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# Precalculus learning recommendations

**Precalculus** typically refers to a course that provides the prerequisites necessary for calculus that have not been covered so far in the curriculum. This typically includes the theory of functions, trigonometry, and some advanced parts of algebra (such as inequalities). Some other topics may be included.

## First-time learning

If this description fits you ... | ... this might be the best recommendation | Cost |
---|---|---|

You have an interest in solving challenging mathematical problems and discovering mathematical ideas through the problem-solving process. | Precalculus by 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 QuoraYou can also take an Art of Problem Solving precalculus class, but this is more expensive. |
~$50 for the book, ~$10 for the solutions manual. $425 for a semester course (prices may change with time) |

You prefer to learn from videos that offer conceptual explanations of ideas, and you don't have an aversion to long videos. | The Center of Math precalculus videos (here) and their corresponding textbooks (store). These introduce ideas in a concepts-first fashion. Unfortunately, at the time of writing (March 2014), their precalculus video set does not cover all sections of the book. | The Worldwide Pre-Calculus book costs $9.95 (digital) and $29.95 (print). Videos require a decent Internet connection, but we expect the Internet connections of most clients to be adequate. |

You just want something basic to get you started. | We don't have a strong recommendation. If you are into video-based learning, and the Center of Math videos do not suit you, consider PatrickJMT. If you are willing to pay, consider Thinkwell's precalculus course | PatrickJMT is free Thinkwell course costs $150 for one year online access, plus more money for a CD set of the videos. |

## Filling in gaps

If you're learning calculus, and discover some gaps in your precalculus knowledge, we recommend watching select videos from PatrickJMT or Khan Academy, or reading any standard precalculus text, to fill in the relevant topical gaps. If you find that your conceptual understanding was inadequate and you're willing to spend more time filling in the gaps, consider watching the Center of Math precalculus videos above.

If you feel that the gaps are sufficiently severe, or are not sure exactly where you have gaps, consider using the ALEKS (website) for diagnosing your areas of weakness.