Math 142A

Winter 2021, Lecture C00 (MWF 3:00-3:50pm)

Introduction to Analysis I

Announcements
Calendar
Syllabus
Piazza
Gradescope
Homeworks

Announcements

March 25: Updated grading scheme

A+ A A- B+ B B- C+ C C-

96 88 83 79 69 66 61 58 51

51 or more points are required to pass the class.
March 23:
- Final exam has been graded. Regrades will be active on Gradescope until March 30.
- Regrades for Homework 8 and Homework 9 will be active on Gradescope until March 30.
- Solutions to the final exam can be downloaded here.
March 17: The information below is only for students who will write the final exam at 3 PM on Wednesday
- exam problems will become available on Canvas at 3 PM;
- Zoom meeting will start at 4 PM; use this link to join the meeting (no password);
- you can joint the Zoom meeting until 4:50 PM, but not later; when you join the meeting wait in the waiting room;
- IMPORTANT: the deadline for submitting your exam to Gradescope is 4:40 PM;
- read these instructions to make sure that you are familiar with all the procedures.
March 15:
- Important: Make sure that you know the time difference between the Pacific Daylight Time (that started in California on March 14) and your local time.
- Updates to the grading scheme: your lowest quiz score and two lowest homework scores will not be taken into account when computing your final score.
- The information below is only for students who will write the final exam at 8 PM on Tuesday
  - exam problems will become available on Canvas at 8 PM;
  - Zoom meeting will start at 9 PM; use this link to join the meeting (no password)
  - you can joint the Zoom meeting until 9:50 PM, but not later; when you join the meeting wait in the waiting room;
  - IMPORTANT: the deadline for submitting your exam to Gradescope is 9:40 PM;
  - read these instructions to make sure that you are familiar with all the procedures
March 11:
- The instructions for the final exam can be found here. It is your responsibility to read and follow these instructions.
- Practice final pdf/solutions.
- Midterm 1 statistics: mean 64.1, median 63.5, standard deviation 17.32.
- Midterm 2 statistics: mean 58.73, median 59.5, standard deviation 24.11.
March 10:
- (IMPORTANT, to ALL students) Please fill in this form link before Sunday, March 14, 11:59 PM and indicate when you are planning to write the exam.
March 8:
- Lecture 23 is now available below.
- Homework 6 and Homework 7 have been graded. Regrades will be active on Gradescope until Friday, March 12.
- Homework 9 has been posted below. Due: Sunday, March 14, 11:59 PM.
- Quiz 5 will take place on Wednesday, March 10 on Canvas and will cover the material of Lectures 17, 18, 19, and 20. More information below.
March 5:
- Lecture 22 is now available below.
March 3:
- Lecture 21 is now available below.
- Important: indicate the time zone in which you will be during the final exam week by filling in this form.
March 1:
- Lecture 20 is now available below.
- Homework 8 has been posted below. Due: Sunday, March 7, 11:59 PM.
- There was a mistake on the last page of Lectre 19. It has been corrected and the pdf file has been updated (changes in red).
- Solutions to Midterm 2 pdf.
February 26: Lecture 19 is now available below.
February 22:
- Lecture 18 is now available below.
- Homework 7 has been posted below. Due: Sunday, Feb 28, 11:59 PM.
- Practice Midterm 2 solutions.
February 21:
- Homework 5 has been graded. Regrades will be active on Gradescope on Monday, Feb 22 - Tuesday, Feb 23.
- Instructions for the second midterm can be found here. Important: Late submissions (after the 70 minute deadline) will not be accepted: it is your responsibility to submit the exam on time.
- Practice Midterm 2 can be downloaded here / solutions.
February 19:
- Lecture 17 is now available below.
- Next week there will be an office hour on Tuesday. There will be no office hours/Q&A sessions on Wednesday. For the times, check the Google calendar below.
- Midterm 1 will take place on Wednesday, February 24. It will cover the material of lectures 8-16.
February 16:
- Quiz 4 will take place on Wednesday, February 17 on Canvas and will cover the material of Lectures 10, 11 and 12. More information below.
- Homework 6 has been posted below. Due: Sunday, Feb 21, 11:59 PM. Contains one extra credit problem.
- Homework 4 has been graded. Regrades will be active on Gradescope on Wednesday, February 17 - Friday, February 19.
February 12: Lecture 15 is now available below.
February 10: Lecture 14 is now available below.
February 8:
- Lecture 13 is now available below.
- Homework 5 has been posted below. Due: Sunday, Feb 14, 11:59 PM.
- Regrades for Homework 3 will be active on Gradescope on Monday, February 8 - Wednesday, February 10.
February 5: Lecture 12 is now available below. There is also a short video with a rigorous proof of the covergence of the series from the Important Example 9. You are not expected to know this proof for any course, quiz or homework.
February 3: Lecture 11 is now available below.
February 1:
- Lecture 10 is now available below.
- Homework 4 has been posted below. Due: Sunday, Feb 7, 11:59 PM.
- Quiz 3 will take place on Wednesday, February 3 on Canvas and will cover the material of Lectures 8, 9. More information below.
- Regrades for Midterm 1 will be active on Gradescope on February 1 and 2 (Monday-Tuesday).
- Regrades for Homework 2 will be active on Gradescope on February 1 and 2 (Monday-Tuesday).
January 29: Lecture 9 is available below.
January 28: Solutions to Midterm 1 pdf.
January 27: Lecture 8 is available below.
January 25: Solutions to Practice Midterm 1 pdf.
January 23:
- Homework 3 has been posted below. Due: Sunday, Jan 31, 11:59 PM.
- Homework 1 has been graded. Regrades will be active on Gradescope on Monday, Jan 24 - Tuesday, Jan 25.
- Midterm 1 will take place on Wednesday, January 27. It will cover the material of lectures 1-7.
- Instructions for the first midterm can be found here. Important: Late submissions (after the 65 minute deadline) will not be accepted: it is your responsibility to submit the exam on time.
- Practice Midterm 1 can be downloaded here / solution.
- Next week there will be an office hour on Tuesday. There will be no office hours/Q&A sessions on Wednesday. For the times, check the Google calendar below.
January 22: Lecture 7 is available below.
January 20: Lecture 6 is available below. There is also an additional short video with several important examples.
January 16:
- Quiz 2 will take place on Wednesday, January 20 on Canvas and will cover the material of Lectures 3, 4 and 5. More information below.
- Homework 2 is available for download below. Due: Friday, January 22, 11:59 PM.
January 15: Lecture 5 is available below.
January 13:
- Lecture 4 is available below.
- There was a typo in Problem 9 of Homework 1; it has been corrected; please check the updated problem sheet below.
January 10:
- Lecture 3 is available below.
- Quiz 1 will take place on Wednesday, January 13 on Canvas and will cover the material of Lectures 1 and 2. More information below.
January 9: Homework 1 is available for download below. Due: Friday, January 15, 11:59 PM.
January 8: Lecture 2 is available below.
January 5: Lecture 1 is available below.
January 4: Welcome to MATH 142A: Introduction to Analysis I!

