Algebraic Structures: Groups and Rings

This lecture introduces the basic notions of groups and rings, the foundation of number manipulations. It covers number theory concepts like enumeration, combinatorial, divisibility, Icm, gcd, prime numbers, and the fundamental theorem of factorization. The lecture draws parallels between number construction and materials structure, emphasizing the different nature of atomic bonds. Next week, the discussion will continue with fields, vector spaces, and deriving results on the cubic structure of materials using prime numbers and basic geometry calculations.