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 C alculus 1.3.1 High School 1.3.2 C ollegiate 1.4 C ombinatorics 1.4.1 Getting Started 1.4.2 Intermediate 1.4.3 Olympiad 1.4.4 C ollegiate 1.5 Geometry 1.5.1 Getting Started 1.5.2 Intermediate 1.5.3 Olympiad 1.5.4 C ollegiate 1.6 Inequalities 1.6.1 Intermediate 1.6.2 Olympiad 1.6.3 C ollegiate 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 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 C ollegiate 4 See also Books by subject Algebra Getting Started AoPS publishes Richard Rusczyk's, David Patrick's, and Ravi Boppana's Prealgebra which is recommended for advanced elementary and middle school students. AoPS publishes Richard Rusczyk's Introduction to Algebra advanced elementary, middle, and high school students. textbook, textbook, which is recommended for Intermediate Algebra by I.M. Gelfand and Alexander Shen. by Titu Andreescu and Zuming textbook, which 101 Problems in Algebra from the Training of the US IMO Team Feng AoPS publishes Richard Rusczyk's and Mathew Crawford's Intermediate Algebra 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 middle and high school students. Calculus The Hitchhiker's Guide to Calculus textbook, which is recommended for advanced by Michael Spivak. Top students swear by this book. by Michael Spivak. -- A fantastic resource for students AP Calculus Problems and Solutions Part II AB and BC 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 recommended for advanced middle and high school students. textbook, which is Intermediate AoPS publishes Dr. David Patrick's Intermediate Counting & Probability recommended for advanced middle and high school students. Mathematics of Choice by Ivan Niven. by Titu Andreescu and Zuming Feng. by Titu Andreescu and Zuming 102 Combinatorial Problems textbook, which is A Path to Combinatorics for Undergraduates: Counting Strategies Feng. Olympiad 102 Combinatorial Problems Generatingfunctionology by Titu Andreescu and Zuming Feng. Collegiate Enumerative Combinatorics, Volume 1 Enumerative Combinatorics, Volume 2 A First Course in Probability by Richard Stanley. by Richard Stanley. by Sheldon Ross Geometry Getting Started AoPS publishes Richard Rusczyk's Introduction to Geometry advanced middle and high school students. textbook, which is recommended for Intermediate Challenging Problems in Geometry on elementary geometry. Geometry Revisited -- A classic. -- A good book for students who already have a solid handle Olympiad Geometry Revisited -- A classic. by Hans Schwerfdtfeger. by Dan Pedoe. Geometry of Complex Numbers Non-Euclidean Geometry Projective Geometry Geometry: A Comprehensive Course by H.S.M. Coxeter. , Geometric Transformations II , and Geometric Transformations by H.S.M. Coxeter. Geometric Transformations I III by I. M. Yaglom. Collegiate Geometry of Complex Numbers Non-Euclidean Geometry Projective Geometry by Hans Schwerfdtfeger. by Dan Pedoe. Geometry: A Comprehensive Course by H.S.M. Coxeter. by H.S.M. Coxeter. Inequalities Intermediate Introduction to Inequalities Geometric Inequalities Olympiad The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities Michael Steele. Problem Solving Strategies Topics in Inequalities Olympiad Inequalities A<B (A is less than B) by Arthur Engel contains significant material on inequalities. Titu Andreescu's Book on Geometric Maxima and Minima by Hojoo Lee by Thomas Mildorf by Kiran S. Kedlaya by Pham Kim Hung by J. Secrets in Inequalities vol 1 and 2 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. by Titu Andreescu, Dorin 104 Number Theory Problems from the Training of the USA IMO Team 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. by Titu Andreescu and Zuming Feng. 103 Trigonometry Problems 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. by Heinrich Dorrie. 100 Great Problems of Elementary Mathematics 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. How to Solve It by George Polya. by Putnam Fellow Ravi Vakil. , Proofs Without Words II by Heinrich Dorrie. A Mathematical Mosaic Proofs Without Words Sequences, Combinations, Limits 100 Great Problems of Elementary Mathematics Olympiad Mathematical Olympiad Challenges Problem Solving Strategies by Arthur Engel. by Loren Larson. Problem Solving Through Problems General interest The Code Book Count Down Fermat's Enigma by Simon Singh. by Simon Singh. by William Dunham. by G. H. Hardy. by Marcus du Sautoy. by Roger B. Nelsen. by Richard Courant, Herbert Robbins and Ian Stewart. by Steve Olson. Godel, Escher, Bach Journey Through Genius A Mathematician's Apology The Music of the Primes Proofs Without Words What is Mathematics? 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. from the AMC. Contest Problem Books 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 ARML books: ARML-NYSML 1989-1994 ARML 1995-2004 Five Hundred Mathematical Challenges The USSR Problem Book Leningrad Olympiads (Published by MathProPress.com) -- An excellent collection of problems (with solutions). (see ARML). at AoPS. Olympiad 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 Hungarian Problem Book III Mathematical Miniatures Mathematical Olympiad Treasures Collections of Olympiads (APMO, China, USSR to name the harder ones) published by MathProPress.com. by Arthur Engel. by Loren Larson. Problem Solving Through Problems Collegiate Three Putnam competition books are available at AoPS .