These sites offer multiple books:

Here are some individual books on the topic of mathematics:

- Intermediate Algebra for Science, Technology, Engineering, and Mathematics Edition ⌈0.99⌉ This textbook is an adaptation from Tyler Wallace’s Beginning and Intermediate Algebra, and my own authored work. I wanted to create a textbook for a stem-track intermediate algebra, Interme- diate Algebra for Science, Technology, Engineering, and Mathematics, that was licensed under a Creative Commons Attribution. I used most of Wallace textbook’s examples in addition to my authored materials in order to fit the course outline of record for SCC’s Intermediate Algebra and course identification Math 70X: https://www.c-id.net/resources
- Trigonometry This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them. So this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged. Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor. In particular, most sections of the book start with a beginning activity that review prior mathematical work that is necessary for the new section or introduce new concepts and definitions that will be used later in that section. Each section also contains several progress checks that are short exercises or activities designed to help readers determine if they are understanding the material. In addition, the text contains links to several interactive Geogebra applets or worksheets. These applets are usually part of a beginning activity or a progress check and are intended to be used as part of the textbook.
- A First Course in Linear Algebra: 10th Anniversary Edition A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students. All major topics of linear algebra are available in detail, as well as justifications of important results. In addition, connections to topics covered in advanced courses are introduced. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the textbook.
- Linear Algebra with Applications: An Open Textbook Linear Algebra with Applications by W. Keith Nicholson, traditionally published for many years is now being released as an open educational resource and part of Lyryx with Open Texts! Supporting today’s students and instructors requires much more than a textbook, which is why Dr. Nicholson opted to work with Lyryx Learning. Overall, the aim of the textbook is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work.
- Linear Algebra: A Course for Physicists and Engineers In order not to intimidate students by a too abstract approach, this textbook on linear algebra is written to be easy to digest by non-mathematicians. It introduces the concepts of vector spaces and mappings between them without dwelling on statements such as theorems and proofs too much. It is also designed to be self-contained, so no other material is required for an understanding of the topics covered.
- Calculus: Early Transcendentals Calculus: Early Transcendentals, originally by D. Guichard, has been redesigned by the Lyryx editorial team. Substantial portions of the content, examples, and diagrams have been redeveloped, with additional contributions provided by experienced and practicing instructors. This approachable textbook provides a comprehensive understanding of the necessary techniques and concepts of the typical Calculus course sequence, and is suitable for the standard Calculus I, II and III courses. To practice and develop an understanding of topics, this textbook offers a range of problems, from routine to challenging, with selected solutions. As this is an open textbook, instructors and students are encouraged to interact with the textbook through annotating, revising, and reusing to your advantage. Suggestions for contributions to this growing textbook are welcome.
- Book of Proof - Third Edition 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. 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.
- Topics in Precalculus Topics in Precalculus is a compilation of ideas and concepts designed to prepare you for the study of Calculus. In addition to re-enforcing content from algebra such as exponential and logarithmic functions, and complex numbers, this book introduces the reader to more novel concepts by investigating in detail two of the most basic shapes in geometry: the circle and the triangle. Join us as we explore this ancient subject that extends our knowledge of these shapes by explaining them in terms of trigonometry
- Differential Calculus for the Life Sciences Calculus arose as a tool for solving practical scientific problems through the centuries. However, it is often taught as a technical subject with rules and formulas (and occasionally theorems), devoid of its connection to applications. In this textbook, the applications form an important focal point, with emphasis on life sciences. This places the techniques and concepts into practical context, as well as motivating quantitative approaches to biology taught to undergraduates. While many of the examples have a biological flavour, the level of biology needed to understand those examples is kept at a minimum. The problems are motivated with enough detail to follow the assumptions, but are simplified for the purpose of pedagogy.
- Discrete Mathematics: An Open Introduction - 3rd Edition Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring 2013, and have been used by other instructors as a free additional resource. Since then it has been used as the primary text for this course at UNC, as well as at other institutions.
