About CalcPath

Each subject is a course: a sequence of chapters, each split into numbered sections you can link to directly. The writing follows one house rule borrowed from the best textbooks: statements are separated from discussion. Definitions, theorems, propositions, proofs, and worked examples sit in clearly marked, numbered blocks (e.g. “Theorem 3.2”), while the surrounding prose motivates and unpacks them. Intuition boxes give the informal picture; every chapter ends with the mistakes students actually make.

Every section is backed by practice questions tied to that exact section, so “Review the explanation for this topic” from any practice question lands you on the material it tests.

Free-response answers are graded by an expression-equivalence engine, not string matching: an exact radical like √2/2, the equivalent fraction, or a sensibly rounded decimal are all accepted when they mean the same thing. Multiple-choice questions grade instantly. Wrong answers offer a hint first, then the full worked solution — every solution shows its steps, not just the result.

If a question ever seems wrongly graded, use Report issue on it. Reports arrive with the exact question and what was typed, and we read every one.

There are no accounts. Progress is stored in your browser and never tied to an identity. If you want it on another device, the progress page exports it as a file you can import elsewhere. There are no analytics, no trackers and no ads.

The content is plain text: every chapter is a Markdown/LaTeX document and every question bank a data file, versioned together with the site’s code. Mathematics renders with KaTeX. Pages are served statically wherever possible, so chapters load fast and read the same on a phone as on a desktop. Because content is data, fixes ship the same way code does — a reported typo is a one-line change away from production.

CalcPath aims to be self-contained, but no single resource should be anyone’s only one. These are the references we ourselves reach for, and the standards the writing here aspires to:

• Linear Algebra Done Right (Sheldon Axler) — the model for how this site separates statements from discussion; a free electronic edition is available from the author.
• MIT OpenCourseWare — full university courses with lectures, notes, and exams, free.
• Paul’s Online Math Notes — thorough calculus and differential-equations notes with many worked problems.
• 3Blue1Brown — visual intuition for linear algebra, calculus, and analysis that pairs well with formal study.
• Khan Academy — gentle video-first coverage when a topic here feels too fast.
• OpenStax — free, peer-reviewed full textbooks for calculus, statistics, and precalculus.
• ProofWiki and Wolfram MathWorld — reference for definitions and named theorems.
• Desmos and GeoGebra — free graphing tools; plotting the function you’re studying is never wasted time.

For deeper study beyond free resources: Abbott’s Understanding Analysis, Spivak’s Calculus, Velleman’s How To Prove It, and Gallian’s Contemporary Abstract Algebra are widely loved companions to the corresponding subjects here.

CalcPath is in active development and shaped directly by reports from people using it. Spotted a wrong answer, an unclear explanation, or anything off? Tell us on the feedback page — or use Report issue right where you found it.