
Course Description
Introduction to Group Theory
This course introduces the student to the basic language and structure of group theory — the study of algebraic systems that capture symmetry and structure. Students will learn the group axioms, recognize and construct examples and non-examples, work with subgroups, cyclic and permutation groups, and study structure-preserving maps (homomorphisms and isomorphisms). The course emphasizes proof-based reasoning, conceptual understanding, and applications of groups in symmetry, geometry, and cryptography. Prior exposure to basic set theory and functions is helpful but not required.
Course Summary
Over five weeks (27 Oct – 28 Nov 2025) with two sessions per week, learners will move from the foundational idea of an algebraic structure to concrete constructions (permutations, cyclic groups), then to structure-preserving maps and quotient constructions, finishing with real-world applications. Assessment includes one CAT, continuous assignments/quizzes, and a final exam. The course balances short proofs and conceptual tasks, minimizing heavy computation while developing rigorous mathematical thinking.
- Teacher: Admin User