Math books

These math books are recommended by Art of Problem Solving administrators and members of the AoPS 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 who are participating in contests like AMC 8/10 and MATHCOUNTS.
  • Intermediate is recommended for students who can expect to pass the AMC 10/12.
  • 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 AoPS Wiki:Linking books page.


Books By Subject

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

Intermediate

Abstract Algebra

Collegiate

Calculus

Getting Started

Single Variable (Intermediate)

Multivariable (Collegiate)

Analysis

Collegiate

Combinatorics

Getting Started

[Combinatorial problems from AMSP] is a great discrete math book covering topics ranging from permutations and combinations to using creativity to count to doing proofs and then gives exposure to advanced topics like probability theory.Great for AMC 8 /10/12

Intermediate

Olympiad

Collegiate

Geometry

Getting Started

Intermediate

Olympiad

Collegiate

Topology

Collegiate

  • Topology by James Munkres. Topology is arguably the most renowned topology textbook of all time. It also contains an excellent introduction to set theory and logic.

Inequalities

Intermediate

Olympiad

Collegiate

Number Theory

Getting Started

Olympiad

Collegiate

Trigonometry

Getting Started

Intermediate

Olympiad

Problem Solving

Getting Started

Intermediate

Olympiad

General Interest

Math Contest Problem Books

Elementary School

Getting Started

Intermediate

Olympiad

Collegiate

See Also