( 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, and emailed to me as a PDF. I will post discussions of the homework/examples prior to the exams, and past discussions of similar examples are already posted here. 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 is PDFs posted here, similar to those from previous years. No cost.
MWF, 2:30-3:20, Vincent 209. Calendar of homework and exams is below. As in all past years, I strongly encourage people who're ill not to come to class.
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 notes and homework/examples are essentially updates of my past courses' versions. Other bits may be added, as we go, depending on students' interest. The outline below is for a two-semester course, so in a single semester we'll probably get about half-way through, depending on how things go. :)
Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
Sept 04 | Sept 06 | |||||
Sept 09 | Sept 11 | Sept 13 | ||||
Sept 16 | Sept 18 | Sept 20 | ||||
Sept 23 hmwk 1 | Sept 25 | Sept 27 exam 1 | ||||
Sept 30 | Oct 02 | Oct 04 | ||||
Oct 07 | Oct 09 | Oct 11 | ||||
Oct 14 hmwk 2 | Oct 16 | Oct 18 exam 2 | ||||
Oct 21 | Oct 23 | Oct 25 | ||||
Oct 28 | Oct 30 | Nov 01 | ||||
Nov 04 hmwk 3 | Nov 06 | Nov 08 exam 3 | ||||
Nov 11 | Nov 13 | Nov 15 | ||||
Nov 18 | Nov 20 | Nov 22 | ||||
Nov 25 | Nov 27 | Thanksgiving | Nov 29 | |||
Dec 02 hmwk 4 | Dec 04 | Dec 06 Exam 4 | ||||
Dec 09 | Dec 11 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
Older notes