Special Colloquium Series On Analysis
Speaker: Kevin Vixie, WSU
Time: 4:10 pm
Date: Oct 26, 2010
Place: Neill 5W
In this series of talks, I explore pieces of analysis that I find interesting for one reason or another, at a level that a motivated, advanced undergraduate can keep up with. The intended audience ranges from those undergraduates to graduate students and even faculty who find the titles and abstracts interesting. I am hoping that physics and engineering students -- actually anybody who uses analysis -- will find these lectures interesting and inspiring. The frequency of these talks will vary. I intend to give them Tuesday's from 4-5 and will begin in Neill Hall 5W.
Lecture 1
Title: Uniform Boundedness Principle and Weak Convergence: how
latex error! exitcode was 2 (signal 0), transscript follows:can look like (almost) any function, yet
latex error! exitcode was 2 (signal 0), transscript follows:as
latex error! exitcode was 2 (signal 0), transscript follows:
Abstract: In this talk I will explore some issues that came up when I was designing a recent exam and ended up reminding myself of some functional analysis. In keeping with the aim of this series of talks, the level will be such that advanced undergraduates will be able to follow the talk, assuming they are willing to pedal a bit to keep up. Weak convergence will be introduced and then a curious property about this kind of convergence will be examined. The uniform boundedness principle will enter when we try to get too crazy, effectively reigning in a complete loss of our bearings. For those who have never heard of weak convergence, it suffices to say that it is ubiquitous in analysis and that, if you are a first year graduate student, you will see it in 502 next semester. If you are an advanced undergraduate, it is not too early to start learning some functional analysis, as it can be very illuminating in mathematics, physics and engineering.