Instructor: Andres del Junco BA6226
Office hours: M 3-4, F 2-3
Lectures: MWF 12-1, BA6183
Announcements: Please check here regularly for new announcements.
Apr. 18: I will hold office hours again Monday 10-1.
Apr. 14: There is a problem session today at the usual place and time.
I will have office hours on Wednesday from 10-1.
Mar. 27: The problem about unions of closed balls in PS5 was mis-stated,
as many people have noticed. The boundary has measure 0 when the radii are
bounded below, but in general the set is only measurable.
Mar. 14: For Fourier analysis we are following Katznelson, Intro to
Harmonic Analysis, 3rd ed. The relevant sections are:
1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 2.1, 2.2, 6.1, 6.2, 6.3. We will likely
not be able to cover all of this.
Feb.25: PS 5 is posted below, due on Mar. 17
Feb. 6. Clarification for problem B on PS4: C[0,1] refers to
C([0,1], R) here.
Feb. 6. I have posted some notes below on locally convex spaces,
specifically the material not found in Folland. They are not a finished
product! Please let me know if you find any significant errors. Please do
*not* send me random minor errors and typos. However, if anyone
wants to undertake to read the notes carefully and send me a comprehensive
list of errors and typos that would be very useful.
Jan 25. PS 4 (updated version) is now posted, due Fri. Feb. 15.
Nov. 27. PS3 is now posted.
Oct. 22. PS2 is now posted below.
Oct. 12. The due date for PS1 is hereby extended to Oct. 22 in
response to several requests. Note however PS2 will be posted very shortly.
If you downloaded PS1 before I announced it in class you may have a
(slightly) different version. Please check that your version
agrees with the currently posted version.
PS1 incorrectly referred to the third edition of Folland. It should
be the second edition. If you are using the first edition be aware that
the problems, including their numbering, has changed so you must consult
the second edition.
Oct. 1. Please note that there will be no lecture this Friday,
Oct. 5 as I will be away at a conference. A make-up lecture will be
scheduled.
Sept. 27. The first problem set, ps1, is now posted below.
Sept. 27. Please note the new office hours: M 3-4, F 2-3.
Sept. 21. The midterms will be on Nov. 14 and Mar. 5, in class.
Sept. 21. Regarding the bonus problem stated in class: prove
without using measure theory that if 0 \leq f_n \leq 1 are continuous
functions which converge pointwise to 0
then the integrals, defined as Riemann integrals, converge
to 0. I have been getting more solutions than I expected so I am
setting a deadline for it: Oct. 31. I will also insist that your
write-up be not over two pages of resonably large legible handwriting
or typing, preferably typed if at all possible, and that the
presentation be well thought out and clear.
I will look at all
submissions after the deadline.
Grading scheme:
Term work will consist of 7 or 8 problem sets, to be handed in
for grading (not all problems will be graded), for
a total of 20% of your course mark and
two in-class midterms each worth 10% of your course mark.
the mid-terms will be held on Nov. 14 and Mar. 5, in class.
The final exam will be worth
60% of
your course mark.
Text: Real analysis by Folland.
References
Introductory real analysis by Kolmogorov and Fomin
Real analysis by Royden
Measure and integration by Wheeden and Zygmund
Real and complex analysis by Rudin
A course in functional analysis by Conway
Integrals and operators by Segal and Kunze
An introduction to harmonic analysis by Katznelson
These references as well as the text should all be on reserve at the
math library. Please let me know if you have any difficulties.
Notes
Locall convex spaces, separation of convex sets and the Krein-Milman theorem Web resources
Lecture notes on functional analysis
from Lecture Notes Online Lecture notes on measure and integration
from MIT Open Course Ware
Problem Sets
Problem Sets