What we will cover
Ward Cheney: Chapters 1-3, Hilbert and Banach Spaces, plus calculus in Banach spaces: https://www.springer.com/gp/book/9780387952796
Joel Franklin: Chapter 3, a very nice introduction to fixed point theory https://epubs.siam.org/doi/book/10.1137/1.9780898719239
My Notes: Pieces of my notes Here and some slides from a short course Here. Note that the first notes are a rough draft (lots of typos) of a book I am writing, In that book we will cover at least chapter 11 carefully, but will take off on other suggested tangents. The slides will be mined for a few interesting applications of the ideas in the course. I suspect we also might look into the fascinating area of convex functions and the Legendre-Fenchel Transform. And, of course, we will poke into geometry and probability in high dimensions — concentration of measure, for example.
When and Where
Date and Time: Wednesdays, 10-12 Pacific Time
Place: Zoom ID = 505 115 089 Password = email me
Course Number: Mathematics 589 (for WSU participants)
The students will meet from 10-11 and discuss the reading, I join from 11-12 (thought I will sometimes be there the entire two hours) to dig into the nuances and explore various subtle details.
Reading/Working Assignments
January 27, 2021: Scan Cheney Sections 1.1-1.4, Focus on Section 1.5 and the problems in that Section
February 3, 2021: Sections 1.6-1.7 of Cheney
February 10, 2021: Sections 1.8-1.10 pf Cheney
Perspective
We are interested in gaining usable instincts, in a context of far ranging interactions with engineering, economics, physics, chemistry, and biology, as well as deeper mathematical insights i.e. mathematics for the sake of mathematics.