# 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