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These Math books are recommended by Art of Problem Solving administrators and members of 

the AoPS-MathLinks Community.

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.

Olympiad is recommended for high school students who are already studying math at an

undergraduate level.

Collegiate is recommended for college and university students.

More advanced topics are often left with the above levels unassigned.

Before adding any books to this page, please review the AoPSWiki:Linking books page.

Contents [hide]

1 Books by subject

1.1 Algebra

1.1.1 Getting Started

1.1.2 Intermediate

1.2 Analysis

1.3 Calculus

1.3.1 High School

1.3.2 Collegiate

1.4 Combinatorics

1.4.1 Getting Started

1.4.2 Intermediate

1.4.3 Olympiad

1.4.4 Collegiate

1.5 Geometry

1.5.1 Getting Started

1.5.2 Intermediate

1.5.3 Olympiad

1.5.4 Collegiate

1.6 Inequalities

1.6.1 Intermediate

1.6.2 Olympiad

1.6.3 Collegiate

1.7 Number Theory

1.7.1 Introductory

1.7.2 Olympiad

1.8 Trigonometry

1.8.1 Getting Started

1.8.2 Intermediate

1.8.3 Olympiad

1.9 Problem Solving

1.9.1 Getting Started

1.9.2 Intermediate

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1.9.3 Olympiad

2 General interest

3 Math contest problem books

3.1 Elementary School

3.2 Getting Started

3.3 Intermediate

3.4 Olympiad

3.5 Collegiate

4 See also

Books by subject

Algebra

Getting Started

AoPS publishes Richard Rusczyk's, David Patrick's, and Ravi Boppana's Prealgebra  textbook,

which is recommended for advanced elementary and middle school students.

AoPS publishes Richard Rusczyk's Introduction to Algebra  textbook, which is recommended for

advanced elementary, middle, and high school students.

Intermediate

Algebra  by I.M. Gelfand and Alexander Shen.

101 Problems in Algebra from the Training of the US IMO Team  by Titu Andreescu and Zuming

Feng

AoPS publishes Richard Rusczyk's and Mathew Crawford's Intermediate Algebra  textbook, which

is recommended for advanced middle and high school students.

Complex Numbers from A to... Z  by Titu Andreescu

Analysis

Counterexamples in Analysis  by Bernard R. Gelbaum and John M. H. Olmsted.

Calculus

High School

AoPS publishes Dr. David Patrick's Calculus  textbook, which is recommended for advanced

middle and high school students.

Calculus  by Michae l 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 Michae l 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.

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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 Niven.

102 Combinatorial Problems  by Titu Andreescu and Zuming Feng.

A Path to Combinatorics for Undergraduates: Counting Strategies  by Titu Andreescu and Zuming

Feng.

Olympiad

102 Combinatorial Problems  by Titu Andreescu and Zuming Feng.

Generatingfunctionology

Collegiate

Enumerative Combinatorics, Volume 1  by Richard Stanley.

Enumerative Combinatorics, Volume 2  by Richard Stanley.

A First Course in Probability  by Sheldon Ross

Geometry

Getting Started

AoPS publishes Richard Rusczyk's Introduction to Geometry  textbook, which is recommended for

advanced middle and high school students.

Intermediate

Challenging Problems in Geometry  -- A good book for students who already have a solid handle

on elementary geometry.

Geometry Revisited  -- A class ic.

Olympiad

Geometry Revisited  -- A class ic.

Geometry of Complex Numbers  by Hans Schwerfdtfeger.

Geometry: A Comprehensive Course  by Dan Pedoe.

Non-Euclidean Geometry  by H.S.M. Coxeter.

Projective Geometry  by H.S.M. Coxeter.

Geometric Transformations I , Geometric Transformations II , and Geometric Transformations

III  by I. M. Yaglom.

Collegiate

Geometry of Complex Numbers  by Hans Schwerfdtfeger.

Geometry: A Comprehensive Course  by Dan Pedoe.

Non-Euclidean Geometry  by H.S.M. Coxeter.

Projective Geometry  by H.S.M. Coxeter.

Inequalities

Intermediate

Introduction to Inequalities

Geometric Inequalities

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Olympiad

The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities  by J.