- Fundamentals of Mathematics Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. This text will help the student develop the insight and intuition necessary to master arithmetic techniques and manipulative skills.
- College Algebra 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.
- Intermediate Algebra Used as a standalone textbook, Intermediate Algebra 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.
- APEX Calculus This text comprises a three–text series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 5 through 8. The third text covers topics common in “Calc 3” or “multivariable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 9 through 14. More information, including free downloads of .pdf versions of the text, is available at www.apexcalculus.com.
- Business Math: A Step-by-Step Handbook Business Math is the study of mathematics required by the field of business. Business professionals will work with taxes, gross earnings, product prices, and currency exchange; they will be offered loans, lines of credit, mortgages, leases, savings bonds, and other financial tools. This textbook covers all of these topics and how these financial tools can maximize their earnings and minimize their costs. It also discusses how to execute smart monetary decisions both personally and for their business.
- Fractal Analysis - Applications in Physics, Engineering and Technology Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory.
- Advances in Statistical Methodologies and Their Application to Real Problems In recent years, statistical techniques and methods for data analysis have advanced significantly in a wide range of research areas. These developments enable researchers to analyze increasingly large datasets with more flexibility and also more accurately estimate and evaluate the phenomena they study. We recognize the value of recent advances in data analysis techniques in many different research fields. However, we also note that awareness of these different statistical and probabilistic approaches may vary, owing to differences in the datasets typical of different research fields. This book provides a cross-disciplinary forum for exploring the variety of new data analysis techniques emerging from different fields.
- OpenIntro Statistics A complete foundation for Statistics, also serving as a foundation for Data Science.
- Introductory Statistics with Randomization and Simulation A new book, Introduction to Modern Statistics (IMS is available on the web, as a PDF, and in paperback), represents the evolution of Introductory Statistics with Randomization and Simulation (ISRS).
- Answering Questions with Data This is a free textbook teaching introductory statistics for undergraduates in Psychology. This textbook is part of a larger OER course package for teaching undergraduate statistics in Psychology, including this textbook, a lab manual, and a course website. All of the materials are free and copiable, with source code maintained in Github repositories. The links below connect to various components of the project. The main OSF project link is https://osf.io/3s68c/.
- Think Stats: Probability and Statistics for Programmers - 2e Think Stats is an introduction to Probability and Statistics for Python programmers. Think Stats emphasizes simple techniques you can use to explore real data sets and answer interesting questions. The book presents a case study using data from the National Institutes of Health. Readers are encouraged to work on a project with real datasets. If you have basic skills in Python, you can use them to learn concepts in probability and statistics. Think Stats is based on a Python library for probability distributions (PMFs and CDFs). Many of the exercises use short programs to run experiments and help readers develop understanding.
- Introductory Business Statistics The book "Introductory Business Statistics" by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions. The author covers topics including descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. Using real-world examples throughout the text, the author hopes to help students understand how statistics works, not just how to "get the right number."
- Wikibooks: Statistics Statistics is used in almost every field of research: the discovery of the Higgs particle, social sciences, climate research,... With this, and with its well established foundations, it is very well suited for a wikibook. This book is an ongoing effort to make this basic knowledge available for free. Since the concepts in probability are essential for statistics, a thorough knowledge of probability is needed before reading this book (especially for the advanced part), and so probability is a prerequisite of this book. Although some concepts in the probability are reviewed, the review is meant to be read by someone who is familiar with those concepts already, and so it is not too detailed. For a more detailed discussion on those concepts, you may refer to the wikibook Probability. This book is divided into two main parts: Basics and Advanced. The Basics part gives a brief introduction and idea about statistics, while the Advanced part gives a more formal and mathematical treatment on statistics.

