Algebra learning recommendations

This page provides subject-specific learning recommendations for the subject algebra. See all our learning recommendations pages |

NOT TO BE CONFUSED WITH abstract algebra learning recommendations (abstract algebra is a component of upper division undergraduate mathematics) and linear algebra learning recommendations (linear algebra is a component of lower division undergraduate mathematics)

This page includes recommendations for learning basic algebra -- starting with the use of variables to denote unknowns and setting up and solving simple linear equations (typically called "prealgebra" in the US school system) and including all high school algebra.

Recommendations

Top recommendations for getting started (with prealgebra)

If this description fits you ...	... this might be the best recommendation	Cost
You want a problem solving-style introduction to the basic techniques, along with supplementary videos and an online practice system.	The Art of Problem Solving book Prealgebra by Richard Rusczyk, David Patrick, Ravi Boppana. The book is part of the Art of Problem Solving (AoPS) book series that has been reviewed very favorably, for example, on Quora. The prealgebra book is accompanied by a series of free videos, which cover all of the topics in the textbook. It is synchronized with the free adaptive online learning system Alcumus. AoPS also offers online classes (paid) that are synchronized with the contents of the books.	~$50 for the book Videos are free Courses: $285 each for Prealgebra 1 and Prealgebra 2
You want a conceptual and visual introduction to algebra that is structured more like a reading experience than a workbook.	Vision in Elementary Mathematics by W. W. Sawyer, ISBN 978-0486425559, Amazon paperback	~$12 (Kindle), ~$13 (used hardcover, may not last for long), ~$27 (paperback), ~$17 (mass market paperback)
You are looking for a relatively straightforward introduction to the subject that is very similar to the school curriculum (this may be ideal for students who are not particularly interested in mathematics, or for people learning very far ahead; it can also be used to supplement the above recommendations).	Consider the courses offered by ThinkWell (pre-algebra) and Live Online Math (pre-pre-algebra and pre-algebra). ThinkWell is a little more fast-paced, whereas Live Online Math is somewhat more slow-paced and has more in-video pauses that give people more of an opportunity to digest material.	$125 (plus extra cost for physical workbooks and CDs of videos) for ThinkWell $100 (plus extra cost for supplementary live tutoring) for Live Online Math.

Top recommendations for mastering a range of advanced algebraic techniques (high school algebra and beyond)

If this description fits you ...	... this might be the best recommendation	Cost estimate (values are approximate)
You want a problem solving-style coverage of high school algebra techniques.	Introduction to Algebra by Richard Rusczyk. The book is part of the Art of Problem Solving book series that has been reviewed very favorably, for example, on Quora. It is synchronized with the free adaptive online learning system Alcumus. AoPS also offers online classes (paid) that are synchronized with the contents of the books.	~$50 for the book Courses: $315 each for Algebra 1 and Algebra 2, $440 for Algebra 3.
You are looking for an old-fashioned book that covers a wide range of algebraic tricks quickly with as little fluff as possible.	Higher Algebra: a Sequel to Elementary Algebra for Schools by Henry Sinclair Hall and Samuel Ratcliff Knight, Amazon paperback. This is considered a classic resource for advanced algebraic tricks.	~$20
You are looking for a book by mathematicians that covers advanced topics in depth and goes into the logic and motivation behind things.	Algebra by Israel M. Gelfand and Alexander Shen, ISBN 978-0817636777, Amazon paperback. The book has received highly positive reviews, and co-author Israel Gelfand is a highly renowned mathematician.	~$22
You are looking for courses in algebra that closely parallel what's taught in schools	Thinkwell's Algebra 1 and Algebra 2 courses Live Online Math's Algebra course	$125 for each Thinkwell course (total $250) + $25 for CD set for the course (total $50) ~$100 for the Live Online Math video course (plus more for supplementary tutoring)