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American Institute of Mathematics - Approved Open Textbooks This site provides a list of open textbooks approved for use by the American Institute of Mathematics. The textbooks cover the major areas of study in mathematics and all texts were judged to meet the Institute's evaluation criteria.
LibreTexts Bookshelves: Mathematics LibreTexts Mathematics Library holds a range of math textbooks that are curated by the LibreTexts development team and can be used as is, or as content for building customized remixes.
Introductory Textbooks
A Gentle Introduction to the Art of Mathematics This open-source textbook covers several topics in the foundations of mathematics (logic, sets, relations, functions and cardinality) and introduces the reader to many techniques of mathematical proof.
Proofs and Concepts: The Fundamentals of Abstract Mathematics Provides an introduction to proofs, logic, sets, functions, and other fundamentals of abstract mathematics. Designed to be a bridge that introduces undergraduates to abstract mathematics.
Mathematics for the Liberal Arts This course was originally developed for the Open Course Library project. Topics covered in the course include problem solving, voting theory, graph theory, growth models, finance, data collection and description, and probability.
Quantitative Problem Solving in Natural Resources This text is intended to support courses that bridge the divide between mathematics typically encountered in U.S. high school curricula and the practical problems that natural resource students might engage with.
Algebra Textbooks
Prealgebra 2e (OpenStax) Prealgebra is a textbook for a one-semester course that serves as a bridge between arithmetic and algebra. It can be used in courses named “Basic Mathematics,” “Introductory Algebra,” “Fundamentals of Algebra."
Algebra and Trigonometry Prealgebra is a textbook for a one-semester course that serves as a bridge between arithmetic and algebra. It can be used in courses named “Basic Mathematics,” “Introductory Algebra,” “Fundamentals of Algebra."
Elementary Algebra 2e (OpenStax) Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course.
Intermediate Algebra 2e (OpenStax) Intermediate Algebra is designed to meet the scope and sequence requirements of a one-semester intermediate algebra course.
Beginning and Intermediate Algebra This text includes many detailed examples for each section along with several problems for students to practice and master concepts.
Linear Algebra
A First Course in Linear Algebra A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile.
Linear Algebra with Applications Linear Algebra with Applications by W. Keith Nicholson, traditionally published for many years is now being released as an Open textbook. It aims to achieve a balance among computational skills, theory, and applications of linear algebra.
Linear Algebra with Applications: An adaptation for MAT223 UTM This open textbook is an adaptation of Linear Algebra with Applications for courses at the University of Toronto Mississauga.
Calculus Textbooks
Precalculus (OpenStax) Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course.
Calculus (OpenStax) Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning.
Contemporary Calculus I This is a textbook for differential calculus with explanations, examples, worked solutions, problem sets and answers.
Applied Calculus I An openly licensed applied calculus textbook, covering derivatives, integrals, and an intro to multivariable calculus. This book is heavily remixed from the Contemporary Calculus I textbook.
Active Calculus Multivariable This textbook engages students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students.
Community Calculus An early transcendentals book covering single variable calculus, infinite series, and multivariable calculus.
Calculus: Early Transcendentals 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.
Other Math Textbooks
Elementary Differential Equations with Boundary Value Problems Written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.
Combinatorics Through Guided Discovery This book is an introduction to combinatorial mathematics, also known as combinatorics and consists almost entirely of problems.
Combinatorics: Enumeration, Graph Theory, and Design Theory Combinatorics provides an introduction to enumeration, graph theory, and design theory. It is aimed at upper-level undergraduate students. It does not assume any background knowledge of combinatorics.