Abstract algebra

Abstract algebra studies the structures that share the rules of ordinary arithmetic. The two published units build binary operations, groups, and subgroups, then cyclic groups, homomorphisms, and Lagrange's theorem, with the symmetries of a square and modular arithmetic as running examples. The outline continues into normal subgroups and quotient groups, then rings, fields, and lattices, carrying the same structural ideas into richer systems.

Proof is the daily work here: you assemble arguments from blocks or fill in a missing step, with shorter checks answered as an expression or a value, and hints on about two thirds of the problems. Two of the five planned units are published today, and the syllabus grows as the rest land.