This course will introduce abstract groups. We will start with definitions, basic properties and constructions and cover many important theorems in basic group theory, such as Lagrange’s theorem, Cauchy’s theorem and Sylow theorems. A major emphasis of the course will be to present numerous worked-out examples and problems. A part of the lecture every week will be devoted to explicit calculations.
INTENDED AUDIENCE:BSc, MSc students studying mathematics PREREQUISITES: Any BSc student who is familiar with high school mathematics can take this course INDUSTRY SUPPORT: NIL
Week 1: Motivation, definition, examples and basic properties Week 2: Subgroups, subgroups of integers, homomorphisms Week 3:Quotient groups, isomorphism theorems Week 4: Group operations, counting formula Week 5: Symmetric groups Week 6: Operations of a group on itself, class equation Week 7: Sylow theorems I Week 8: Sylow theorems II