The course discusses how algebra allows us to abstract out the geometric objects and numbers. This leads to an understanding of fundamental properties of geometry and numbers as well as allows us to manipulate them in ways not possible directly. This has resulted in some of the most remarkable applications of mathematics in real life.
INTENDED AUDIENCE: All undergraduate science and engineering students
COURSE LAYOUT Week 1: Introduction to abstraction,Introduction to GroupsWeek 2: Properties of Finite Groups,Applications of GroupsWeek 3: Introduction to Rings,Properties of Finite RingsWeek 4: Introduction to IdealsWeek 5: Properties of IdealsWeek 6: Applications of Ideals and RingsWeek 7: Introduction to FieldsWeek 8: Applications of Finite Fields