Course Information

Textbooks:
- The required textbook for this course is
  
  Elementary analysis: the theory of calculus, by Kenneth A. Ross; 2nd edition
  Reading and homework assignments will refer to this textbook as Ross.
- The link above goes to UCSD library website, where the textbooks can be downloaded freely and legally if you are connecting from a UCSD IP address.
Coursework: There will be
- homework assignments due roughly every week, typically on Fridays (starting in Week 2); they are posted below;
- quizzes taking place on Thursdays of Weeks 2, 3, 5, 7 and 10; details below;
- two midterm exams on Weeks 4 and 8; details below;
- and a final exam; details below.
The list of the important dates can be found here.

Piazza is an online discussion forum. It will allow you to post messages (openly or anonymously) and answer posts made by your fellow students, about course content, homework, exams, etc. The instructors and TAs will also monitor and post to Piazza regularly.
- For all questions related to the course, ask your questions on Piazza before contacting the instructor/TAs directly.
- You can sign up here.
- Note: Piazza has an opt-in "Piazza Careers" section which, if you give permission, will share statistics about your Piazza use with potential future employers. It also has a "social network" component, based on other students who've shared a Piazza-based class with you, that comes with the usual warnings about privacy concerns. Piazza is fully FERPA compliant, and is an allowed resource at UCSD. Nevertheless, you are not required to use Piazza if you do not wish.

