American Institute of Mathematics Open Textbook Initiative

American Institute of Mathematics Open Textbook Initiative

AIM Approved Textbooks
https://textbooks.aimath.org/textbooks/approved-textbooks/

Liberal Arts Math

Math in Society
David Lippman
https://www.opentextbookstore.com/mathinsociety/

Mathematical Discovery
Andrew M. Bruckner, Brian S. Thomson, Judith B. Bruckner
https://classicalrealanalysis.info/com/Mathematical-Discovery.php
https://classicalrealanalysis.info/com/FREE-PDF-DOWNLOADS.php

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Elementary and Intermediate Algebra

ORCCA: Open Resources for Community College Algebra
Portland Community College
https://www.pcc.edu/math-resources/orcca/

Elementary Algebra
Katherine Yoshiwara
https://yoshiwarabooks.org/yoshiwarabooks.html

Intermediate Algebra: Functions and Graphs
Katherine Yoshiwara
https://yoshiwarabooks.org/yoshiwarabooks.html

College Algebra and Precalculus

Modeling, Functions, and Graphs: Algebra for College Students
Katherine Yoshiwara
https://yoshiwarabooks.org/mfg.html

Precalculus
David H. Collingwood, K. David Prince, Matthew M. Conroy
https://sites.math.washington.edu//~m120/

Precalculus / College Algebra / Trigonometry
Carl Stitz and Jeff Zeager
https://stitz-zeager.com/

Trigonometry

Trigonometry
Katherine Yoshiwara
https://yoshiwarabooks.org/trig.html

College Trigonometry
Carl Stitz and Jeff Zeager
https://stitz-zeager.com/

Mathematics for Elementary Teachers

Mathematics for Elementary Teachers
Michelle Manes
https://pressbooks-dev.oer.hawaii.edu/math111/

Business Calculus

Business Calculus with Excel
Mike May and Anneke Bart
https://excelcalculus.org/LandingPage.html

Calculus

Calculus
David Guichard
https://www.whitman.edu/mathematics/multivariable/

Active Calculus
Matt Boelkins
https://activecalculus.org/
https://scholarworks.gvsu.edu/books/20/

APEX Calculus
Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar
https://www.apexcalculus.com/
https://leanpub.com/apexcalculus
https://www.openintro.org/

CLP Calculus
Joel Feldman, Andrew Rechnitzer, Elyse Yeager
https://personal.math.ubc.ca/~CLP/
https://github.com/arechnitzer
https://github.com/ecyeager/CLP1Slides
Volume 1: Differential calculus
Volume 2: Integral calculus
Volume 3: Multivariable calculus
Volume 4: Vector calculus
Large number of exercises

Calculus in Context
James Callahan, Kenneth Hoffman, David Cox, Donal O’Shea, Harriet Pollatsek, Lester Senechal
https://www.science.smith.edu/~callahan/
https://www.science.smith.edu/~callahan/intromine.html

Calculus I, II, III
Jerrold E. Marsden and Alan Weinstein
https://authors.library.caltech.edu/records/00arw-c5851
https://authors.library.caltech.edu/records/hb74n-f9x09
https://authors.library.caltech.edu/records/rg25s-crx26
https://authors.library.caltech.edu/records/7ejp1-f6z72/files/CalcUnlimited.pdf?download=1

Elementary Calculus
Vector Calculus
Michael Corral
https://www.mecmath.net/calculus/
https://www.mecmath.net/

Linear Algebra

Understanding Linear Algebra
David Austin
https://understandinglinearalgebra.org/home.html
https://scholarworks.gvsu.edu/books/26/

Linear Algebra Done Right
Sheldon Axler
https://linear.axler.net/

A First Course in Linear Algebra
Rob Beezer
http://linear.ups.edu/
http://linear.ups.edu/download.html

Introduction to Applied Linear Algebra
Stephen Boyd and Lieven Vandenberghe
https://web.stanford.edu/~boyd/vmls/
https://web.stanford.edu/~boyd/vmls/vmls.pdf
https://web.stanford.edu/~boyd/vmls/vmls-slides.pdf

Linear Algebra
Jim Hefferon
https://hefferon.net/linearalgebra/

Linear Algebra Done Wrong
Sergei Treil
https://sites.google.com/a/brown.edu/sergei-treil-homepage/linear-algebra-done-wrong

Differential Equations

Elementary Differential Equations (with Boundary Value Problems)
William F. Trench
https://digitalcommons.trinity.edu/mono/8/

Notes on Diffy Qs
Jiří Lebl
https://www.jirka.org/diffyqs/

The Ordinary Differential Equations Project
Tom Judson
https://judsonbooks.org/ode-project/

Introduction to Proofs

An Introduction to Proof via Inquiry-Based Learning
Dana Ernst
https://danaernst.com/IBL-IntroToProof/

A Gentle Introduction to the Art of Mathematics
Joseph E. Fields
https://osj1961.github.io/giam/

