Math textbooks
This Math textbooks page is for compiling a list of textbooks for mathematics -- not problem books, contest books, or general interest books. See math books for more titles.
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Contents
Math textbooks by subject
Levels of reading and math ability are loosely defined as follows:
- Elementary is for elementary school students up through possibly early middle school.
- Getting Started is recommended for students grades 6 to 9.
- Intermediate is recommended for students grades 9 to 12.
- Collegiate is recommended for college and university students.
Algebra
Getting Started
- Art of Problem Solving is currently designing an Introductory Algebra textbook.
- Algebra I: An Integrated Approach
Intermediate
- Art of Problem Solving is currently designing an Intermediate Algebra textbook.
- Algebra and Trigonometry by Michael Sullivan.
Calculus
High School
- Calculus by Michael Spivak. Top students swear by this book.
- The Hitchhiker's Guide to Calculus by Michael Spivak.
- AP Calculus Problems and Solutions Part II AB and BC -- A fantastic resource for students mastering the material required for the AP exam.
Collegiate
- Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus by Michael Spivak.
Combinatorics
Getting Started
- AoPS publishes Dr. David Patrick's Introduction to Counting & Probability textbook, which is recommended for advanced middle and high school students.
Intermediate
- Mathematics of Choice by Ivan Nevin.
Collegiate
Geometry
Getting Started
- AoPS publishes Richard Rusczyk's Introduction to Geometry textbook, which is recommended for advanced middle and high school students.
- Geometry by Serge Lang and Gene Murrow.
Intermediate
- Advanced Euclidean Geometry by Alfred S. Posamentier.
- Challenging Problems in Geometry -- A good book for students who already have a solid handle on elementary geometry.
- Geometry Revisited -- Not a traditional textbook, but close enough to list this classic.
Collegiate
- Geometry: A Comprehensive Course by Dan Pedoe.
Number Theory
Getting Started
- The AoPS Introduction to Number Theory by Mathew Crawford.
Collegiate
- Quadratic Diophantine Equations by Titu Andreescu and Dorin Andrica.
- Elementary Number Theory by Gareth A. Jones and Josephine M. Jones.
- An Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright.
Analytic Number Theory
- Introduction to Analytic Number Theory by Tom M. Apostol.
- A Primer of Analytic Number Theory by Jeffrey Stopple.
Elliptic Curves
- Elliptic Curves: Function Theory, Geometry, Arithmetic by Henry McKean and Victor Moll.
Probability
Getting Started
- AoPS publishes Dr. David Patrick's Introduction to Counting & Probability textbook, which is recommended for advanced middle and high school students.
Collegiate
- Probability and Statistical Inference by Nitis Mukhopadhyay.
Statistics
Collegiate
- Probability and Statistical Inference by Nitis Mukhopadhyay.
- Statistical Theory and Bayesian Analysis by James O. Berger.
- Bayesian Data Analysis by Andrew Gelman.
- Markov Chain Monte Carlo in Practice by W.R. Gilks.
- Monte Carlo Statistical Methods
