Math 140B, Spring 2020
Foundations of Real Analysis II


Announcements:

* The Final Exam will be "No Fault." See the email I sent on Monday June 8 at 4:57 PM titled "140B Final Exam will be No Fault" for details.
* During finals week, your TA will have office hours Tuesday 12:00 - 2:00 and will be available by appointment on Wednesday.
* During finals week, I will have office hours Wednesday 10:30 - 12:00 and 3:00 - 5:00.
* Your TA will have extra office hours for the exam Thurs. May 21 10:00 - 2:00 (same meeting ID as normal office hours)
* I will have extra office hours for the exam Thurs. May 21 2:00 - 4:00 (same Meeting ID as normal office hours)
* My office hours have changed again. For the rest of the quarter they will be W 10:30 - 12:00 and F 10:00 - 11:30.
* Your TA will have extra office hours for the exam Thurs. April 23 10:00 - 2:00 (same meeting ID as normal office hours)
* I will have extra office hours for the exam Thurs. April 23 4:00 - 6:00 pm via Zoom (same Meeting ID as normal office hours)
* Due to low activity on Piaza I have shifted all of my office hours to be on Zoom (I will still respond to posts on Piazza though). My new office hours are W 10:30-12, W 3-3:30, and F 10:15-11:15


Course Information

Professor: Brandon Seward (pronouns: he/him/his)
Lecture: MWF 1:00-1:50 via Zoom (navigate to https://ucsd.zoom.us/j/878269867 or open the Zoom app and use Meeting ID 878-269-867)
Email: bseward@ucsd.edu
Office Hours via Zoom: W 10:30 - 12:00, F 10:00 - 11:30 AM (navigate to https://ucsd.zoom.us/j/796484022 or open the Zoom app and use Meeting ID 796-484-022)
Note: Office hours and lecture have different Meeting IDs!

Teaching Assistant: Andres Rodriguez (pronouns: he/him/his)
A01 Discussion: Mon. 4:00-4:50 via Zoom (navigate to https://ucsd.zoom.us/j/613798086 or open the Zoom app and use Meeting ID 613-798-086)
A02 Discussion: Mon. 5:00-5:50 via Zoom (navigate to https://ucsd.zoom.us/j/352538894 or open the Zoom app and use Meeting ID 352-538-894)
Email: a3rodrig@ucsd.edu
Office Hours via Zoom: Tu 12:00-2:00 and Th 10:00-12:00 (navigate to https://ucsd.zoom.us/j/555398131 or open the Zoom app and use Meeting ID 555-398-131)
Website for Discussion: https://arodriguezrey12.wordpress.com/teaching/math-140b/

Course Descritption:
Second course in a rigorous three-quarter sequence on real analysis. Topics include: differentiation, integration, sequences and series of functions, some special functions.

Textbook: Principles of Mathematical Analysis by Walter Rudin, 3rd edition. We will cover most of chapters 5 through 8.

Additional Study Materials: (you will not be tested on these)

Lecture:
Lecture will occur live on Zoom (use meeting ID: 878-269-867 or navigate to https://ucsd.zoom.us/j/878269867). Videos of our lectures can be found on our Canvas page under the Media Gallery tab. Lecture Notes PDF

Community Interaction: Typically meeting in the classroom allows students the opportunity to get to know one another and discuss the course material together. Since class meetings will not occur, as a substitute we have a discussion forum on Piazza that everyone is strongly encouraged to use. As part of their weekly office hours, the professor and teaching assistant will spend time each week responding to discussions on piazza (see above for specific hours). Our piazza page is here: http://piazza.com/ucsd/spring2020/math140b

Homework: Homework will be assigned regularly and due on Fridays at 2:30. No late homework will be accepted, but your lowest homework score will be dropped when computing your final grade. On each assignment, a few problems will be graded for correctness, while the others will be graded simply for completion. We will use Gradescope for turning in homework. When registering for gradescope, please register using your UCSD email address.

