Algebra II
A continuation of Algebra I from MIT OpenCourseWare, covering the structures that build on group theory: rings, ideals, and fields. The course moves through polynomial rings, modules, and factorization before turning to number theory questions like the behavior of integers in quadratic number fields. The back half develops field extensions and Galois theory, the machinery that explains which polynomial equations can be solved by radicals and which cannot. Materials include lecture notes, problem sets, and exams with solutions, following MIT's standard OpenCourseWare format for upper-level undergraduate mathematics. No enrollment or certificate is offered; the course is self-study material released under a Creative Commons license, aimed at students who have already completed a first course in abstract algebra covering groups and basic ring theory.