- Wolfram MathWorld Contains resources, explanations, and study guides on hundreds of mathematical concepts.

- Lumen Learning 11 full courses
- MIT OpenCourseWare 180+ full courses in mathematics
- myOpenMath Open courses for student self-study or for instructors to use or adapt
- Foundations of Real World Math In this course, we study essential math concepts that will enrich your understanding of the world and illuminate a larger, mathematically-rich universe. The three courses in the Real World Math series discuss basic algebra and geometry topics and show you how to apply these concepts to everyday life. The material focuses on how math relates to common real-world situations, transactions, and phenomena, such as personal finance, business, and the sciences. This real-world focus will help you grasp the importance of the mathematical concepts you encounter in these courses and understand why you need quantitative and algebraic skills to succeed in college and your day-to-day life.
- Algebra Algebra lets us solve many different types of calculations by using basic formulas and steps that work regardless of the specific numbers in the problem. For example, we can use an algebraic formula to calculate a monthly payment or to pay off a loan of any size using a given interest rate. In this course, we explore how to use standard mathematical and business formulas and how to translate verbal descriptions into mathematical equations to establish relationships and create predictions. In the later units, we explore how to use graphs to make these same predictions. You can apply the problem-solving strategies we discuss in this course to business, science, and many other fields.
- College Algebra In this course, you will explore intermediate-level algebraic operations and learn how algebraic methods are used in real-world applications. Topics include systems of linear equations and inequalities, quadratic equations, exponential and logarithmic functions, and operations with rational expressions. Using algebra involves graphing functions and relating functions' properties to their graphs. You will apply these skills to create mathematical models for word problems. Each unit will include many application problems that will draw on your knowledge of the concepts presented in that unit. This course requires prior knowledge of basic algebra.
- Geometry In geometry, we study the rules of the spaces and objects in our world. Geometry lets us make accurate predictions about the sizes of triangles, circles, and rectangles, which lets us calculate, design, and build. Geometry helps architects design studios, farmers buy the right amount of seeds for their land, engineers build houses, and pilots calculate the amount of time they need to fly to reach another city. We use geometry to calculate how much paint we need to buy to cover a wall and the exact angle we should use to launch a rocket to hit a distant target. In this course, we also study the relationships between lines and angles. Urban planners study lines and angles to efficiently arrange houses, buildings, roads, and highways. Our street maps, water supply, and electrical connections all depend on these precise geometric calculations. How much space is inside a three-dimensional object? You may not realize you are using principles of geometry when you are getting ready for a trip, and you need to calculate how to fit two adults, three kids, four suitcases, and a dog into your car.
- Calculus I This course is divided into five learning sections, or units, plus a reference section, or appendix. The course begins with a unit that provides a review of algebra specifically designed to help and prepare you for the study of calculus. The second unit discusses functions, graphs, limits, and continuity. Understanding limits could not be more important, as that topic really begins the study of calculus. The third unit introduces and explains derivatives. With derivatives, we are now ready to handle all of those things that change mentioned above. The fourth unit makes visual sense of derivatives by discussing derivatives and graphs. The fifth unit introduces and explains antiderivatives and definite integrals. Finally, the reference section provides a large collection of reference facts, geometry, and trigonometry that will assist you in solving calculus problems long after the course is over.
- Introduction to Statistics The purpose of this course is to introduce you to the subject of statistics as a science of data. There is data abound in this information age; how to extract useful knowledge and gain a sound understanding of complex data sets has been more of a challenge. In this course, we will focus on the fundamentals of statistics, which may be broadly described as the techniques to collect, clarify, summarize, organize, analyze, and interpret numerical information. This course will begin with a brief overview of the discipline of statistics and will then quickly focus on descriptive statistics, introducing graphical methods of describing data. You will learn about combinatorial probability and random distributions, the latter of which serves as the foundation for statistical inference. On the side of inference, we will focus on both estimation and hypothesis testing issues. We will also examine the techniques to study the relationship between two or more variables; this is known as regression. By the end of this course, you should gain a sound understanding of what statistics represent, how to use statistics to organize and display data, and how to draw valid inferences based on data by using appropriate statistical tools.
- Introduction to Probability, Statistics, and Random Processes This site is the homepage of the textbook Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik. It is an open access peer-reviewed textbook intended for undergraduate as well as first-year graduate level courses on the subject. This probability textbook can be used by both students and practitioners in engineering, mathematics, finance, and other related fields.

- SageMath SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. Access their combined power through a common, Python-based language or directly via interfaces or wrappers. Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.

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