Descriptif

Prerequisites: MAA203, MAA204

MAA303 mainly focuses on general group theory. The first part of the course will be dedicated to the basic notions that one uses to study groups: normal subgroups, quotient group, simple groups... The second part of the course will focus on group actions. After introducing them, we will see a number of interesting applications in algebra, geometry and arithmetic, such as the so-called Sylow theorems. At the very end of the course, we will move on from groups to other usual algebraic structures, such as rings and fields. This part of the course will only be a short introduction to ring and field theory. Extra material not covered during the course itself will be provided for those students who would like to go further and understand how groups, rings and fields are deeply related through the study of algebraic equations and Galois theory.