after graduation, making their acquired skills obsolete. As an open-source software program, R offers a solution to this challenge. It is freely accessible to anyone, including students, after they graduate. Therefore, I decided to write a freely available book for those interested in becoming crime analysts, focusing on learning statistics without delving too deeply into mathematics. Moreover, this book emphasizes practical applications by utilizing R for data analysis, ensuring students can develop relevant skills beyond the university. I hope that students can easily follow the instructions in this book and replicate the same outcomes using the provided data. This practical experience will demonstrate the value of statistics and R, ideally inspiring students to further their learning in these areas.
![Statistics Through an Equity Lens [Revised Edition]](/api/files/covers/otl-1625.webp)
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Statistics Through an Equity Lens [Revised Edition]
Yvonne Anthony · ROTEL · 2023
This Open Educational Resource (OER) carries a significant responsibility by presenting statistics through an equity lens. The metaphor of a lens is used intentionally–as the glasses one wears can have a profound effect on what one sees. The book encourages further inspection of the ways in which data is collected, interpreted, and analyzed on a variety of social justice issues, such as health disparities, hunger and food insecurity, homelessness, behavioral health (mental health and substance use), and incarceration of males of color. It also attempts to reveal how the misuse of data can reinforce inequities, for example, by stigmatizing people and labeling neighborhoods as high poverty, violent, and having poor educational opportunities. Whether an intended or unintended consequence, irresponsible data use can contribute to racist impressions of people and communities.