Six pillars of higher mathematics. Each page is a cluster: who it helps, what you should be able to do, and a study order into explainers, calculators, glossary entries, and pathways that already live on this site.
Choose a pillar
A pillar is a map of one subject. A pathway is an ordered route for one audience, with checkpoints you produce. Start on a pillar when you want the ideas and the links. Follow a pathway when you want the sittings. There are three pathways: an AP Calculus AB bridge, a linear algebra first course, and intro to proofs. Probability does not have a separate pathway. Its pillar is the order.
Choose by the work in front of you, not by which title sounds more advanced. If algebra and graphs are the actual gap, open calculus foundations or linear algebra and use the glossary when a word is doing real work. The FAQ on how to use the site describes the same loop: topic, explainer, glossary, calculator, then a pathway.
Audience. Readers beginning calculus, or readers who can differentiate and still cannot say what the derivative measures.
Next step. What a derivative actually measures. If computation is already easy, use the AP Calculus AB bridge.
Audience. Readers with single variable calculus who are meeting partial derivatives, gradients, or vector fields.
Next step. The linear algebra pathway if matrices are new. Otherwise Jacobian matrices, then the Jacobian matrix calculator.
Audience. Readers starting vectors and matrices, or preparing for several variables.
Next step. Eigenvalues in plain language, the Gram Schmidt calculator, or the first course pathway for ordered sittings. For a 3 by 3 matrix, the same map includes a determinant and inverse, row reduction, and the 3x3 eigenvalue calculator.
Audience. Readers beginning chance or data, or mixing up the two directions of a conditional probability.
Next step. Bayes theorem without the fog, then the Bayes theorem calculator once you can name the prior and the two likelihoods.
Audience. Readers whose calculus was mostly computation, and whose next course will ask for arguments.
Next step. Epsilon delta intuition, then the intro to proofs pathway to write the checkpoints.
Audience. Readers meeting equations that relate a function to its derivative, including separable equations and slope fields.
Next step. Separate one equation on paper, then read the separable walkthrough. A linear equation y' + P(x) y = Q(x) is the integrating factor calculator. Constant coefficients, after that, are the second order calculator, the Wronskian calculator, and the Laplace transform calculator.
If you can compute derivatives and freeze on "for every epsilon there exists a delta," read calculus foundations through the derivative and integral ideas, then switch to real analysis and proof habits. The intro to proofs pathway is the writing practice for that switch.
If the next course is multivariable calculus, do linear algebra through eigenvalues before multivariable and vector calculus. Jacobian matrices in plain language is the handoff. Matrices as pictures make that page shorter.
If the interesting object is a rate that depends on the current amount, stay on differential equations and the separable explainer. Series and proof habits can wait unless the course lists them. If the interesting object is a conditional probability, stay on probability and statistics. Calculus is not a gate for Bayes theorem.
The pillars link into the pathways. The pathways link back. Use the pathways hub to compare audience, starting point, and time shape.
A full book or course notes, when a pillar stops on purpose, is on the sources page. Questions about the study loop are on the FAQ.
Open the pillar that matches the course in front of you. Calculus foundations if change and accumulation are the gap. Linear algebra if matrices are the gap. Probability and statistics if chance or data are the gap. Real analysis if proofs are the gap. Multivariable calculus and differential equations usually come after a first calculus course. If you are unsure, pick the page whose first checkpoint you can actually do this week.
A pillar is a cluster: the ideas, the outcomes, the pitfalls, and a suggested order into pages that already exist. A pathway is a longer ordered route for one audience, with checkpoints you produce. There are three pathways. Start on a pillar for the map. Follow a pathway when you want the sittings.
No. Each pillar says what to hold in mind and which lesson on this site to open next. A full development lives in an open book or course notes. The sources page lists OpenStax, MIT OpenCourseWare, and other references used across the site.
From the pillars into explainers
From calculus foundations. Also the repair if Jacobian language feels empty.
From calculus foundations, when a curve is a relation rather than a formula for y.
From calculus foundations and from real analysis.
From linear algebra, before the 2 by 2 calculator.
The handoff from linear algebra into multivariable calculus.
From vector calculus, after you can say what a curl is asking.
From multivariable calculus, after gradients are perpendicular to level curves.
From probability and statistics, after a small counting update.
After you can name what the output should mean. The FAQ says how the tools fit the loop.