Course Contents

Groups, Examples and consequences, Subgroups, Subgroup lattice, Relation between groups, System of generators and relations in a group, Cyclic groups, Group and symmetries, Complexes and Coset decomposition of a group, Lagrange’s theorem, Normalizer and Centralizer, Conjugacy relation in a group, Normal Subgroups, Quotient groups, Group homomorphism, Kernel of homomorphism, Isomorphism theorems, Cayley’s theorem, Permutation groups, cyclic permutation, Order of a permutation, Even and odd permutation, Alternating group, Generators of the symmetric and Alternating groups.

Course Learning Outcomes

This Course focuses on basic topics in abstract algebra while introducing to students the language of advanced mathematics and techniques involved in proofs. It is expected that the students will understand and produce proofs. Once a student successfully completes the course, the student shall be ready to take other theoretical courses. This is the fundamental course in abstract algebra, the majority of follow up courses in both pure and applied mathematics assumes the material covered in this course.