( 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 four 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 (optional) 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. For feasibility/scheduling reasons, since I aim to get commented-upon write-ups back before the exam, in general no late homeworks will be accepted. Homework should be typeset, presumably via (La)TeX, and emailed to me as a PDF. Discussions of the homework/examples are posted on-line. If you do use ideas from these 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. It 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 is PDFs posted here, similar to those from previous years, with updates and corrections. No cost.
Office hours MWF briefly after class, in the same room, and, even better, email anytime: I do like talking/writing about math, and responding to questions that I've already thought about is no burden at all. :) Also, thinking about an issue enough to formulate a question in email is usually a productive exercise in itself. :)
The outline below is for a two-semester course.
| Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
| Jan 22 | Jan 24 | |||||
| Jan 27 | Jan 29 | Jan 31 | ||||
| Feb 03 | Feb 05 | Feb 07 | ||||
| Feb 10 hmwk 05 | Feb 12 | Feb 14 exam 05 | ||||
| Feb 17 | Feb 19 | Feb 21 | ||||
| Feb 24 | Feb 26 | Feb 28 | ||||
| Mar 03 hmwk 06 | Mar 05 | Mar 07 exam 06 | ||||
| Mar 10 | Mar 12 | Mar 14 | ||||
| Mar 17 | Mar 19 | Mar 21 | ||||
| Mar 24 | Mar 26 | Mar 28 | ||||
| Mar 31 | Apr 02 | Apr 04 | ||||
| Apr 07 hmwk 07 | Apr 09 | Apr 11 exam 07 | ||||
| Apr 14 | Apr 16 | Apr 18 | ||||
| Apr 21 | Apr 23 | Apr 25 | ||||
| Apr 28 hmwk 08 | Apr 30 | May 02 exam 08 | ||||
| May 05 last class |
Older notes