Michael Steele.

Problem Solving Strategies  by Arthur Engel contains significant material on inequalities.

Titu Andreescu's Book on Geometric Maxima and Minima

Topics in Inequalities  by Hojoo Lee

Olympiad Inequalities  by Thomas Mildorf 

A<B (A is less than B)  by Kiran S. Kedlaya

Secrets in Inequalities vol 1 and 2  by Pham Kim Hung

Collegiate

Inequalities  by G. H. Hardy, J. E. Littlewood, and G. Polya.

Number Theory

Introductory

The AoPS Introduction to Number Theory  by Mathew Crawford.

Olympiad

Number Theory: A Problem-Solving Approach  by Titu Andreescu and Dorin Andrica.

104 Number Theory Problems from the Training of the USA IMO Team  by Titu Andreescu, Dorin

Andrica and Zuming Feng.

Problems in Elementary Number Theory  by Hojoo Lee.

Trigonometry

Getting Started

Trigonometry  by I.M. Gelfand and Mark Saul.

Intermediate

Trigonometry  by I.M. Gelfand and Mark Saul.

103 Trigonometry Problems  by Titu Andreescu and Zuming Feng.

Olympiad

103 Trigonometry Problems  by Titu Andreescu and Zuming Feng.

Problem Solving

Getting Started

the Art of Problem Solving Volume 1  by Sandor Lehoczky and Richard Rusczyk is recommended

for avid math students in grades 7-9.

Mathematical Circles  -- A wonderful peak into Russian math training.

100 Great Problems of Elementary Mathematics  by Heinrich Dorrie.

Intermediate

the Art of Problem Solving Volume 2  by Sandor Lehoczky and Richard Rusczyk is recommended

for avid math students in grades 9-12.

The Art and Craft of Problem Solving  by Paul Zeitz, former coach of the U.S. math team.

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How to Solve It  by George Polya.

A Mathematical Mosaic  by Putnam Fellow Ravi Vakil.

Proofs Without Words , Proofs Without Words II

Sequences, Combinations, Limits

100 Great Problems of Elementary Mathematics  by Heinrich Dorrie.

Olympiad

Mathematical Olympiad Challenges

Problem Solving Strategies  by Arthur Engel.

Problem Solving Through Problems  by Loren Larson.

General interest

The Code Book  by Simon Singh.

Count Down  by Steve Olson.

Fermat's Enigma  by Simon Singh.

Godel, Escher, Bach

Journey Through Genius  by W illiam Dunham.

A Mathematician's Apology  by G. H. Hardy.

The Music of the Primes  by Marcus du Sautoy.

Proofs Without Words  by Roger B. Nelsen.

What is Mathematics? by Richard Courant, Herbert Robbins and Ian Stewart.

Math contest problem books

Elementary School

Mathematical Olympiads for Elementary and Middle Schools (MOEMS) publishes two excellent

contest problem books .

Getting Started

MathCounts books  -- Practice problems at all levels from the MathCounts competition.

Contest Problem Books  from the AMC.

More Mathematical Challenges  by Tony Gardiner. Over 150 problems from the UK Junior

Mathematical Olympiad, for students ages 11-15.

Intermediate

The Mandelbrot Competition has two problem books for sale  at AoPS.

ARML books:

ARML-NYSML 1989-1994  (see ARML).

ARML 1995-2004

Five Hundred Mathematical Challenges  -- An excellent collection of problems (with so lutions).

The USSR Problem Book

Leningrad Olympiads (Published by MathProPress.com)

Olympiad

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USAMO 1972-1986  -- Problems from the United States of America Mathematical Olympiad.

The IMO Compendium: A Collection of Problems Suggested for The International Mathematical

Olympiads: 1959-2004

Mathematical Olympiad Challenges

Problem Solving Strategies  by Arthur Engel.

Problem Solving Through Problems  by Loren Larson.

Hungarian Problem Book III

Mathematical Miniatures

Mathematical Olympiad Treasures

Collections of Olympiads (APMO, China, USSR to name the harder ones) published by

MathProPress.com.

Collegiate

Three Putnam competition books are available at AoPS .