Course Eleven · The Complete Micro-Course
The whole college algebra canon, rebuilt as 263 numbered videos — each one a single idea, built in the order the ideas depend on each other. Not a problem set with the reasoning removed: the rules themselves, and why each one has to be true given the last.
How the course works
Algebra is the subject where students most often learn the steps without the reason, and then cannot tell a rule from a habit. This course is built the other way. Each new kind of number is introduced so the old rules stay true; polynomials behave like integers because they were built to; every logarithm law is an exponent law seen from the other side. Nothing appears before the thing it depends on, and every dependency is a number you can follow back.
Three kinds of video: atoms (one definition, rule, or distinction, about twenty seconds), procedures (one method, worked start to finish — classifying a number, solving a system), and capstones (several ideas run together on one problem).
A whole family of entries exists to name the error and put it beside the rule it breaks — the invisible-parentheses error, the zero-power error, the negative-exponent sign error, the radical split. Naming a mistake precisely is usually what stops it.
The whole map
New videos post daily until the course is complete. Live ones link straight to the short; the rest are on their way.
The receipts
Behind the course sits a reference document in which every rule and worked example is traced to its source. The anchor is an openly licensed university text — OpenStax’s College Algebra — and mathematics has an advantage the other courses do not: most claims here can be checked by derivation rather than citation. Every worked example is recomputed and logged before its video is made.
Spot an error? Tell me the video number and the step — corrections get made in the open. In a subject where the answer is checkable, a wrong step is a wrong step, and it gets fixed.
Follow along
The course releases in order on YouTube — one idea at a time until all 263 are live. Subscribe to catch each one, or leave your email for an occasional note when a course finishes.
A note when a course finishes. Nothing else.