Explore polynomials in this 1-hour 15-minute lecture from CMU's "Great Ideas in Theoretical Computer Science" course. Delve into fields, prime power, and polynomial operations including addition, multiplication, and division. Learn about evaluation, interpolation, and fitting polynomials to data. Discover applications in error-correcting codes and the Lagrange interpolation method. Gain insights into theoretical computer science concepts through clear explanations and examples provided by Professor Ryan O'Donnell.