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Our Introduction Series is designed as a complete curriculum for high-performing students in grades 6-10.
Please also see our User's Guide and Frequently Asked Questions about AoPS texts.
Below is a brief guide to the books in our Introduction Series. We have provided two diagnostic tests for each book in the series. The pre-test is a brief diagnostic test covering the material necessary to begin the book. Students should be able to solve all (or almost all) of the problems on the pre-test before starting with the book. The post-test is a diagnostic test that consists of problems similar to those in the book. If a student can comfortably solve most or all of the problems on the post-test, then the book would primarily serve as review for the student. Parents and teachers can also use the books' table of contents and indexes as guides to the material covered in each book.
We recommend that new students start with the Introduction to Algebra text. All of the other books will require proficiency with basic algebra concepts.
As students gain more proficiency with algebra, they can proceed to either of our discrete math books: Introduction to Counting & Probability and Introduction to Number Theory. These texts require some knowledge, but not complete mastery, of basic algebra. Students need not have completed Introduction to Algebra before proceeding with one of the discrete math books.
The discrete math topics covered in Introduction to Counting & Probability and Introduction to Number Theory are becoming increasingly important in a wide variety of scientific and technical careers, but unfortunately are still significantly underrepresented in most middle and high school math curricula. These topics are also highly represented in competitions such as MATHCOUNTS, the AMC contests, and ARML. In our experience, students who learn this material in middle or high school have a much easier time in later college-level coursework than students who see this material in college for the first time.
Generally, students will wait until they have finished Introduction to Algebra before proceeding to Introduction to Geometry.
Students should have mastered the Introduction Series before proceeding to the Intermediate Series. The Introduction Series books' post-tests (shown above) will serve as a guideline—if the student has mastered a Introduction book's post-test, then he or she is most likely ready for the corresponding Intermediate book.
