Set theory

Set theory builds the language much of the rest of mathematics is written in. The two published units cover sets and their operations, then relations, functions, and the idea of cardinality that lets you compare the sizes of infinite collections. The outline continues into infinite sets and cardinal arithmetic, ordinals and transfinite induction, and the axiom of choice together with the statements equivalent to it.

The practice runs on proof in several forms: arguments you assemble from blocks, gaps you fill one step at a time, and responses you write out, alongside direct checks of definitions. Hints back about two thirds of the problems. Two of the five planned units are published today, with the transfinite material still to come.