Digital library
Textbooks, references and open learning resources.
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Basic Analysis: Introduction to Real Analysis
Jirí Lebl · Jirí Lebl · 2016
This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.
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Calculus for the Life Sciences: A Modeling Approach
James Cornette; Ralph Ackerman · A.T. Still University · 2011
Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course. In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.
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Vector Calculus
Michael Corral · Michael Corral · 2013
This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals. The book also includes discussion of numerical methods: Newton's method for optimization, and the Monte Carlo method for evaluating multiple integrals. There is a section dealing with applications to probability. Appendices include a proof of the right-hand rule for the cross product, and a short tutorial on using Gnuplot for graphing functions of 2 variables There are 420 exercises in the book. Answers to selected exercises are included.
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OpenIntro Statistics
David Diez; Christopher Barr; Mine Cetinkaya-Rundel · OpenIntro · 2019
OpenIntro Statistics covers a first course in statistics, providing a rigorous introduction to appliedstatistics that is clear, concise, and accessible. This book was written with the undergraduate levelin mind, but it’s also popular in high schools and graduate courses.We hope readers will take away three ideas from this book in addition to forming a foundationof statistical thinking and methods. • Statistics is an applied field with a wide range of practical applications.• You don’t have to be a math guru to learn from real, interesting data.• Data are messy, and statistical tools are imperfect. But, when you understand the strengthsand weaknesses of these tools, you can use them to learn about the world.
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Precalculus
Carl Stitz; Jeff Zeager · Stitz Zeager Open Source Mathematics · 2013
A casual glance through the Table of Contents of most of the major publishers' College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled “Functions First.” To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic “equations first, then the Cartesian Plane and THEN functions” approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class. The material is presented at a level that definitely prepares a student for Calculus while giving them relevant Mathematics which can be used in other classes as well. Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The answers to nearly all of the computational homework exercises are given in thetext and we have gone to great lengths to write some very thought provoking discussion questions whose answers are not given. One will notice that our exercise sets are much shorter than the traditional sets of nearly 100 “drill and kill” questions which build skill devoid of understanding. Our experience has been that students can do about 15-20 homework exercises a night so we very carefully chose smaller sets of questions which cover all of the necessary skills and get the students thinking more deeply about the Mathematics involved.
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College Trigonometry
Carl Stitz; Jeff Zeager · Stitz Zeager Open Source Mathematics · 2011
Covers chapters 10-11 of Precalculus.
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Whitman Calculus
David Guichard · David Guichard · 2010
An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available. This textbook has been used in classes at: Boise State University, Claremont McKenna College, University of Minnesota, University of Puget Sound, Western Connecticut State University, Whitman College.
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Linear Algebra
Jim Hefferon · Jim Hefferon · 2016
This text covers the standard material for a US undergraduate first course: linear systems and Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications. It has extensive exercise sets with worked answers to all exercises, including proofs, beamer slides for classroom use, and a lab manual for computer work. The approach is developmental. Although everything is proved, it introduces the material with a great deal of motivation, many computational examples, and exercises that range from routine verifications to a few challenges. Ancillary materials are available at the publisher link.
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Elementary Algebra
John Redden · Saylor Foundation · 2011
It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course. This text is, by far, the best elementary algebra textbook offered under a Creative Commons license. It is written in such a way as to maintain maximum flexibility and usability. A modular format was carefully integrated into the design. For example, certain topics, like functions, can be covered or omitted without compromising the overall flow of the text. An introduction of square roots in Chapter 1 is another example that allows for instructors wishing to include the quadratic formula early to do so. Topics such as these are carefully included to enhance the flexibility throughout. This textbook will effectively enable traditional or nontraditional approaches to elementary algebra. This, in addition to robust and diverse exercise sets, provides the base for an excellent individualized textbook instructors can use free of needless edition changes and excessive costs! A few other differences are highlighted below: Equivalent mathematical notation using standard text found on a keyboard A variety of applications and word problems included in most exercise sets Clearly enumerated steps found in context within carefully chosen examples Alternative methods and notation, modularly integrated, where appropriate Video examples available, in context, within the online version of the textbook Robust and diverse exercise sets with di
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College Algebra
Carl Stitz; Jeff Zeager · Stitz Zeager Open Source Mathematics · 2013
College Algebra is an introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended). Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The authors also offer a Precalculus version of this text, which has two extra chapters covering Trigonometry.
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Calculus
Gilbert Strang · Wellesley-Cambridge Press · 1991
Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.
