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Explore fundamental concepts in group theory through this 75-minute lecture from MIT's Principles of Discrete Applied Mathematics course. Begin with the formal definition of a group and examine concrete examples including addition modulo n and multiplication modulo n. Learn the essential definitions of subgroups and cosets, then work through the statement and complete proof of Lagrange's theorem, a cornerstone result in group theory. Apply this powerful theorem to prove Fermat's Little Theorem, demonstrating the practical connections between abstract algebra and number theory. Gain a solid foundation in group-theoretic concepts that are fundamental to discrete mathematics and its applications.
