Mathematics 402: Mathematical Analysis for Undergraduates
This class is a step up from 401 — it will be run closer to a Graduate mathematics class in style and flavor. That does not imply I will be less engaged! On the contrary, the help sessions are now pretty much full-on Labs that everyone is expected to participate in.
Who and Where and When
This semester, while Katrina will be there on Wednesdays and will probably help with a bit of grading now and then and show up at the help sessions occaitionally, she will not be in class every day and she is not being paid to help. She remains very interested in analysis (of course!) and will be helpful if you ask her questions.
Office Hours and Collaborative Learning sessions: M 5:00-10:00 pm, Neill Hall, Room 5W
Student Run Collaborative Study Session: TBD
What we will cover
The first two weeks we will review topics from 401. After that we will cover chapters 3-5 of Wendell Fleming’s Functions of Several Variables. I will also refer to Tom Lindstrom’s Book, Spaces: An Introduction to Real Analysis from time to time, and that book is a good second reference due to the fact that it is so well written and does most things correctly according to my tastes.
I still recommend George F. Simmons’ Introduction to Topology and Modern Analysis as a helpful reference.
We will exploit the rich connections between geometry and analysis that make analysis an area that can be navigated more easily than most students usually think.
Expectations
You are expected to do the reading before you come to class and master that reading and the assigned problems. You should also try your hand at the other problems I send out from time to time that are not going to be graded, as well as digging around the texts for problems that look interesting to you.
There will also be a collaborative working session every Monday evening.
Grades
Grading will be determined through attendance, participation in the help sessions and completion of the homework (Problems below). The split will be, roughly, 50% participation/attendance and 50% homework.
Reading, Exercises and Problems assignments are listed here. The Problems will be the homework that you have to eventually turn in. Exercises I do absolutely expect you to have looked at before the help/Lab sessions on Monday evening. Though I expect to discuss them in detail with all of you, I will not collect or grade them. The Due Dates for Exercises are the date by which you should have looked carefully at them and the date at which we will begin discussing them.
Initial assignments (Old):
Reading #1 — Due January 24, 2020: Chapter 2-3 of my notes (listed above, updated often) , and scan chapter 2 of Fleming’s book.
Reading #2 — Due Monday, January 27, 2020: Section 4.3 of my notes and 3.1-3.3 of Fleming’s book. I will be presenting these ideas that week, so it is OK to have read them completely but not fully mastered them by Monday.
Exercises #1 — Due January 20, 2020: Problems 1-5 in section 3.2 of Fleming’s book
Notes, Exercises and Problems Document: Here is where all the new notes, exercises and problems will go - Link to the notes, exercises and problems document. The new exercises for the semester will be interspersed throughout the notes. I will update this document frequently.
Other Reading: Mathematical and Otherwise
I will post here the other books and papers I recommend.
(2) Bailey and Borwein’s November 2011 AMS Notices Paper, Exploratory Experimentation and Computation. Read the short section “Limits of Computation” on page 1418. Pretty amazing, actually.
