The goal of this course is to introduce and study the basic notions of abstract algebra.
This is an introductory course to the theory of rings and fields.
The students are going to solidify their knowledge of ring and module theory with a major emphasis on commutative algebra and a minor emphasis on homological algebra.
The aim of this course is to learn the basics of the modern scheme theoretic language of algebraic geometry.
This is a course about group schemes, with an emphasis on structural theorems for algebraic groups (e.g. Barsotti--Chevalley's theorem). All the basics will be covered towards the proof of such theorem, with an estress on the modern presentation using scheme theory and modern algebraic geometry.