WSGT-2024

The Department of Applied Sciences, Indian Institute of Information Technology Allahabad (IIIT-A) is going to organize a weekly seminar series on group theory starting from August 2024 to November 2024 in a hybrid mode (preferably offline). It aims to provide students with a comprehensive understanding of fundamental concepts, structures, and applications of group theory through a series of structured lectures, interactive discussions, and collaborative problem-solving sessions. We will focus on enhancing students’ ability to construct and present rigorous mathematical proofs, use theoretical knowledge in problem-solving, foster a collaborative learning environment to encourage peer-to-peer learning, and prepare them for further studies or research in abstract algebra and related fields by gaining confidence and proficiency in group theory. The concept of group theory will also be illustrated by examples from geometry, linear algebra, and combinatorics point of view.

Student Learning Outcomes:

* Recognize groups and prove they are groups
* Identify subgroups, normal subgroups, order of elements, and prove that the identification is correct
* Find multiple examples of groups having specified properties (commutative, noncommutative, cyclic, non-cyclic, finite, finite exponent, etc.)
* Find the number of group homomorphisms between two groups
* Prove and apply the Fundamental Homomorphism Theorem, the isomorphism theorems, and Lagrange’s theorem
* Classify finite groups as abelian, non-abelian, cyclic, direct products, etc.
* Find the commutator subgroup of a given group
* Identify solvable and nilpotent groups
* Apply group theory
* Take benefit for competitive exams also.