Announcements:
·
(Jan 14)
Note that there are errata for some Folland
questions, in some printings of Folland; see this page. (For instance, Q17 of Chapter 3 has a
misprint in the first five printings.)
·
(Jan 25)
It has come to my attention that some of the solutions submitted for HW
questions have been copied more or less directly from the internet or similar
sources. While I encourage attempts to
work together or research these problems by a variety of means, I would like at
least to see the solutions expressed in one’s own words, to demonstrate innate
understanding of the solution.
Accordingly, I am asking Tim, whenever he sees two or more solutions
that are essentially identical in terms of notation, logical structure,
wording, and minor errors, to split the points for that question equally among
all students submitting that solution.
[It should also be noted that attempting the homework questions unassisted
will be excellent practice for the midterm and final; conversely, if you find
yourself unable to do a majority of the HW questions without assistance, this
does not bode particularly well for your performance at these exams.]
·
(Feb
4) Midterm solutions are available here.
·
(Mar 2)
The final has been changed from a 3-hour examination to a take home format, to
be distributed on Friday and returned on Monday, as I will be out of the
country on the scheduled day of the final.
More details below. You can use
any books, notes, or on-line references to assist you, but if you use any
assistance outside of the textbook, lecture notes, or your own notes, then they
must be cited, or the points for any solution using the citation will be
forfeited. As with the homework, if two or
more solutions to a given problem are essentially identical, then the points
for these problems will be shared equally between the solutions.
· Instructor: Terence Tao, tao@math.ucla.edu, x64844, MS 6183
· Lecture: MWF 10-10:50, MS 5117.
·
Discussion section: Th
10-10:50, MS 5117
·
Office Hours: Tu
2-2:50, W 1-2
· TA: Tim Austin timaustin@math.ucla.edu, MS 3931. See also Tim’s web page for this course.
· TA Office hours: Tu 11:30-12:30; Thu 1:30-2:30
· Textbook: Folland, Real Analysis, Second Edition; we will also use Stein-Shakarchi’s Real Analysis as a supplementary text. We will cover the Radon-Nikodym theorem from Chapter 3 of Folland (or Chapter 6.4 of Stein-Shakarachi), as well as large parts of Chapters 4-6 of Folland (Point Set Topology, Functional Analysis, L^p spaces); some variation from this plan may develop depending on time constraints. I will also write some supplemental lecture notes to these texts on my blog.
· Prerequisite: Math 245A. The material here will rely heavily on that in Math 245A, so be sure you have a firm grasp of the material from that course.
· Grading: Homework (30%), Midterm (30%), Final (40%). In addition, each student must present at least one homework problem at the blackboard during at least one discussion section in order to gain the Homework portion of the grade. You may use any resource to solve homework problems, so long as the final solution is in your own words; duplicate solutions will have the points for that question shared equally between them. For some of the homeworks, due to time constraints, only a subset of the questions (chosen at random) will be graded in full.
· Exams: The midterm will be on Wednesday, Feb 4, in MS 5117, and will consist of three questions of a level comparable to the HW, covering measure theory, L^p spaces, Hilbert spaces, the Hahn-Banach theorem, and the basic theory of normed vector spaces. The optional notes on the blog will not be covered. Some sample questions (taken from my previous course web pages) are given at this page. The exam is open book and open notes (and any result from lecture, notes, or text can be cited freely), but no electronic devices will be allowed. The final will be a take-home exam of approximately seven questions (comparable to that of the homework, and focusing on the material covered in second half of the quarter), handed out in the final class on Friday March 13, and due before noon, Monday March 16, to my office or (less preferably) in my mailbox. Sample exams can be found at my web pages for previous 245B classes.
· Homework: There will be approximately seven homework assignments, due in discussion sections. There will be roughly 10 questions in each assignment; unless otherwise indicated, they will be from Folland.
· Assignment 1 (Due Thu, Jan 15): Folland Chapter 3, Q 3, 7, 10, 11, 17; Chapter 5, Q 1, 5, 9
· Assignment 2 (Due Thu, Jan 22): Folland Chapter 6, Q 10, 15; Chapter 5, Q 7, 11
· Assignment 3 (Due Thu, Jan 29): Folland Chapter 5, Q 19, 20, 56, 62, 67; Chapter 6, Q 6, 12
· Assignment 4 (Due Thu, Feb 12): Folland Chapter 5, Q 22c, 30, 32, 42
· Assignment 5 (Due Fri, Feb 20): Folland Chapter 4, Q28ab, 43, 59, 65
· Assignment 6 (Due Thu, Feb 26): Folland Chapter 4, Q63; Chapter 5, Q47, 48, 51
· Assignment 7 (Due Thu, Mar 5): Folland, Chapter 4, Q3, 46, 68; Chapter 5, Q53