Gradescope is an online tool for uploading and grading assignments and exams (it is now under the umbrella of Turnitin). You will turn in your homework through Gradescope, and you will access your graded exams there as well.
- Access the class Gradescope site here.
- Homework 0 below will guide you through the Gradescope sign up process for this class.

Canvas is a learning management system (LMS) used by UCSD. We will use Canvas for Quizzes and for sharing certain course materials. Make sure that you have acces to the MATH 142A course.

Instructional Staff and Office Hours

Name	Role	Office	E-mail	Office hours	Zoom link
Yuriy Nemish	Instructor	-	ynemish@ucsd.edu	Monday 6:00-7:00pm Wednesday 4:00-5:00pm	link
Chengjie Huang	Teaching Assistant	-	chh164@ucsd.edu	Thursday 8:00-9:00pm Friday 4:00-5:00pm	link link

Please, check the following calendar for possible reschedulings of the office hours.

Calendar

Zoom Meetings

	Date	Time	Zoom link
Live Q&A (YN)	Monday, Wednesday, Friday	3:00 - 3:30pm	link
Discussion C01 (CH)	Thursday	6:00 - 6:50pm	link
Discussion C02 (CH)	Thursday	7:00 - 7:50pm	link

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Important dates

	Week	Date	Time
Quiz 1	2	Wednesday, Jan 13	see Quizzes
Quiz 2	3	Wednesday, Jan 20	see Quizzes
Midterm Exam 1	4	Wednesday, Jan 27	see Midterm Exams
Quiz 3	5	Wednesday, Feb 3	see Quizzes
Quiz 4	7	Wednesday, Feb 17	see Quizzes
Midterm Exam 2	8	Wednesday, Feb 24	see Midterm Exams
Quiz 5	10	Wednesday, Mar 10	see Quizzes
Final Exam	Finals	Wednesday, Mar 17	3pm - 6pm; see Final Exam

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Syllabus

Welcome to Math 142A: a one quarter course introduction to analysis (I). According to the UC San Diego Course Catalog, the topics covered are the real number system, numerical sequences and series, infinite limits, limits of functions, continuity, differentiation.

Here is a more detailed listing of course topics, in the sequence they will be covered, together with the relevant section(s) of the textbook. While each topic corresponds to approximately one lecture, there will be some give and take here. This is a rough schedule that will be updated during the term.

Q&A	Week	Topic	Ross	Slides	Lecture videos	Preliminary Slides	Additional Videos
1/4	1	Administrivia	-	-	-	-	-
1/6	1	ℕ and ℚ	§§ 1-2	Slides 1	Lecture 1	-
1/8	1	Ordered field	§ 3	Slides 2	Lecture 2	Slides 2
1/11	2	Completeness Axiom	§§ 4-5	Slides 3	Lecture 3	Slides 3
1/13	2	Limits of Sequences	§§ 7-8	Slides 4	Lecture 4	Slides 4
1/15	2	Limit Theorems for Sequences	§ 9	Slides 5	Lecture 5	Slides 5
1/18	3	Martin Luther King, Jr. Holiday
1/20	3	Limit Theorems for Sequences	§ 9	Slides 6	Lecture 6	Slides 6	Lecture 6 - Important Examples
1/22	3	Monotone Sequences	§ 10	Slides 7	Lecture 7	Slides 7
1/25	4	Cauchy Sequences	§ 10	Slides 8	Lecture 8	Slides 8
1/27	4	Midterm 1
1/29	4	Subsequences	§ 11	Slides 9	Lecture 9	Slides 9
2/1	5	Subsequences	§§ 11-12	Slides 10	Lecture 10	Slides 10
2/3	5	Series	§ 14	Slides 11	Lecture 11	Slides 11
2/5	5	Series	§§ 14-15	Slides 12	Lecture 12	Slides 12	Important Example 9
2/8	6	Continuous Functions	§ 17	Slides 13	Lecture 13	Slides 13
2/10	6	Properties of Continuous Functions	§ 18	Slides 14	Lecture 14	Slides 14
2/12	6	Uniform Continuity	§ 19	Slides 15	Lecture 15	Slides 15
2/15	7	President's Day Holiday
2/17	7	Uniform Continuity	§ 19	Slides 16	Lecture 16	Slides 16
2/19	7	Limits of Functions	§ 20	Slides 17	Lecture 17	Slides 17
2/22	8	Limits of Functions	§ 20	Slides 18	Lecture 18	Slides 18
2/24	8	Midterm 2
2/26	8	Basic Properties of the Derivative	§ 28	Slides 19	Lecture 19	Slides 19	Lecture 19 - Important Examples
3/1	9	The Mean Value Theorem	§ 29	Slides 20	Lecture 20	Slides 20
3/3	9	L'Hôpital's rule	§ 30	Slides 21	Lecture 21	Slides 21
3/5	9	Taylor's Theorem	§ 31	Slides 22	Lecture 22	Slides 22
3/8	10	Taylor's Theorem	§ 31	Slides 23	Lecture 23	Slides 23
3/10	10	Review		-	-	-	-
3/12	10	Review		-	-	-	-

