Polynomials

Explore the fundamental concepts of polynomials in this comprehensive lecture. Delve into formal definitions of fields and finite fields before examining polynomials in depth. Learn about adding, multiplying, and dividing polynomials, as well as the concept of "division with remainder." Investigate polynomials in F[x], polynomial evaluation, and roots. Discover Lagrange Interpolation and various methods of representing polynomials. Gain insights into practical applications, including sending messages on noisy channels and using repetition codes. This in-depth exploration provides a solid foundation for understanding polynomials and their diverse applications in mathematics and communication theory.