Group Theory Prep for IIT JAM and Mathematics Exams

Group theory is a cornerstone of abstract algebra, but preparing for competitive mathematics exams requires more than just memorizing definitions. This text-only course provides a structured path to deeply understanding algebraic structures, helping you build the problem-solving speed and mathematical intuition needed to excel in exams like the IIT JAM. What you'll learn: - Learn the foundational definitions of groups, subgroups, and cyclic structures. - Master Lagrange's theorem, cosets, and normal subgroups with step-by-step proofs. - Apply group homomorphisms and isomorphism theorems to solve complex algebraic equations. - Analyze symmetric groups, alternating groups, and permutation representations. - Explore the basics of group actions and Sylow theorems for advanced classification. - Practice solving exam-style mathematical problems. Starting with core definitions and binary operations, you will progress systematically through structural properties, homomorphisms, and advanced classifications. This course is designed for undergraduate mathematics students preparing for competitive exams, with no prior abstract algebra experience required. Begin your journey into abstract algebra and elevate your exam preparation today.