Math 142B: Introduction to Analysis II, Spring 2020

Time and Place: TuTh 8:00am-9:20am on Zoom

Instructor: Ioan Bejenaru
E-mail: ibejenar@ucsd.edu
Office: AP&M 6230
Office Hours: Mo 3-4pm, Th 2-3pm.

Section A01: F 3-3:50pm
Section A02: F 4-4:50pm
Teaching Assistant: Xindong Tang
E-mail xit039@ucsd.edu
Office: TBA
Office Hours: Mo 2-3pm, Wed 2-3pm

Lecture format: All lectures will take place live in Zoom during the regular classtimes. A link will be provided to everyone the day before the lecture.

Announcements:

Final Exam information.
Practice final is available here . Solutions for the practice final are available here
Special office hours during the final week: Mo 1:30-2:30pm, Tu 8:30-9:30pm, Wednesday 1-3pm.
Material covered: all chapters taught during the quarter; Exceptions:
- Chapter 4.26: Proof of Abel's theorem is not requested
- Chapter 4.27 will not be covered
- Chapter 4.28: Proof of Theorem 28.4 (Chain rule) is not requested
- Chapter 4.30: Proof of Theorem 30.2 (L'Hospital rule) is not requested
- Chapter 4.31: Proof of Theorem 31.7 (Binomial Series Theorem) - if requested, then steps will be provided
- Chapter 4.31: Example 3 - if requested, then steps will be provided
- Chapter 4.31: we have not covered 31.8 - 31.12, so they are not requested
- Chapter 4.32: Proof of Theorem 32.9 is not requested
- Chapter 4.33: Section 33.11 and 33.12 are not requested.
Fifth Quiz information. Note: this is an optional quiz and will count only towards grading scheme 2 described below.
Material covered: Chapter 6.33 (only Definition 33.7, Theorems 33.8 and 33.9) and Chapter 34. This material is what was covered in Lectures 17 and 18; Homework covered: HW 9.
Quiz 4 solutions are available here .
Fourth Quiz information. Material covered: Chapters 6.32, 6.33 (up to not including Definition 33.7); also Defintion 32.8, Theorem 32.9 and Corollary 32.10 will not be covered. This material is what was covered in Lectures 13 through 16; Homework covered: HW 7 and 8.
Quiz 3 solutions are available here .
Third Quiz information. Material covered: Chapters 5.29,5.30,5.31; in 5.31 up to (not including) Example 3, page 257. This material is what was covered in Lectures 8 through 12; Homework covered: HW 4,5 and 6.
Quiz 2 solutions are available here .
Second Quiz information. Material covered: Chapters 4.25,4.26,5.28. - this is what was covered in Lectures 3 through 7; Homework covered: HW 3 and 4 (but not the problems from 5.29)
Quiz 1 solutions are available here
First Quiz information. Material covered: Chapters 4.23, 4.24., 4.25 (up to and including Theorem 25.4). - this is what was covered in Lectures 1,2 and 3; Homework covered: HW 1 and 2
The quiz will be notes and homework based.
As for a practice quiz: pick a problem from HW1, a problem from HW 2 and a theoretical concept/example/proof from the Lectures 1,2 and 3 and that will be your practice quiz.
Hints for preparing for the quiz: Make sure you read the theory and examples, both from textbook and notes, and go over the homework problems. If time allows, practice on the problems which were not assigned (but related to Chapters covered by this quiz.).
All course information will be updated on this site.

Prerequisites: Math 142A, or consent of instructor.
Course description: Second course in an introductory two-quarter sequence on analysis. Topics include: Sequences and series of functions, differentiation and integration. Students may not receive credit for both Math 140 and Math 142B.
Textbook: Elementary Analysis (Second Edition) by K. Ross. We will cover most of chapters 4-6.

Homework: Homework will be assigned weekly. Homework should be submitted on Gradescope. Homework is due every Monday by 11:00pm. No late homework will be accepted. If, for any reason, you cannot turn in a homework assignment, keep in mind that the lowest score will be dropped.

Quizzes: There will be four quizzes during the time of the lecture: April 16, April 30, May 14, May 28. There will be an additional optional Quiz 5 on June 4. This will be used only in grading scheme 2.
Final exam: The final exam is scheduled for Thursday, June 11, 8am-11am.

Follow-up exam: An oral exam, at the discretion of the instructor, may be administered following each quiz or final exam. This will be used mostly to clarify potential academic integrity violations or under special circumstances, such as loss of Zoom connectivity during the exam time, etc.

Academic integrity : given the online nature of this course, there will be several disclosed and undisclosed measure that I will take to ensure a fair grading policy. Cheating will be taken very seriously and automatically reported to the Academic Integrity Office.

Grading: Your final score will be calculated based on the following grading scheme:
There are two grading schemes.
Scheme 1: 20% Homework + 12% Each Quiz (not including Quiz 5) + 32% Final Exam
Scheme 2: 20% Homework + 18% each of the quizzes 1,2,3,4 + 9% Quiz 5 (do not worry that this adds up to 101%).
Important: No A or B+ grades will be assigned on Scheme 2. In scheme 2 a student can only get a P/NP or any grade up to a B. If you aim for grades B+, A-, A, or A+, you must take the final exam. A student who takes Quiz 5 may choose to skip the final exam and take the grade based on Scheme 2 (the grades on Scheme 2 will be released by Monday June 8). A student planning to take the final may skip quiz 5 and go straight to Scheme 1. A student may take both Quiz 5 and the final and will get the best grade out of the two Schemes.
Regrades: Requests for homework and midterm exams can be made within a week after their grades have been released.

List of homework assignments:
- Homework 1, due April 6: Problem 1: 23.1(b,c,e,f),23.2(c,d),23.6; Problem 2: 23.7,23.9; Problem 3: 24.2,24.3 Solutions
- Homework 2, due April 13: Problem 1: 24.6,24.8,24.9; Problem 2: 24.10, 24.11,24.13,24.15; Problem 3: 25.3,25.4,25.5 Solutions
- Homework 3, due April 20: Problem 1: 25.6,25.9,25.10; Problem 2: 25.12,25.14,26.3; Problem 3: 26.4,26.5,26.6 Solutions
- Homework 4, due April 27: Problem 1: 28.1(b,c,d),28.2(c,d),28.3(b); Problem 2: 28.6,28.8,28.9,28.11; Problem 3: 29.1(b,c,f),29.2, 29.3 Solutions
- Homework 5, due May 4: Problem 1: 29.5,29.7,29.9; Problem 2: 29.10,29.13,29.14; Problem 3: 29.15,29.18; Solutions
- Homework 6, due May 11: HW6; Solutions
- Homework 7, due May 18: Problem 1: 31.5; Problem 2: 32.1,32.3, 32.4; Problem 3: 32.5,32.6; Solutions
- Homework 8, due May 26: HW8; Solutions
- Homework 9, due June 1: 33.10,33.11,33.13 Problem 2: 34.1,34.2,34.3 Problem 3: 34.5,34.6,34.11,34.12; Solutions