Homework 1 (Due Friday April 10): Chapter 5 problems 2, 4, 6, 8, 9, 14, 19, 26 (Note: Convex function are defined in exercise 23 on page 101 of the textbook)
Homework 2 (Due Friday April 17): Chapter 5 problems 11, 15, 17, 22 and Chapter 6 problems 1, 2, 3, 4
Homework 3 (Due Friday April 24): Chapter 6 problems 5, 7, 8
Homework 4 (Due Friday May 1): Chapter 6 problems 6, 10(abc), 11, 12, 13(abd), 15, 19 (Hint: Use problem 10 to solve two other problems)
Homework 5 (Due Friday May 8): Chapter 7 problems 1, 2, 3, 4, 8, 9, 14
Homework 6 (Due Friday May 15): Chapter 7 problems 7, 10, 13, 15, 16, 18, 19 (Note: Uniformly closed is defined in Definition 7.28. For #19, you can assume the truth of Ch. 2 problem 26)
Homework 7 (Due Friday May 22): Chapter 7 problems 20, 21, 23
Homework 8 (Due Friday May 29): Chapter 8 problems 1, 2, 4, 5, 6, 7, 9(a) (Note: These problems do not require any particular material from chapter 8 aside from standard calculus identities for exponential, logarithmic, and trigonometric functions.)
Homework 9 (Due Friday June 5): Chapter 8 problems 10, 11, 12, 13, 14, 22 (Only prove Newton's binomial theorem), 23 (Note: Theorems 8.14 and 8.16(85) will be useful for problems 12-14)

Exams: The midterm exams will be taken at home and solutions will be uploaded to Gradescope. The exams will be open-book and open-note, but the use of online resources and help from other humans is forbidden. If cheating is suspected, students will be required to have a one-on-one zoom meeting where students will have to solve similar problems and/or comment on their exam solutions.
Grading: The grading scheme has been updated. See the email I sent on Monday June 8 at 4:57PM titled "140B Final Exam will be No Fault."

Below is a record of the originally planned grading scheme:
Your final grade will be the maximum of the following two weighted averages:
Special Accommodations: Students requiring accommodations should provide an OSD letter of certification and OSD accommodation recommendation to the instructor as soon as possible.


Course Schedule (items in gray may change)

Week
Monday
Wednesday
Friday
1 March 30
The derivative of a real function
April 1
The derivative of a real function
Mean value theorems
April 3
Mean value theorems
The continuity of derivatives
2 April 6
L'Hospital's rule
Derivatives of higher order
Taylor's theorem
April 8
Differentiation of vector-valued functions
April 10 - HW 1 Due
Definition and existence of the integral

3 April 13
Definition and existence of the integral
April 15
Definition and existence of the integral
April 17 - HW 2 Due
Definition and existence of the integral
Properties of the integral
4 April 20
Properties of the integral
April 22
Properties of the integral
Integration and differentiation
April 24 - HW 3 Due
First Midterm (Solutions)
Practice Exam A Practice Exam B
Solutions A Solutions B
5 April 27
Integration and differentiation
Integration of vector-valued functions
Rectifiable curves
April 29
Discussion of main problem
Uniform convergence
May 1 - HW 4 Due
Uniform convergence
Uniform convergence and continuity

6 May 4
Uniform convergence and continuity
Uniform convergence and integration
Uniform convergence and differentiation
May 6
Uniform convergence and differentiation
Equicontinuous families of functions
May 8 - HW 5 Due
Equicontinuous families of functions
7 May 11
The Stone--Weierstrass theorem
May 13
The Stone--Weierstrass theorem
May 15 - HW 6 Due
The Stone--Weierstrass theorem
8 May 18
Power series
May 20
Power series
May 22 - HW 7 Due
Second Midterm (Solutions)
Practice Exam A Practice Exam B
Solutions A Solutions B
9 May 25
Memorial Day
May 27
The exponential and logarithmic functions
The trigonometric functions

May 29 - HW 8 Due
The trigonometric functions
The algebraic completeness of the complex field

Fourier Series
10 June 1
Fourier Series
June 3
Fourier Series
June 5 - HW 9 Due
Fourier Series

11
Thursday June 11, 11:30AM-2:30PM
Final Exam (Solutions)
Practice Final A, Practice Final B
Solutions A, Solutions B