( 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.
Prerequisite for 8702: 8701 or equivalent.
Grades fall and spring will be determined by in-class midterms , scheduled as 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.
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. If we are meeting in person, a paper copy is good. Or email a PDF to me. 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. If you find things in prior years' example discussions, or elsewhere on the internet, or in books, cite . Also, collaboration with other people is fine, and acknowledge . 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 (seemingly out of the blue?) in your work, you can recognize them and act accordingly.
Text will be PDFs posted here, similar to those from previous years.
MWF, 2:30-3:20, Vincent 301 for Spring 2022
As in all past years, I strongly encourage people who're ill not to come to class.
Office hours MWF after class, in the same room, and email anytime: I do like talking about math, and answering questions that I already know-the-answers-to is no burden at all. :)
The notes and homework/examples are roughly copies of the 2020-21 versions, as placeholders, being updated as we go. Other bits may be added, as we go, depending on what seems good to include. Prior years' documents may be updated to correct errors, but will have stable URLs (to the extent I can control it!)
|Jan 19||Jan 21|
|Jan 24||Jan 26||Jan 28|
|Jan 31 hmwk 05||Feb 02||Feb 04 exam 05|
|Feb 07||Feb 09||Feb 11|
|Feb 14||Feb 16||Feb 18|
|Feb 21||Feb 23||Feb 25|
|Feb 28 hmwk 06||Mar 02||Mar 04 exam 06|
|Spring Break||Mar 07||Mar 09||Mar 11|
|Mar 14||Mar 16||Mar 18|
|Mar 21||Mar 23||Mar 25|
|Mar 28||Mar 30||Apr 01|
|Apr 04 hmwk 07||Apr 06||Apr 08 exam 07|
|Apr 11||Apr 13||Apr 15|
|Apr 18||Apr 29||Apr 22|
|Apr 25 hmwk 08||Apr 27||Apr 29 exam 08|
|May 02 last class|
Text will be PDFs posted here, similar to those from 2014-15.
PDFs of handwritten stuff from lectures