Polynomials: Definitions and Operations

This lecture introduces the concept of polynomials, defining them as expressions of the form P(x) = a₀ + a₁x + ... + aₙxⁿ. It covers the properties of polynomials, such as degree and coefficients, and explores operations like addition and multiplication. The lecture also discusses the structure of polynomials as an algebraic system and the relationship between polynomials and functions. Additionally, it delves into the concept of polynomial rings and the role of polynomials in forming A-modules. The lecture concludes with a study of the degree of polynomials, including the properties of degree in polynomial addition and multiplication.