Prerequisite: MATH 31CH or MATH 109 or concent of instructor.

Lecture: You are responsible for material presented in the lecture whether or not it is discussed in the textbook. You should expect questions on the exams that will test your understanding of concepts discussed in the lecture.

Homework: Homework assignments are posted below, and will be due at 11:59pm on the indicated due date. You must turn in your homework through Gradescope; if you have produced it on paper, you can scan it or simply take clear photos of it to upload. Your lowest homework score will be dropped. It is allowed and even encouraged to discuss homework problems with your classmates and your instructor and TA, but your final write up of your homework solutions must be your own work.

Quizzes: The quizzes will take place on the dates listed above.

You will able to access the quiz on the course Canvas page starting at 12am (PST) on the day of the quiz. The quiz will be accessible for 24 hours; however, once you start the quiz, you will only have 30 minutes to complete it (unless you start it later than 11:30pm (PST), in which case the 24 hour deadline is enforced since it comes before the end of your 30 minutes). For example, if you start the exam at 11:40pm (PST), you will need to submit it within 20 minutes to receive credit since the 24 hour deadline would come before the end of your 30 minutes.
There will be no makeup quizzes. See below for other policies.

Midterm Exams: The midterm exams will take place on January 27 and February 24 as listed above.

The exam will be available for 24 hours on Gradescope starting at 12am (PST) on the scheduled date: however, once you start the exam, you will have 65 minutes to finish and submit your exam. The exam is intended to take 50 minutes: the remaining 15 minutes are intended for the scanning and submission of the exam on Gradescope. In particular, we will not accept submissions after the 65 minute deadline: it is your responsibility to submit the exam on time. For example, if you choose to write the exam for 65 minutes and do not leave yourself enough time to scan the exam, then you will not receive credit for the exam.
As with the quizzes, the 24 hour deadline supersedes your allotted 65 minutes for the exam. For example, if you start the exam at 11:40pm (PST), you will need to submit it within 20 minutes to receive credit since the 24 hour deadline would come before the end of your 65 minutes.
There will be no makeup midterm exams. See below for other policies.

Final Exam: The final examination will be held at the officially scheduled time: 3pm - 6pm (PST) on March 17.

It is your responsibility to ensure that you do not have a schedule conflict involving the final examination; you should not enroll in this class if you cannot take the final examination at its scheduled time.
The written portion of the exam will be available on Gradescope at 3pm (PST) on March 17. Submissions are due at 4:30pm (PST) on Gradescope.
After the written portion, students will join a Zoom room from 4:30pm - 6pm (PST). During this time, the instructional staff will randomly select students for a follow-up oral exam to ensure academic integrity. A determination will be made based on the oral exam whether or not to file a case with the Office of Academic Integrity. If a student fails to report to the Zoom room, then they will automatically receive no points for the final exam.
There will be no makeup final exam. See below for other policies.
Zoom links and more detailed instructions will be announced later.

