About MathCastle

MathCastle is a free place to learn mathematics the way a good textbook and a patient tutor would teach it: every course is written as a book with definitions, worked examples, proofs of the formulas, practice at each step, cumulative reviews and a final. It runs from Grade 4 arithmetic through Algebra, Geometry, Trigonometry, Precalculus, Calculus, Multivariable Calculus, Linear Algebra, Differential Equations, Statistics, Number Theory and Proof Writing, and then up the competition ladder: MathCounts, AMC 8/10/12, AIME, USAMO and the Putnam.

The problems

Every problem on the site is original. Nothing is copied from a past contest or another book. Each answer is checked by a program independently of the person who wrote it, and a problem is only published when the check passes. Most problems carry a complete worked solution, and the solve page can also unfold it one step at a time.

Still, mistakes happen. Every solve page has a Report a problem link. Reports go straight to the editors, and a problem with a confirmed error is pulled until it is fixed.

How difficulty works

Problems are labelled Easy, Medium, Hard, Challenge and Superchallenge relative to their topic. The site also records, anonymously, whether attempts on a problem are right or wrong, and problems that turn out to be much harder or easier than their label are recalibrated. A short placement quiz sets your starting range.

Your progress

Progress is kept on your device first, so you never need an account to use the site. With a free account it is also synced to the server, so lessons, streaks, flashcards and missed-problem reviews follow you between devices. See the privacy page for exactly what is stored.

Contact

Found an error, have a problem idea, or want to help write a course? Use the Suggest a problem page for problems and the report link on any solve page for corrections.