Topology and Analysis
In the Spring 2019 semester I intend to run a 3hr course which meets from 4:20-5:50pm on Monday and Friday. I intend to post the Lectures from this course at:
Playlist from Topology & Analysis
Note, the title of the course does not indicate that this course involves honest to goodness "research". In truth, this is a small section special topics course. Although, this might be a course you would find at any number of universities which a larger selection of the math curriculum.
The particular structure of this course intends to fill a gap I percieve in the required course load of our Mathematics major. In particular, we will study elementary topology and the rudiments of basic measure theory in this course. We'll cover a lot of ground and I will not prove most theorems that are given. Our goal here is more geared towards gaining some intuition for the topics covered as well as an appreciation of the difficulty and necessity for the constructions considered. In short, this is not intended to replace a graduate level course in Topology or Real Analysis. Rather, we hope to provide a foundation which allows students to deeply understand the graduate courses which cover Topology and Analysis.
The texts I intend to primarily follow are:
- Introduction to Topology, 2nd edition by Gamelin and Greene, available from Dover Publishers.
- Real Analysis: Measure Theory, Integration and Hilbert Spaces, by Stein and Shakarchi, Princeton Lectures in Analysis III, Princeton University Press.
I have taught some Topology in previous courses so I have some preference for problems to assign from Gamelin and Greene. In contrast, I have not taught Measure Theory before and thus I am hesistant to choose problems blindly. Instead I allow students in this course to select Exercises ( in contrast, "Problems" from the Real Analysis text are more problematic) of their choosing to help the reading come alive.
Previous Topology Courses:
I should mention, in Spring of 2016 I ran a small course in basic Topology from Manetti's text. At the conclusion of the course I gave a couple talks about supermanifolds and we actually created a new example. The course planner and You Tube videos from that course are linked below.
In fact, we also studied Algebraic Topology from Rotman as a follow-up reading course in Fall 2016. I have not yet posted all the videos, perhaps I will sometime when I get a chance to organize my terabytes of videos. Nathan BeDell(went to graduate school at Tulane University) and Daniel Freese (went to graduate school at Indiana University) taught the classes I did not teach in this one:
The background picture is based on a picture I saw at this website
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Last Modified: 1-3-2019