Introduction to Functional Analysis
18.102/18.1021 -- Spring 2018
Homework, tests and grades
- Final exam scheduled for Monday, May 21 from 1:30 to 4:30 PM in Walker Gym.
- Lectures in 4-370, Tuesday and Thursdays 11AM-12:30PM.
- My office hour Wednesdays 3-4PM, 2-480
- Grader: Kaavya Valiveti, New Office hour Fridays 2:30-3:30PM, 2-231.
- Please ask questions!
- Comments and remarks:
- Lecture April 24. Baire's Theorem, uniform boundedness, open mapping, closed graph theorems.
- Problems for Test2 finally up.
- Lecture April 10. Spectral theorem for compact self-adjoint operators, funtional calculus..
- After requests I have put up Problem set 7.
- Lecture April 5: Neumann series, invertible operators, spectrum of an operator, norm for self-adjoint operators. Notes Chapter 3, Sections 16, 17.
- Lecture April 3: Compact operators, weak convergence, Neumann series.
- Changed problem 5.7 since it was a repeat.
- Problem set 5 up.
Syllabus -- this briefly describes what I expect to talk about with pointers to material you should read before lectures.
- Lecture notes for the course
- Don't be afraid to email to me at rbm AT math.mit.edu -- I will likely answer! I am always interested to get some feedback on how hard/easy you are finding things.
- Sources Lecture notes etc.
- Problem sets will be due on Saturdays, at 7AM even though the stated due dates are Fridays.
- Solutions must be submitted through Stellar (unless anyone has a better idea).
- This does not mean that you need to learn LaTeX (although of course that is probably a good idea). You can write out your solutions and scan-to-pdf (there are several places you can do this as you no doubt know better than me).
- Photographs with cell-phones are generally not clear enough to be acceptable.
- The weird time is not meant to encourage you to all-nighters but seems the easiest to enforce.
- You may consult any source you want, even old solutions, but I insist that you absorb the material and write out the solution completely on your own.
- If you collaborate/consult with others you should briefly list them.
- No extension on homework will be given, however
- Late homework will be graded, probably by me, so don't expect too much generosity.
- How many marks you get for late homework is decided by me based on a secret, highly dubious, formula. Try to avoid this route.
- Problem sets:-
- Problems1 Due 16 Feb
- Problems2 Due 23 Feb
- Problems3 Due 2 Mar, v2 up 24 February, 2018.
- Problems4 Due 16 Mar.
- Problems5 Due 30 Mar, v2 up 21 March, 2018.
- Problems6 Due 6 April, 2018.
- Problems7 Due 13 April, 2018.
- Two in-class tests to make sure you are on the rails:
- 8 March: This is a bit earlier than I would like, but I will be away.
- 19 April: Here are the problems from which those on the test will be selected
- Final exam: Monday, May 21 from 1:30 to 4:30 PM in Walker Gym.
- Grades will be computed by two methods -- the cumulative and the hope-springs-eternal method with the actual grade the greater of the two.
- First method: Homework 30, Tests 30, Final 40.
- Second method is based purely on the final. Try not to rely on this.