Introduction

We will focus this semester on mastery of the art of inequalities and the wild (and practically crucial) universe of metric spaces. The texts will be Lindstrom’s book, Spaces (very well written — maybe too well written), and my notes, In and Around Geometric Analysis: An Invitation (still very full of typos). You can find a link to my notes below — they will be updated from time to time. It is very important to read the reading of course, but it is crucial that this reading be done very deeply — immerse yourself, take the time to think, to ponder, to experiment with plenty of paper and a pencil/pen in hand. While some (or many) of you might be tempted to get by with a few hours of work out of class, true mastery will take many hours a week. I will have the assignments up by the end of the first week. We will cover the important pieces of chapters 1-4 of Lindstrom and chapters 4 and 5 of my notes.

My Notes

These notes are very much a work in progress and will be updated from time to time:

In and Around Geometric Analysis: An Invitation

As mentioned above, this semester we will cover the contents of chapters 4 and 5 of my notes (in addition to the ideas in chapters 1-4 of Lindstrom’s book).

Assignments

Here is a link to a pdf that will be updated as I add problems: Fall 2021 401 Problems Document

Here is a link to the take-home final text: Fall 2021 401 Final Test

Logistics

The classroom we meet in is Todd 320. The class time is 10:10 - 11:00 MWF. I will send out emails with logistical updates as needed. Office hours will be 7-10 on Mondays. the first hour will be on zoom only, the last two in person and on zoom. the location for the in person part will be Neill Hall 203. (This may change later to a bigger place if the demand calls for it.) The zoom coordinates for the office hours are 221 067 057 password 314159.

Other Reading and Listening

Here I will keep adding to a list of books, papers, videos and other things — mathematical and otherwise — that I recommend in the journey to mastery of mathematics and life.

  • Range, by David Epstein

  • The Culture Code, by Daniel Coyle

  • No Time To Think, A google tech talk, given by David Levy. Here is a link.

  • Functions of Several Variables, by Wendell Fleming. This is a fairly advanced book on beginning analysis that I recommend very highly — but it is not easy.

  • Introduction to Topology and Modern Analysis, by George F. Simmons. Very well written — inspiring, both the writing and the mathematics. I recommend that every serious student of mathematics own this book.

  • On Proof and Progress in Mathematics, by Bill Thurston. This is a provocative article that first appeared in 1994. Here is a link to the article.

  • Living Proof: Stories of Resilience Along the Mathematical Journey, by Henrich, Lawrence, Pons and Taylor. This is a book that the authors give away a PDF for — here is a download link. While I will not agree with every attitude in this book, nor subscribe to all the philosophies that are at least implicitly held by those whose stories fill the book, there are good reasons for listening to the stories of the people in the book. Anyway, very much like the premise of the book and the fact that the honesty and clarity it brings to the reality of mastery can be deeply encouraging to almost anyone. And, I suspect that the points of disagreement I will have after I have read the whole thing will account for a pretty small part of the book.