Math 240B, Winter 2022

Real Analysis II

## Announcements:

## Course Information

Real Analysis II

- Jan. 24: Homework 3 will be due Mon. Jan. 31. When we return to
in-person classes, my office hours wil be W 2 - 3:30 and F 1 - 2:30.

- Jan. 6: Classes will be remote until at least Monday Jan. 31

- Jan. 1: Following university policy, the first two weeks of class will be remote.

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.

## Course Schedule (items in gray are tentative)

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.