Math 142A Introduction to Analysis I

Winter 2022, Lecture C00: MWF 3:00-3:50pm, PETER 102


Course Information

Instructional Staff and Office Hours

NameRoleOfficeE-mailOffice hours Zoom link
Yuriy Nemish Instructor -
  • Wednesday 5:30 - 6:30 PM
  • Friday 1:30 - 2:30 PM
Zilu Ma Teaching Assistant -
  • Thursday 1:00 - 2:30 PM

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


(Zoom) Meetings

DateTimeZoom link
Lectures (live Q&A) Monday, Wednesday, Friday3:00 - 3:50pmlink
Discussion C01 Monday5:00 - 5:50pmlink


Important dates

Week Date Time
Midterm Exam 1 4 Wednesday, Jan 26 see Midterm Exams
Midterm Exam 2 8 Wednesday, Feb 23 see Midterm Exams
Final Exam Finals Wednesday, Mar 163pm - 6pm; see Final Exam



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&AWeekTopicRossSlidesLecture videosPreliminary SlidesAdditional Videos
1/31 Administrivia -----
1/51 ℕ and ℚ §§ 1-2Slides 1Lecture 1Slides 1
1/71 Ordered field § 3Slides 2Lecture 2Slides 2
1/102 Completeness Axiom §§ 4-5Slides 3Lecture 3Slides 3
1/122 Limits of Sequences §§ 7-8Slides 4Lecture 4Slides 4
1/142 Limit Theorems for Sequences § 9Slides 5Lecture 5Slides 5
1/173 Martin Luther King, Jr. Holiday
1/193 Limit Theorems for Sequences § 9Slides 6Lecture 6Slides 6Lecture 6 - Important Examples
1/213 Monotone Sequences § 10Slides 7Lecture 7Slides 7
1/244 Cauchy Sequences § 10Slides 8Lecture 8Slides 8
1/264 Midterm 1
1/284 Subsequences § 11Slides 9Lecture 9Slides 9
1/315 Subsequences §§ 11-12Slides 10Lecture 10Slides 10
2/25 Series § 14Slides 11Lecture 11Slides 11
2/45 Series §§ 14-15Slides 12Lecture 12Slides 12Important Example 9
2/76 Continuous Functions § 17Slides 13Lecture 13Slides 13
2/96 Properties of Continuous Functions § 18Slides 14Lecture 14Slides 14
2/116 Uniform Continuity § 19Slides 15Lecture 15Slides 15
2/147 Uniform Continuity § 19Slides 16Lecture 16Slides 16
2/167 Limits of Functions § 20Slides 17Lecture 17Slides 17
2/188 Limits of Functions § 20Slides 18Lecture 18Slides 18
2/217 President's Day Holiday
2/238 Midterm 2
2/258 Basic Properties of the Derivative § 28Slides 19Lecture 19Slides 19Lecture 19 - Important Examples
2/289 The Mean Value Theorem § 29Slides 20Lecture 20Slides 20
3/29 L'Hôpital's rule § 30Slides 21Lecture 21Slides 21
3/49 Taylor's Theorem § 31Slides 22Lecture 22Slides 22
3/710 Taylor's Theorem § 31Slides 23Lecture 23Slides 23
3/910 Review ----
3/1110 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.


Midterm Exams:  The two midterm exams will take place during the lecture time at the dates listed above.

Final Exam:  The final examination will be held at the date and time stated above.

The above exam policies will be applied to in-person exams. The exam policies will be changed in case of the changes in exam modality.

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

Regrade Policy:  

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

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.


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.



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