Understanding Cosets: Foundations and Applications in Mathematics

This lecture explores cosets, an essential concept in abstract algebra. Starting with their definition and importance, it delves into their origins and foundational group theory principles. Key attributes like left and right cosets, normal subgroups, and group partitions are examined. Applications are highlighted in cryptography, error correction, modular arithmetic, and real-world examples in physics and mathematics. The session concludes with insights into their significance for advanced...