Translating polynumbers and the Derivative | Arithmetic and Geometry Math Foundations 69 скачать в хорошем качестве

Translating polynumbers and the Derivative | Arithmetic and Geometry Math Foundations 69

We begin moving towards calculus with polynumbers/polynomials by introducing the Derivative D=D_1 in a simple algebraic way. First we discuss composition of integral polynumbers, and the translation of a polynumber by an integer. This leads to the Taylor (bi) polynumber/polynomial of a polynumber/polynomial, which contains not only the usual derivative, but also higher analogs called sub-derivatives, denoted D_2, D_3 etc. This lecture should be disorienting but exciting to those who have been indoctrinated into thinking that calculus is analysis, resting on limit notions and so called `real numbers'. A dramatical shift of the mathematical landscape is at our doorstep: a shift going back to Euler and Lagrange. This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. Video Content: 00:00 Introduction 4:28 Composition of polynumbers 8:47 Translation of a polynumber 11:26 ?Examples of left translates 13:24 When a polynumber is translated twice 16:22 Translating a polynumber by an integer 20:21 Recasting using Bi polynumbers 25:34 An exercise to calculate a Taylor polynumber 29:38 Another look at the Taylor polynumber 35:02 Exercise ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated. *********************** My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses are being developed at openlearning.com. The first one, already underway, is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at Patreon,   / njwildberger   . Your support would be much appreciated. Here are the Insights into Mathematics Playlists:    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист