Translating Polynumbers and the Derivative - Arithmetic and Geometry Math Foundations

Explore the foundations of calculus through an algebraic approach to polynomials and derivatives in this 37-minute mathematics lecture. Delve into the composition and translation of polynumbers, leading to the introduction of Taylor polynomials and sub-derivatives. Challenge traditional calculus concepts by examining the subject without relying on limits or real numbers. Engage with exercises to calculate Taylor polynumbers and gain a fresh perspective on mathematical foundations. This lecture, part of the MathFoundations series, aims to reshape understanding of calculus, drawing inspiration from the works of Euler and Lagrange.

Introduction
Composition of polynumbers
Translation of a polynumber
?Examples of left translates
When a polynumber is translated twice
Translating a polynumber by an integer
Recasting using Bi polynumbers
An exercise to calculate a Taylor polynumber
Another look at the Taylor polynumber
Exercise