Introduction to Functional Analysis: 18.102 -- Spring 2014
- Lectures in 4-163, Tuesday and Thursdays 1-2:30PM.
- Office hour in E17-340 TBD.
- Please ask questions!
- Comments and remarks:
- Old remarks
- Lecture schedule and informal notes -- this briefly describes what I expect to talk about/did talk about with pointers for more details.
- Lecture 1: 4 February.
- Lecture 2: 6 February.
- Lecture 3: 11 February.
- Lecture 4: 13 February.
18 February is an MIT Monday.
- Lecture 5: 20 February.
- Lecture 6: 25 February.
- Lecture 7: 27 February.
- Lecture 8: 4 March.
- Lecture 9: 6 March.
- Lecture 10: 11 March.
- Lecture 11: 13 March.
- Lecture 12: 18 March.
- Lecture 13: 20 March.
- Lecture 14: 1 April
- Lecture 15: 3 April.
- Lecture 16: 8 April.
- Lecture 17: 10 April.
- Lecture 18: 15 April.
- Lecture 19: 17 April.
- Lecture 20: 24 April.
- Lecture 21: 29 April.
- Lecture 22: 1 May.
- Lecture 23: 6 May.
- Lecture 24: 8 May.
- Lecture 25: 13 May.
- Lecture 26: 15 May.
- Graders:
- Don't be afraid to email to me at rbm AT math.mit.edu -- it will likely be answered! I am always interested to get some feedback on how hard/easy you are finding things.
- Sources. For the first part of the course I suggest you look at some of the following on-line notes to broaden your viewpoint!
- I.F. Wilde's notes Only the first four chapters are really relevant for us and I will proceed a little more slowly.
- The coverage of WWL Chen's notes is a bit closer to what we will do
The first two chapters should help you to recall some of 18.100.
- Another useful set of notes are those by T.B. Ward Especially Chapters 1-5, but I will do a bit more on Lebesgue integration.
- For integration I will use a heavily modified version of (Jan) Mikusinski's approach which you can find in Debnaith and (Piotr) Mikusinski ``An introduction to Hilbert spaces with applications'' (Academic Press)
- A nice reference for Hilbert spaces is G.F. Simmons ``Introduction to Topology and Modern Analysis''
- You might like to look at P. Halmos' ``A Hilbert space problem book''
- A good over-all reference, a little more advanced than this course, is P.D. Lax's book ``Functional Analysis'' (Wiley-Interscience) -- a nice book to have.
Homework, tests and grades
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Problem sets will be due on Saturdays, at 4AM. 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). The weird time is not meant to encourage you to all-nighters but seems the easiest to enforce.
LATE HOMEWORK will be graded. However, this will probably be done 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.
So, homework will due on, Saturdays (at 4AM, so really the preceding Thursday),
- First problem set Problems1.pdf Due 16 Feb.
- Second problem set Problems2.pdf Due 23 Feb.
- Third problem set Problems3.pdf Due 1 Mar.
- Fourth problem set Problems4.pdf Due 15 Mar.
- Fifth problem set Problems5.pdf 28 March, 2013.
- Sixth problem set Problems6v4.pdf Due 12 Apr.
- Seventh problem set Problems7.pdf Due 3 May.
- Two in-class tests on 6 March and April in in 4-163
- Final exam in exam period.
- 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.
Notes for the course