Math Books - AOPS Recommended.pdf

Math books

Math books

These

These

 _{are recommended by}

 _{are recommended by Art of Problem Solving}

_{Art of Problem Solving administrators and members}

 _{administrators and members}

of the

of the AoPS-MathLinks Community

AoPS-MathLinks Community..

Levels of reading and math ability are loosely defined as follows:

Levels of reading and math ability are loosely defined as follows:

Elementary is for elementary school students up through possibly early middle school.

Elementary is for elementary school students up through possibly early middle school.

Getting Started is recommended for students grades 6 to 9.

Getting Started is recommended for students grades 6 to 9.

Intermediate is recommended for students grades 9 to

Intermediate is recommended for students grades 9 to 12.

12.

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

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

an undergraduate level.

an undergraduate level.

Collegiate is recommended for college and university students.

Collegiate is recommended for college and university students.

More advanced topics are often left with the

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

above levels unassigned.

Books by subject

Books by subject

 Algebra

 Algebra

AoPS publishes Richard Rusczyk's Introduction to Algebra textbook, which is recommended AoPS publishes Richard Rusczyk's Introduction to Algebra textbook, which is recommended for advanced elementary, middle, and high school

for advanced elementary, middle, and high school students.students.

Intermediate

Intermediate

Algebra by I.M. Gelfand and Alexander Shen. Algebra by I.M. Gelfand and Alexander Shen.

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

Zuming Feng

AoPS publishes Richard Rusczyk's and Mathew Crawford's Intermediate Algebra textbook, AoPS publishes Richard Rusczyk's and Mathew Crawford's Intermediate Algebra textbook, which is recommended for advanced middle and

which is recommended for advanced middle and high school students.high school students. Complex Numbers from A to... Z by Titu Andreescu

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

 Analysis

 Analysis

Counterexamples in Analysis by Bernard R. Gelbaum

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

Calculus

Calculus

High School

High School

Calculus by Michael Spivak. Top

Calculus by Michael Spivak. Top students swear by this book.students swear by this book. The Hitchhiker's Guide to Calculus by Michael Spivak.

The Hitchhiker's Guide to Calculus by Michael Spivak.

AP Calculus Problems and Solutions Part II AB and BC -- A fantastic resource for students AP Calculus Problems and Solutions Part II AB and BC -- A fantastic resource for students mastering the material required for the AP

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 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 classic.

Olympiad

Geometry Revisited -- A classic.

Geometry of Complex Numbers by Hans Schwerfdtfeger. Geometry: A Comprehensive Course by Dan Pedoe. Non-Euclidean 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

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

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

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. 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 William 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.

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:

o ARML-NYSML 1989-1994 (see ARML). o ARML 1995-2004

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

The USSR Problem Book

Leningrad Olympiads (Published by MathProPress.com)

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 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