( See also: [ vignettes ] ... [ functional analysis ] ... [ intro to modular forms ] ... [ representation theory ] ... [ Lie theory, symmetric spaces ] ... [ buildings notes ] ... [ number theory ] ... [ algebra ] ... [ complex analysis ] ... [ real analysis ] ... [ homological algebra ] )
The main prerequisite for 8701 is good understanding of undergrad real analysis, such as our 5615H-5616H or equivalent, with substantial experience writing proofs . Courses named Advanced Calculus are insufficient preparation. On another hand, there is no assumption of substantial previous experience with complex analysis, in light of the peculiarities of undergrad math curricula in the U.S.
Students coming into this course should have a range of experience in proof writing, not only in a previous course in analysis, but also in abstract algebra, rigorous linear algebra, and some point-set topology. All these play significant roles in 8701-2, both directly, and in terms of mathematical maturity and vocabulary.
Coherent writing is essential. Contrary to some myths, the symbols do not speak for themselves.
Prerequisites for 8702: 8701 or equivalent.
Grades both fall and spring will be determined by midterms , scheduled as in the table below. You are not competing against other students in the course, and I will not post grade distributions. Rather, the grade regimes are roughly 90-100 = A, 75-90 = B, 65-75 = C, etc., with finer gradations of pluses and minuses. So it is possible that everyone gets a "A", or oppositely. That is, there are concrete goals, determined by what essentially all mathematicians need to know, and would be happy to know. Pandemic version: the exams will occur during the regularly scheduled course time, under the honor system, and exams sent back to me either photographed, scanned, or as modified PDFs.
There will be homework/example assignments preparatory to exams, as scheduled below, on which I'll give feedback about mathematical content and writing style. The homeworks will not directly contribute to the course grade, and in principle are optional, but it would probably be unwise not to do them and get feedback. No late homeworks will be accepted. Homework should be typeset, presumably via (La)TeX, and, [update] emailed to me as PDF. I will post discussions of the homework/examples prior to the exams. Many of the examples will resemble prior years', since, after all, there are just a relative few central examples and ideas. This course is not a gauntlet to be run. The course is about increasing awareness and exposure to important, useful (also crazy and entertaining) ideas, so that in the future when they show up (out of the blue?) in your work, you can recognize them and act accordingly.
MWF, 2:30-3:20, Vincent Hall 209
Pandemic version: to avoid making other people sick or killing them... we will not meet in person. We will have "Zoom" meetings at the scheduled time, with a URL that I'll email you each day.
Since "Zoom" does not really work so well, office hours will be by email , at any time during the day or week. I'll respond quickly!
Upon further consideration of technical issues, contrary to my earlier tentative plans, I will not record the class meetings... Rather, I will screen-share while going through the PDF notes (that are or will be online, resembling prior years'), using software to mark up things (in real time), to highlight the main points, and/or subtle-but-important points. I will probably post the marked-up PDFs. The potential benefit of the audio portion is the pep-talk aspect, as well as tone-of-voice while marking up the PDFs, but this part will not be recorded.
Given the crazy circumstances, the technical mess, and the variation in individual preferences, in particular, attendance at these "Zoom" classes/meetings is not strictly mandatory... especially considering that it really doesn't work that well. I'll respond to email questions ... whenever you ask.
Text will be notes posted here, similar to those from 2014-15, but, naturally, waaaaaay better. :) Seriously: trying to compensate for compromised in-person interactions.
PDFs of handwritten stuff from lectures
|Sept 09||Sept 11|
|Sept 14||Sept 16||Sept 18 hmwk 01|
|Sept 21||Sept 23||Sept 25 exam 01|
|Sept 28||Sept 30||Oct 02|
|Oct 05||Oct 07||Oct 09|
|Oct 12||Oct 14||Oct 16 hmwk 02|
|Oct 19||Oct 21||Oct 23 exam 02|
|Oct 26||Oct 28||Oct 30|
|Nov 02||Nov 04||Nov 06|
|Nov 09||Nov 11||Nov 13 hmwk 03|
|Nov 16||Nov 18||Nov 20 exam 03|
|Nov 23||Nov 25||Thanksgiving||Nov 27|
|Nov 30||Dec 02 hmwk 04||Dec 04 hmwk 04|
|Dec 07||Dec 09||Dec 11 exam 04|
|Dec 14||Dec 16 last class|