The Weierstrass Approximation Theorem (WAT)

No you are not dreaming, Math for Math's Sake has come back to life!

Thanks to Betty Mock for graciously agreeing to give this talk. She writes:

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The Weierstrass Approximation Theorem (WAT) is an essential theorem in analysis. People know of it, but rarely appreciate how deeply entangled it is in analysis, and how essential to so many other theorems and so much other work.

The standard proof using Bernstein polynomials was introduced in 1912 and is still in use. But in the late 1950's the mathematician Pavel Korovkin created a startling generalization of it, which includes almost all the generalizations currently in use, and substantially reduces the amount of work it takes to apply the theorem. The path of this lecture leads from basics to Korovkin's theorem. It includes a description of how the classical 1912 proof is an example of Korovkin's work.

Usually WAT is introduced in graduate school, but I have cleared a path through the jungle, and you can follow the lecture fine if you have only a basic understanding of mathematics. Here and there I do use something from calculus, but if you haven't studied or have forgotten calculus, you can still follow along without difficulty.
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For Dr. Mock's complete notes on WAT, see https://moxart.com/reports/WAT.cfm

Dr. Mock supplies the following bio:

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Betty Mock holds a PhD in mathematics from the Courant Institute at New York University. Her thesis was in the area of approximation and linear algebra. She has nine years of teaching experience at the college level, but spent most of her career in commercial programming. As a founder of the consulting firm Sundance Software she analyzed and either coded or managed the coding of about 200 applications, some small, some very big and complex. She developed a specification method which greatly reduced cost and time overruns in development. She is an accomplished amateur pianist and since retirement she has founded and run two successful music non-profits. She lives in the Philadelphia area with Mabel the orange cat.
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