Book of Proof
Richard Hammack
https://richardhammack.github.io/BookOfProof/

Mathematical Reasoning: Writing and Proof
Ted Sundstrom
https://www.tedsundstrom.com/mathematical-reasoning-writing-and-proof
http://scholarworks.gvsu.edu/books/24
http://scholarworks.gvsu.edu/books/28

Discrete Math

Applied Discrete Structures
Alan Doerr and Kenneth Levasseur
https://discretemath.org/

Discrete Mathematics: An Open Introduction
Oscar Levin
https://discrete.openmathbooks.org/dmoi4.html
https://youtube.com/playlist?list=PLZh9gzIvXQUtB1t57_Xyk3yp9MK2iIFXX&feature=shared
https://youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS&feature=shared

Discrete Mathematics: First and Second Course
Edward A. Bender and S. Gill Williamson
https://cseweb.ucsd.edu/~gill/BWLectSite/

Combinatorics

Applied Combinatorics
Mitchel T. Keller and William T. Trotter
https://appliedcombinatorics.org/appcomb/

Counting Rocks!
H. Adams, K. Emmrich, M. Gillespie, S. Golden, R. Pries
https://www.mathematicalgemstones.com/maria/OER.html
https://youtube.com/playlist?list=PL5J6K3znOvOkci83fWQbvpXOvuhEguikI&feature=shared

Combinatorics Through Guided Discovery
Kenneth Bogart
https://bogart.openmathbooks.org/

Foundations of Combinatorics with Applications
Edward A. Bender and S. Gill Williamson
https://mathweb.ucsd.edu/~ebender/CombText/
https://freecomputerbooks.com/Foundations-of-Combinatorics-with-Applications.html

Computing and Numerical Analysis

Sage for Undergraduates
Gregory Bard
http://www.gregorybard.com/books.html
http://www.discrete-math-hub.com/textbook-in-progress.html

Computational Mathematics with SageMath
Paul Zimmermann et al.
https://www.sagemath.org/sagebook/english.html

Tea Time Numerical Analysis
Leon Q. Brin
https://lqbrin.github.io/tea-time-numerical/

Number Theory

Number Theory: In Context and Interactive
Karl-Dieter Crisman
https://math.gordon.edu/ntic/

Elementary Number Theory: Primes, Congruences, and Secrets
William Stein
https://wstein.org/ent/

A Computational Introduction to Number Theory and Algebra
Victor Shoup
https://shoup.net/ntb/

Abstract Algebra

Abstract Algebra: Theory and Applications
Tom Judson
https://judsonbooks.org/aata/

Elements of Abstract and Linear Algebra
E. H. Connell
https://www.math.miami.edu/~ec/book/

Algebra: Abstract and Concrete
Frederick Goodman
http://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/algebrabook.html

Real Analysis

Basic Analysis: Introduction to Real Analysis
Jiří Lebl
https://www.jirka.org/ra/

Introduction to Real Analysis
William F. Trench
https://digitalcommons.trinity.edu/mono/7/

Elementary Real Analysis
Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner
https://www.classicalrealanalysis.info/com/Elementary-Real-Analysis.php

Mathematical Analysis I
Elias Zakon
http://www.trillia.com/zakon-analysisI.html

How We Got from There to Here: A Story of Real Analysis
Robert Rogers and Eugene Boman
https://milneopentextbooks.org/how-we-got-from-there-to-here-a-story-of-real-analysis/

Complex Analysis

A First Course in Complex Analysis
Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka
https://matthbeck.github.io/complex.html

Complex Analysis
Russell Howell and John Mathews
https://complexanalysis.org/

Geometry and Topology

Geometry with an Introduction to Cosmic Topology
Michael P. Hitchman
https://mphitchman.com/gct/

Probability

Introduction to Probability
Charles M. Grinstead and J. Laurie Snell
https://chance.dartmouth.edu/teaching_aids/books_articles/probability_book/book.html

Probability: Lectures and Labs
Mark Huber
https://www.markhuberdatascience.org/probability-textbook

Statistics

OpenIntro Statistics
David M. Diez, Christopher D. Barr, Mine Çetinkaya-Rundel
https://www.openintro.org/

Introduction to Modern Statistics
Mine Çetinkaya-Rundel and Johanna Hardin
https://www.openintro.org/book/ims/
https://github.com/OpenIntroStat/ims/
https://openintro-ims.netlify.app/

Introductory Statistics for the Life and Biomedical Sciences
Julie Vu and David Harrington
https://www.openintro.org/
https://www.openintro.org/book/stat/

SticiGui
Philip Stark
https://www.stat.berkeley.edu/~stark/SticiGui/

Online Statistics Education
David Lane, lead author
https://onlinestatbook.com/

Logic

A Friendly Introduction to Mathematical Logic
Christopher C. Leary and Lars Kristiansen
https://milneopentextbooks.org/a-friendly-introduction-to-mathematical-logic/

Data Science and Machine Learning

Mathematics for Machine Learning
Marc Peter Deisenroth, A. Aldo Faisal, Cheng Song Ong
https://mml-book.github.io/

Probability for Data Science
Stanley H. Chan
https://probability4datascience.com/