Introduction to Functional Analysis
18.102/18.1021 -- Spring 2017
- Lectures in 4-163, Tuesday and Thursdays 11AM-12:30PM.
- My office hour in 2-480, Wed 3-4. Or by arrangement.
- Grader: Ethan Jaffe, Office hour Friday 4PM -- in the space outside 2-231.
- Please ask questions!
- Comments and remarks:
- Enjoy your summer; grades should be up very soon.
- The median on the final was 72/80, several people got the top mark of 78.
Old remarks
- Lectures
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.
Homework, tests and grades
- Problem sets will be due on Saturdays, at 7AM even though the stated due dates are Fridays.
- Solutions must be submitted electronically to me at rbm AT math.mit.edu (not to the grader, that will not work) and dated by then.
- 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:-
- First problem set Problems1.pdf Due 10 Feb.
- Solutions to second problem set Problems2-sol.pdf Due 17 Feb
v2: Solution to Problem 2.5 amended.
- Third problem set Problems3.pdf Due 24 Feb.
v2: Problem 3.5 changed by making the inequality a.e.
v3: Problem 3.4 changed by defining the function everywhere.
- Fourth problem set Problems4.pdf Due 3 March.
28 February, 2017 v2 Typo corrected in 4.5
28 February, 2017 v3 A few hints added -- more available on request.
3 March, 2017 v4 Added a hint on completeness in 4.3.
Solutions Problems4Solutions.pdf
- Fifth problem set Problems5.pdf Due 17 March.
v2: Q5.6 heaving revised.
- Sixth problem set Problems6.pdf Due 31 March.
v2: `a sequence' inserted into P6.3
- Seventh problem set Problems7-comments.pdf Due 7 April.
v2. Problem 7.4 corrected (ST and TS were interchanged).
v3. Ethan's comments
- Eighth problem set Problems8-comments.pdf Due 14 April.
v2 -- Added comment about Fourier basis for problem 8.5.
- Ninth problem set Problems9.pdf Due 28 April.
v2 26 April, 2017: Typos fixed
- Tenth and final problem set Problems10.pdf Due 5 May.
- Two in-class tests to make sure you are on the rails:
- 9 March: Test1-pre.pdf
- 25 April: Test2-pre.pdf
- Final exam: May 22 from 1:30 to 4:30 PM in 50-340.
Final-Pre.pdf
- 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.