Three self study maps through pages that already live on Higher Math Guide. Use one when you want an order, not a single article. They are educational routes, not official curricula, and not a substitute for a course or a tutor.
Choose a route
The useful differences are who the route is for, which page you should open first, and what kind of work the sittings contain. None of these maps promises a number of hours. The shape is the point.
Audience. Readers who already differentiate and integrate in an AP Calculus AB course and want meaning, series, or a first differential equation.
Starting point. Calculus foundations if the rules feel rusty. Otherwise what a derivative actually measures.
Time shape. Reading plus short checks on the derivative, limit, and Riemann calculators. Series and separable equations add sittings when they are new.
Audience. Readers starting vectors and matrices who want geometry before a pile of formulas. Calculus can wait until the Jacobian.
Starting point. The linear algebra topic, then the glossary entries for vector and matrix.
Time shape. Picture checks on 2 by 2 examples. Proofs of abstract facts are slower and belong with intro to proofs.
Audience. Readers whose calculus was mostly computation and whose next course will ask for arguments.
Starting point. Real analysis and proof habits, then epsilon delta intuition.
Time shape. Slower, because each checkpoint asks you to write and rewrite. A numerical table is scratch, not a proof.
If you can compute derivatives but freeze when a definition says “for every epsilon there exists a delta,” start the AP Calculus AB bridge through the derivative and integral steps, then switch to intro to proofs for the epsilon delta explainer and the three written checkpoints.
If the next course is multivariable calculus, do the linear algebra first course through eigenvalues, then read Jacobian matrices in plain language before the multivariable and vector calculus intro. Matrices as pictures make that handoff shorter.
If algebra and graphs are the actual gap, do not start on a pathway. Read calculus foundations or the linear algebra topic first, and use the glossary when a word is doing real work. The site FAQ describes the same loop: topic, explainer, glossary, calculator, then a pathway.
These maps do not invent articles. They order pages that already exist, and a few pages serve more than one route.
Choose by the work in front of you. AP Calculus AB skills that need meaning: the AP Calculus AB bridge. A first matrix course: the linear algebra first course. A first course that asks for arguments: intro to proofs. If you are unsure, pick the starting point you can actually do this week.
Yes. They overlap on purpose. Finish the checkpoints on one route before you hop, so the order still does its job. A natural pair is the calculus bridge and then intro to proofs, or linear algebra and then the multivariable topic.
No. A pathway is a reading order on this site. It does not list every theorem in a course, and it does not claim to match an exam board. For open textbooks and courseware, see the sources page.
Explainers these pathways use
Early on the AP Calculus AB bridge, and a repair if Jacobian language feels empty.
On the AP Calculus AB bridge, after the derivative explainer.
On the calculus bridge and the proofs pathway.
Core of the linear algebra first course, before the 2 by 2 calculator.
The later bridge from the linear algebra route toward several variables.
The study loop, if you want it before you pick a pathway.