Lecture: MWF 11:00 - 11:50 in AP&M B402A. Recorded lectures are available at
https://learn.evt.ai/. Also see the
Lecture Notes.
Coronavirus Considerations:
Lectures will be recorded and available online, and office hours will
be available both in-person and over Zoom. So if you are feeling ill or
have been exposed to COVID19, then you are encouraged to not come to
class or office hours. Additionally, if I ever feel sick or have been
exposed, then classes will occur remotely over Zoom until it is safe
for me to return to campus.
Professor: Brandon Seward
(pronouns: he/him or they/them)
Email: bseward@ucsd.edu
Office Hours: W 2 - 3:30 and F 1 - 2:30 in AP&M 5739 and at Zoom ID 967 0420 1807 (
https://ucsd.zoom.us/j/96704201807)
TA and Grader: Qingyuan Chen
Email: qic069@ucsd.edu
Office Hours: Thurs. 5:00 - 7:00 pm at Zoom ID 964 2787 7552 (
https://ucsd.zoom.us/j/96427877552)
Course Description:
Second course in a three-quarter graduate sequence on real analysis.
Topics covered include point set topology, functional analysis, L^p
spaces, and Radon measures.
Prerequisites: Math 240A and Math 140ABC or equivalent
Textbook: Real Analysis: Modern Techniques and Applications by Gerald B. Folland, 2nd edition
. We will cover most of Chapters 4 through 7.
Textbook Errata: See
Folland's homepage
Homework: Homework
will be assigned most weeks and due on Fridays by midnight. We will use
Gradescope
for turning in homework. When registering for gradescope, please
register using your "@ucsd.edu" email address and use Entry Code 6P4K5Z
.
Homework 1 (due Fri. Jan. 14):
Ch. 5 problems 2, 3, 6, 12(abcd), 17, 18 and Ch. 6 problem 5
Homework 2 (due Fri. Jan. 21): Ch. 5 problem 7 and Ch. 6 problems 2, 7, 8, 11, 13, 15 (in #13, "separable" means there exists a countable dense subset)
Homework 3 (due Mon. Jan. 31): Ch. 6 problems 31, 32, 33 (see page 132 for the definition of C_0) and Ch. 5 problems 27, 29, 31, 32
Homework 4 (due Mon. Feb. 14): Ch. 5 problems 37, 39, 59, 61, 66 and Ch. 4 problems 4, 5
Homework 5 (due Fri. Feb. 18): Ch. 4 problems 8, 10, 15, 16, 20, 21, 25
Homework 6 (due Fri. Feb. 25): Ch. 4 problems 32, 34, 35, 38, 40, 41, 46
Homework 7 (due Fri. March 4): Ch. 4 problems 47, 49, 51, 54, 56, 59, 63
Homework 8 (due Fri. March 11): Ch. 5 problems 43, 44, 47, 48abc, 51, 63 and Ch. 6 problem 20a
Exams: There will be one midterm and one final exam.
- Midterm: Friday Feb. 4. Will cover sections 5.1, 5.2, and 6.1 through 6.3. Additional details to be announced.
- Final Exam: Monday March 14 from 11:30 AM to 2:30 PM. Will cover everything learned in the class.
Grading: Your course grade will be computed from the following weighted formula: 30% homework + 30% midterm + 40% final
Course Schedule (items in gray are tentative)
Week
|
Monday
|
Wednesday
|
Friday
|
1
|
Jan. 3
5.1 Normed vector spaces
|
Jan. 5
5.1 Normed vector spaces
5.2 Linear functionals
|
Jan. 7
5.2 Linear functionals
|
2
|
Jan. 10
6.1 Basic theory of L^p spaces
|
Jan. 12
6.1 Basic theory of L^p spaces
|
Jan. 14 (HW 1 Due)
6.2 The dual of L^p
|
3
|
Jan. 17
Martin Luther King Jr. Holiday
|
Jan. 19
6.2 The dual of L^p
|
Jan. 21 (HW 2 Due)
6.3 Some useful inequalities
|
4
|
Jan. 24
6.3 Some useful inequalities
5.3 The Baire Category Theorem and its consequences
|
Jan. 26
5.3 The Baire Category Theorem and its consequences
5.5 Hilbert spaces
|
Jan. 28
5.5 Hilbert spaces
|
5
|
Jan. 31 (HW 3 Due)
5.5 Hilbert spaces
|
Feb. 2
5.5 Hilbert spaces
4.1 Topological spaces
|
Feb. 4
Remote Midterm Exam
(no lecture)
|
6
|
Feb. 7
4.1 Topological spaces
|
Feb. 9
4.2 Continuous maps
|
Feb. 11
4.2 Continuous maps
|
7
|
Feb. 14 (HW 4 Due)
4.2 Continuous maps
4.3 Nets
|
Feb. 16
4.3 Nets
4.4 Compact spaces
|
Feb. 18 (HW 5 Due)
4.5 Locally compact Hausdorff spaces
|
8
|
Feb. 21
President's Holiday
|
Feb. 23
4.5 Locally compact Hausdorff spaces
|
Feb. 25 (HW 6 Due)
4.6 Two compactness theorems
|
9
|
Feb. 28
4.6 Two compactness theorems
5.4 Topological vector spaces
|
March 2
5.4 Topological vector spaces
|
March 4 (HW 7 Due)
5.4 Topological vector spaces
7.1 Positive linear functionals on C_c(X)
|
| 10 |
March 7
7.1 Positive linear functionals on C_c(X)
|
March 9
7.1 Positive linear functionals on C_c(X)
7.2 Regularity and approximation theorems
|
March 11 (HW 8 Due)
7.2 Regularity and approximation theorems
|
11
|
Monday March 14, 11:30AM-2:30PM
Remote Final Exam
|