The list below groups open textbooks by course title. All the books have been judged to meet the evaluation criteria set by the AIM editorial board.
Liberal Arts Math
Math in Society
David Lippman
Mathematical Discovery
Andrew M. Bruckner, Brian S. Thomson, Judith B. Bruckner
Elementary and Intermediate Algebra
ORCCA: Open Resources for Community College Algebra
Portland Community College
Elementary Algebra
Katherine Yoshiwara
Intermediate Algebra: Functions and Graphs
Katherine Yoshiwara
College Algebra and Precalculus
Modeling, Functions, and Graphs: Algebra for College Students
Katherine Yoshiwara
Precalculus
David H. Collingwood, K. David Prince, Matthew M. Conroy
Precalculus / College Algebra / Trigonometry
Carl Stitz and Jeff Zeager
Mathematics for Elementary Teachers
Mathematics for Elementary Teachers
Michelle Manes
Business Calculus
Business Calculus with Excel
Mike May and Anneke Bart
Calculus
Calculus
David Guichard
Active Calculus
Matt Boelkins
APEX Calculus
Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar
CLP Calculus
Joel Feldman, Andrew Rechnitzer, Elyse Yeager
Calculus in Context
James Callahan, Kenneth Hoffman, David Cox, Donal O’Shea, Harriet Pollatsek, Lester Senechal
Calculus I, II, III
Jerrold E. Marsden and Alan Weinstein
Elementary Calculus
Vector Calculus
Michael Corral
Linear Algebra
Understanding Linear Algebra
David Austin
Linear Algebra Done Right
Sheldon Axler
A First Course in Linear Algebra
Rob Beezer
Introduction to Applied Linear Algebra
Stephen Boyd and Lieven Vandenberghe
Linear Algebra
Jim Hefferon
Linear Algebra Done Wrong
Sergei Treil
Differential Equations
Elementary Differential Equations (with Boundary Value Problems)
William F. Trench
Notes on Diffy Qs
Jiří Lebl
The Ordinary Differential Equations Project
Tom Judson
Introduction to Proofs
An Introduction to Proof via Inquiry-Based Learning
Dana Ernst
A Gentle Introduction to the Art of Mathematics
Joseph E. Fields
Book of Proof
Richard Hammack
Mathematical Reasoning: Writing and Proof
Ted Sundstrom
Discrete Math
Applied Discrete Structures
Alan Doerr and Kenneth Levasseur
Discrete Mathematics: An Open Introduction
Oscar Levin
Discrete Mathematics: First and Second Course
Edward A. Bender and S. Gill Williamson
Combinatorics
Applied Combinatorics
Mitchel T. Keller and William T. Trotter
Counting Rocks!
H. Adams, K. Emmrich, M. Gillespie, S. Golden, R. Pries
Combinatorics Through Guided Discovery
Kenneth Bogart
Foundations of Combinatorics with Applications
Edward A. Bender and S. Gill Williamson
Computing and Numerical Analysis
Sage for Undergraduates
Gregory Bard
Computational Mathematics with SageMath
Paul Zimmermann et al.
Tea Time Numerical Analysis
Leon Q. Brin
Number Theory
Number Theory: In Context and Interactive
Karl-Dieter Crisman
Elementary Number Theory: Primes, Congruences, and Secrets
William Stein
A Computational Introduction to Number Theory and Algebra
Victor Shoup
Abstract Algebra
Abstract Algebra: Theory and Applications
Tom Judson
Elements of Abstract and Linear Algebra
E. H. Connell
Algebra: Abstract and Concrete
Frederick Goodman
Real Analysis
Basic Analysis: Introduction to Real Analysis
Jiří Lebl
Introduction to Real Analysis
William F. Trench
Elementary Real Analysis
Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner
Mathematical Analysis I
Elias Zakon
How We Got from There to Here: A Story of Real Analysis
Robert Rogers and Eugene Boman
Complex Analysis
A First Course in Complex Analysis
Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka
Complex Analysis
Russell Howell and John Mathews
Geometry and Topology
Geometry with an Introduction to Cosmic Topology
Michael P. Hitchman
Probability
Introduction to Probability
Charles M. Grinstead and J. Laurie Snell
Probability: Lectures and Labs
Mark Huber
Statistics
OpenIntro Statistics
David M. Diez, Christopher D. Barr, Mine Çetinkaya-Rundel
Introduction to Modern Statistics
Mine Çetinkaya-Rundel and Johanna Hardin
Introductory Statistics for the Life and Biomedical Sciences
Julie Vu and David Harrington
SticiGui
Philip Stark
Online Statistics Education
David Lane, lead author
Logic
A Friendly Introduction to Mathematical Logic
Christopher C. Leary and Lars Kristiansen
Data Science and Machine Learning
Mathematics for Machine Learning
Marc Peter Deisenroth, A. Aldo Faisal, Cheng Song Ong
Probability for Data Science
Stanley H. Chan
Additional Resources
Course materials that can supplement the approved textbooks or serve as resources for reading courses and independent study.
A Course on Number Theory
Peter Cameron
Games and Puzzles
Volker Ecke and Christine von Renesse
Abstract Algebra: Examples and Applications
Justin Hill and Chris Thron
SIAM Guidebooks on Math Modeling
Karen M. Bliss, Kathleen R. Kavanagh,
Benjamin J. Galluzzo, Rachel Levy
Books Using Sage
Several of the textbooks on the approved list make extensive use of Sage.
A First Course in Linear Algebra
Rob Beezer
Applied Discrete Structures
Alan Doerr and Kenneth Levasseur
Sage for Undergraduates
Gregory Bard
Computational Mathematics with SageMath
Paul Zimmermann et al.
Understanding Linear Algebra
David Austin
The Ordinary Differential Equations Project
Tom Judson
Counting Rocks!
H. Adams, K. Emmrich, M. Gillespie, S. Golden, R. Pries
Abstract Algebra: Theory and Applications
Tom Judson
Number Theory: In Context and Interactive
Karl-Dieter Crisman
Elementary Number Theory: Primes, Congruences, and Secrets
William Stein