Polynomials and Sequence Spaces - Wild Linear Algebra - NJ Wildberger

Polynomials and Sequence Spaces - Wild Linear Algebra - NJ Wildberger

Explore polynomials and sequence spaces in this comprehensive lecture on Wild Linear Algebra. Delve into the interpretation of polynomials as functions and sequences, introducing concepts like falling and rising powers using D. Knuth's notation. Examine the connection between these powers and forward and backward difference operators. Investigate specific sequences, such as square pyramidal numbers, through the lens of difference calculus. Learn about various polynomial bases, including standard, lowering power, and raising power bases. Study important theorems like Newton's theorem and Archimedes' formula. Practice with exercises on finding the next term in sequences and applying the concepts learned throughout the lecture.