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.
Before adding any books to this page, please review the AoPSWiki:Linking books page.
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.
General Introduction / Multiple Topics
Getting Started
- Getting Started with Competition Math, a textbook meant for true beginners (on-target middle school students, or advanced elementary school students). It is written by AoPS Community Member cargeek9, currently a junior in high school. It covers the basics of algebra, geometry, combinatorics, and number theory, along with sets of accompanying practice problems at the end of every section.
Algebra
Getting Started
- AoPS publishes Dr. Richard Rusczyk's Introduction to Algebra textbook, which is recommended for advanced middle and high school students.
- Algebra I: An Integrated Approach
Intermediate
- AoPS publishes Dr. Richard Rusczyk's Intermediate Algebra textbook, which is recommended for advanced middle and high school students.
- 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
- AoPS publishes Dr. David Patrick's Intermediate Counting & Probability textbook, which is recommended for advanced middle and high school students.
- 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.
Intermediate
- AoPS publishes Dr. David Patrick's Intermediate 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
