Polynomial Applications: Combinatorial Computations

This lecture explores the combinatorial applications of polynomials, highlighting the connection between arithmetic operations and operations with finite sets. Through examples like paying a sum with different coins, the instructor demonstrates how to use polynomials to speed up combinatorial computations. The lecture also covers operations with polynomials, including addition, multiplication, substitution, differentiation, and integration. Furthermore, it delves into identities with binomial coefficients, showcasing proofs and computations using binomial theorem and induction.