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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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

• 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

• 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

• 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

• A Path to Combinatorics for Undergraduates by Titu Andreescu and Zuming Feng.

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

See also

• Math books
• Science books