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Book of Proof
Richard Hammack · Richard Hammack · 2018
This is a book about how to prove theorems. Until this point in your education, you may have regarded mathematics primarily as a computational discipline. You have learned to solve equations, compute derivatives and integrals, multiply matrices and find determinants; and you have seen how these things can answer practical questions about the real world. In this setting, your primary goal in using mathematics has been to compute answers. But there is another approach to mathematics that is more theoretical than computational. In this approach, the primary goal is to understand mathematical structures, to prove mathematical statements, and even to invent or discover new mathematical theorems and theories. The mathematical techniques and procedures that you have learned and used up until now have their origins in this theoretical side of mathematics. For example, in computing the area under a curve, you use the fundamental theorem of calculus. It is because this theorem is true that your answer is correct. However, in your calculus class you were probably far more concerned with how that theorem could be applied than in understanding why it is true. But how do we know it is true? How can we convince ourselves or others of its validity? Questions of this nature belong to the theoretical realm of mathematics. This book is an introduction to that realm. This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems,explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics. This text has been used in classes at: Virginia Commonwealth University, Lebanon Valley College, University of California - San Diego, Colorado State University, Westminster College, South Dakota State University, PTEK College - Brunei,
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A First Course in Linear Algebra
Robert Beezer · Robert Beezer · 2015
A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way. A unique feature of this book is that chapters, sections and theorems are labeled rather than numbered. For example, the chapter on vectors is labeled "Chapter V" and the theorem that elementary matrices are nonsingular is labeled "Theorem EMN." Another feature of this book is that it is designed to integrate SAGE, an open source alternative to mathematics software such as Matlab and Maple. The author includes a 45-minute video tutorial on SAGE and teaching linear algebra. This textbook has been used in classes at: Centre for Excellence in Basic Sciences, Westmont College, University of Ottawa, Plymouth State University, University of Puget Sound, University of Notre Dame, Carleton University, Amherst College, Felician College, Southern Connecticut State University, Michigan Technological University, Mount Saint Mary College, University of Western Australia, Moorpark College, Pacific University, Colorado State University, Smith College, Wilbur Wright College, Central Washington U (Lynwood Center), St. Cloud State University, Miramar College, Loyola Marymount University.
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Criminology
Jeff Bry · Minnesota State Colleges and Universities · 2024
This textbook is designed as a free, open-source textbook to be used, shared, and changed as the user sees fit. Many outside OER sources and authors have been cited in this textbook, these resources are also open-source resources. Based on the different sources used, some chapters may be formatted somewhat differently from others. The “voice” of each chapter may be somewhat different also because of different authors being used. Personally, I think this adds to the textbook and provides a more open perspective on the material. To add insight and substance to this text I have included “In a Student’s Own Words” which will provide student perspectives to the content. My hope and intent are to add detail and examples to other students, using my students from prior semesters as a resource. No attributions have been given to the students, course or semester to avoid identifying individual students. The two prompts below will let the reader know the content is student created.
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Tort Law: Cases and Commentaries
Samuel Beswick · CanLII: Canadian Legal Information Institute · 2021
The law of obligations concerns the legal rights and duties owed between people. Three primary categories make up the common law of obligations: tort, contract, and unjust enrichment. This casebook provides an introduction to tort law: the law that recognises and responds to civil wrongdoing. The material is arranged in two parts. Part I comprises §§1-11 and addresses intentional and dignitary torts and the overarching theories and goals of tort law. Part II comprises §§12-25 and addresses no-fault compensation schemes, negligence, nuisance, strict liability, and tort law’s place within our broader legal systems. This casebook was compiled and edited by Assistant Professor Samuel Beswick of the University of British Columbia Peter A. Allard School of Law. Maddison Zapach (J.D. expected 2023) provided research assistance on the first edition (published July 2021). We gratefully acknowledge the influence on our approach to this subject of Professor Joost Blom QC of the Allard School of Law, Professor John C.P. Goldberg of Harvard Law School, and Associate Professor Rosemary Tobin of the University of Auckland Faculty of Law. The support of Open UBC and the UBC Teaching and Learning Enhancement Fund is also gratefully acknowledged.
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Open Access International Human Rights Law
Stuart Wallace; Clare James · University of Leeds Open Books · 2026
Open Access International Human Rights Law provides an accessible and comprehensive introduction to the principles, institutions and substantive protections that underpin international human rights law.
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The Office of the Presidency: Powers and Responsibilities
Jakob Miller · Jakob Miller · 2025
Popular imagination gives the President of the United States vast, sweeping power. The Constitution tells a different story. This book is about the gap between the two. The Office of the Presidency: Powers and Responsibilities is a free, introductory political science textbook for undergraduate students. It examines the American presidency through the lens of the leadership dilemma — the persistent gap between what the public expects presidents to accomplish and what the office actually empowers them to do. Each chapter explores a key dimension of presidential power: the constitutional origins of the office, nominations and campaigns, the tools and limits of executive authority, the relationship with Congress and the courts, war and foreign policy, and the presidency's management of public opinion and the media. Throughout, the focus is not on the presidents who have held the office, but on the office itself — its surprising constraints, its creative expansions, and the enduring tension between expectation and reality that has shaped every presidency from Washington to the present.
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Antitrust: Principles, Cases, and Materials
Daniel Francis; Christopher Sprigman · Daniel Francis and Christopher Jon Sprigman · 2026
Antitrust: Principles, Cases, and Materials (4th Edition) is a free antitrust law textbook designed for a three-credit or four-credit antitrust course (we teach the four-credit course at NYU School of Law).
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Introduction to Criminology and Criminal Justice: An Australasian Perspective
Nadine Connell; Lucy Forrester; Steph Friend · Griffith University · 2024
This textbook introduces students to the disciplines of criminology and criminal justice, using contemporary Australasian examples to combine theory with practical applications.
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Constitutional Law with a Twist: Less Is More
Alisa Klein · CALI's eLangdell® Press · 2025
Constitutional Law with a Twist: Less is More is designed for a one-semester survey course on federal constitutional law. The casebook covers the content of a typical four-credit survey course: the structure of the U.S. government and individual rights (other than First Amendment rights and rights unique to criminal law). What differentiates this casebook from most other constitutional law casebooks is that this book is deliberately short. It reflects the author’s philosophy that students often experience more joy, more depth, and more growth in an introductory course on constitutional law when there is less reading, more emphasis on contemporary cases, and more feedback on interim work. The book’s preface and the introduction to the accompanying teacher’s manual describe the book’s approach in detail to help faculty decide whether this casebook is a good fit for them and their students.