Art of Problem Solving Precalculus Set
This package includes the following items:
Covers complex numbers, vectors, matrices, and trigonometry at a deeper level than a typical high school course.
The intermediate series picks up where the introductory series leaves off. Please read that description (immediately preceding this one) as it applies to this series as well. Note that all AOPS books are intended for high-performing (motivated) math students. These are rigorous texts that require a high level of commitment from students, but the benefits are worth the extra effort. For comparison, this curriculum is more advanced than Saxon and rather like Life of Fred on steroids. It is like LOF in that often, teaching takes place through problem solving, even in the solutions to the problems. These books are huge compared to the LOF volumes which are, even then, largely devoted to the story of Fred's life. Math in LOF is taught in that context; we understand that Fred needs to calculate the derivative of a stock market equation in order to invest his penny while the slope is increasing AND why discovering that vertical asymptote resulted in his becoming a millionaire. Here, the heart of the course is the problem-solving. Virtually all of the text is devoted to this. Students are preparing for problem-solving competitions here and learning techniques and strategies to win. The other MAJOR difference is the amazing, complete solution manual provided in the AOPS curriculum. After working in LOF Calculus with Stephen, I REALLY appreciate having more than just an answer (honestly, it would be nice to not have to work through the problems myself when a question arises-call me lazy).
Students beginning this series should have either completed the Introductory level or, if coming from another curriculum, have completed Algebra I and Geometry at a minimum. Even then, they should take the diagnostic test for AOPS Introduction to Algebra and only tackle Intermediate Algebra if indicated. After completing Intermediate Algebra, students can choose to take either Intermediate Counting & Probability or Precalculus next, or do both simultaneously. Both should be completed before beginning Calculus. A brief description of courses appears below; see our website Table of Contents pages for a more complete scope and sequence.