Exam policies

Quizzes and exams are open textbook, and you can rewatch lectures and review the lecture slides.
Keep in mind that any computations on exams must be supported by clear explanations. Simply writing down an answer without any justification or work will receive 0 points, even if the answer is correct (unless the problem specifically says that no justification is required).
You are not allowed to use calculators, computer algebra systems, or similar software. Of course, this also means that you will not be asked to solve problems on exams that require the aid of an electronic computing device.
You are not allowed to consult other people or resources on the internet. In particular, contract cheating and other instances of academic dishonesty can result in suspension or dismissmal. According to the Academic Integrity Office,

About 15% of students reported for cheating are suspended or dismissed from UCSD.

Administrative Links: Here are two links regarding UC San Diego policies on exams:

Exam Responsibilities An outline of the responsibilities of faculty and students with regard to final exams

Policies on Examinations The Academic Senate policy regarding final examinations (These are the rules!)

Regrade Policy:

Your exams and homeworks will be graded using Gradescope. You will be able to request regrades directly from your TA through Gradescope for a specified window of time. Be sure to make your request within the specified window of time; no regrade requests will be accepted after the deadline. Note: Your grader will consider your regrade request only if you have explained clearly, thoroughly, and politely why you think an error in grading was made.

Grading: Your cumulative average will be computed as the best of the following weighted averages:

20% Homework, 15% Quizzes, 15% Midterm 1, 15% Midterm 2, 35% Final Exam
20% Homework, 15% Quizzes, 15% Best midterm, 50% Final Exam

Your course grade will be determined by your cumulative average at the end of the quarter, and will be based on the following scale:

A+	A	A-	B+	B	B-	C+	C	C-
97	93	90	87	83	80	77	73	70

The above scale is guaranteed: for example, if your cumulative average is 80, your final grade will be at least B-. However, your instructor may adjust the above scale to be more generous.

Academic Integrity: UC San Diego code of academic integrity outlines the expected academic honesty of all studentd and faculty, and details the consequences for academic dishonesty. The main issues are cheating and plagiarism, of course, for which we have a zero-tolerance policy. (Penalties for these offenses always include assignment of a failing grade in the course, and usually involve an administrative penalty, such as suspension or expulsion, as well.) However, academic integrity also includes things like giving credit where credit is due (listing your collaborators on homework assignments, noting books or papers containing information you used in solutions, etc.), and treating your peers respectfully in class. In addition, here are a few of our expectations for etiquette in and out of class.

Noise and common courtesy: When class/section begins, please stop your conversations. Do not disturb others by engaging in disruptive behavior. Disruption interferes with the learning environment and impairs the ability of others to focus, participate, and engage.
Electronic devices: No visual or audio recording of the class meetings is allowed without prior permission of the instructor (whether by camera, cell phone, or other means).
E-mail etiquette: You are expected to write as you would in any professional correspondence. E-mail communication should be courteous and respectful in manner and tone. Please do not send e-mails that are curt or demanding.

Accommodations:

Students requesting accommodations for this course due to a disability must provide a current Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities (OSD) which is located in University Center 202 behind Center Hall. The AFA letter may be issued by the OSD electronically or in hard-copy; in either case, please make arrangements to discuss your accommodations with me in advance (by the end of Week 2, if possible). We will make every effort to arrange for whatever accommodations are stipulated by the OSD. For more information, see here.

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Homework

Weekly homework assignments are posted here. Homework is due by 11:59pm on the posted date, through Gradescope. Late homework will not be accepted.

Homework 0, due Friday, January 8.

Homework 1, due Friday, January 15.

Homework 2, due Friday, January 22.

Homework 3, due SUNDAY, January 31.

Homework 4, due SUNDAY, February 7.

Homework 5, due SUNDAY, February 14.

Homework 6, due SUNDAY, February 21.

Homework 7, due SUNDAY, February 28.

Homework 8, due SUNDAY, March 7.

Homework 9, due SUNDAY, March 14.