Complex Analysis, Math 8701-2

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( 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 207

As in all past years, I strongly encourage people who're ill not to come to class. Currently everyone in a classroom is required to wear a mask (and "wear" means "properly"). Btw, I have been vaccinated, and take precautions. I strongly encourage everyone to get vaccinated, if you've not already.

In fact , given the need to accommodate the inevitable quarantining of people exposed to COVID, and to accommodate people who have the inevitable symptoms of other bad things... it seems that there is a strong likelihood of the course turning to all-on-line (=Zoom "meeting" in which I screen-share, and talk... and save PDFs of my writing.) This is far less than ideal... but better than getting seriously ill or making other people seriously ill or ... An apparent necessity to funnel my presentations through my iPad, etc., reduce the situation to what I'd done last year purely on-line anyway, so there's scant point to be in the friggin' room for it... Sadly.

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!)

Exam and homework-example schedule, fall 2021

Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Sept 08 Sept 10
Sept 13 Sept 15 Sept 17 hmwk 01
Sept 20 Sept 22 Sept 24 exam 01
Sept 27 Sept 29 Oct 01
Oct 04 Oct 06 Oct 08
Oct 11 Oct 13 Oct 15 hmwk 02
Oct 18 Oct 20 Oct 22 exam 02
Oct 25 Oct 27 Oct 29
Nov 01 Nov 03 Nov 05
Nov 08 Nov 10 Nov 12 hmwk 03
Nov 15 Nov 17 Nov 19 exam 03
Nov 22 Nov 24 Thanksgiving Nov 26
Nov 29 Dec 01 Dec 03 hmwk 04
Dec 06 Dec 08 Dec 10 exam 04
Dec 13 Dec 15 last class


MWF 2:30-3:20

Text will be PDFs posted here, similar to those from 2014-15.

PDFs of handwritten stuff from lectures

Exam and homework-example schedule, spring 2021:

Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Jan 20 Jan 22
Jan 25 Jan 27 Jan 29 hmwk 05
Feb 01 Feb 03 Feb 05 exam 05
Feb 08 Feb 10 Feb 12
Feb 15 Feb 17 Feb 19
Feb 22 Feb 24 Feb 26 hmwk 06
Mar 01 Mar 03 Mar 05 exam 06
Mar 08 Mar 10 Mar 12
Mar 15 Mar 17 Mar 19
Mar 22 Mar 24 Mar 26 hmwk 07
Mar 29 Mar 31 Apr 02 exam 07
Spring break Apr 05 Apr 07 Apr 09
Apr 12 Apr 14 Apr 16
Apr 19 Apr 21 Apr 23 hmwk 08
Apr 26 Apr 28 Apr 30 exam 08
May 03 last class