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High school mathematics learning recommendations
This page lists recommendations for learning high school mathematics.
Contents
Subject-specific recommendations
See detailed recommendations for each subject:
- Algebra learning recommendations
- Precalculus learning recommendations
- Single-variable calculus learning recommendations
General recommendations
Textbooks
We recommend the Art of Problem Solving textbooks. Information below:
| Book | Author | ISBN and purchase links | Why we're recommending it |
|---|---|---|---|
| Introduction to Algebra | Richard Rusczyk | ISBN 978-1-934124-14-7, paperback | This is a first year high school algebra textbook published by Art of Problem Solving that teaches elements of mathematical thinking and problem solving, as opposed to rote drill. The series has been reviewed very favorably, for example, on Quora. |
| Introduction to Geometry | Richard Rusczyk | ISBN 978-1-934124-08-6, paperback | This is a high school geometry textbook published by Art of Problem Solving that teaches elements of mathematical thinking and problem solving, as opposed to rote drill. The series has been reviewed very favorably, for example, on Quora. |
| Measurement | Paul Lockhart | ISBN 978-0674057555, Amazon paperback | Paul Lockhart is a professional mathematician who spent years teaching high school and developing innovative curriculum. This offers his take on geometry and calculus. The portion on geometry can be learned concurrently with geometry, and the portion on calculus can be learned concurrently with calculus. |
| Intermediate Algebra | Richard Rusczyk and Matthew Crawford | ISBN 978-1-934124-04-8, paperback | This is a second year high school algebra textbook published by Art of Problem Solving, that teaches elements of mathematical thinking and problem solving, as opposed to rote drill. The series has been reviewed very favorably, for example, on Quora. |
| Precalculus | Richard Rusczyk | ISBN 978-1-934124-16-1, paperback | This is a precalculus textbook, published by Art of Problem Solving, that teaches elements of mathematical thinking and problem solving, as opposed to rote drill. The series has been reviewed very favorably, for example, on Quora. |
| Calculus | David Patrick | ISBN 978-1-934124-24-6, paperback | |
| Excursions in Calculus: An Interplay of the Continuous and the Discrete | Robert M. Young | ISBN 978-0883853177, Amazon paperback | This book has some very nice applications of calculus, and studying it concurrently with calculus will help reinforce your understanding of calculus. |
Online resources
See our online mathematics learning resources for a comprehensive list of resources, most of them including content specific to high school mathematics.
If you're looking for more
Contest mathematics
See our contest mathematics learning recommendations. For more on the benefits of learning contest mathematics, see contest mathematics learning benefits.
Sneak peek of higher mathematics
If you're a high school student interested in math for its own sake, you should consider learning some higher math while in high school.
Some books that we recommend for learning higher math that you can learn from without knowing calculus are:
- Groups and Symmetry: A Guide to Discovering Mathematics and Knots and Surfaces: A Guide to Discovering Mathematics by David Farmer and Theodore Stanford.
- The Knot Book by Colin Adams.
- The Shape of Space by Jeffrey Weeks.
- Yearning for the Impossible: The Surprising Truths of Mathematics by John Stillwell.
- Elementary Number Theory by Jones and Jones.
- Galois' Theory Of Algebraic Equations by Jean-Pierre Tignol.
We also recommend the following books, that assume calculus as a prerequsite:
- A Primer of Analytic Number Theory: From Pythagoras to Riemann by Jeffrey Stopple.
- Excursions in Calculus: An Interplay of the Continuous and the Discrete by Robert Young.
Proper study of undergraduate-level mathematics
See these recommendations pages:
- Lower division undergraduate mathematics learning recommendations: Specifically, multivariable calculus learning recommendations and linear algebra learning recommendations.
- Upper division undergraduate mathematics learning recommendations: Specifically, undergraduate analysis learning recommendations, abstract algebra learning recommendations, and topology learning recommendations.
General mathematical enrichment
See:
- Mathematics reading recommendations: This lists books about mathematics that are meant for wide audiences and can be read without paper and pencil. Most of them do not require knowledge of mathematics beyond high school.
- Books about mathematical history provides a more detailed list of books specifically about the history of mathematics.
