Math 142B: Introduction to Analysis

Spring 2020

Lectures / office hours / Q&A sessions / etc. on Zoom will be recorded and reposted.


Elementary Analysis: The Theory of Calculus (Second Edition), Kenneth A. Ross,

Springer 2013, ISBN-10: 1461462703, ISBN-13: 978-1461462705 (The textbook is available for free to UCSD students on the campus network, and can be found by searching in UCSD's Library Catalog).

Course Description

We aim to cover most parts of Chapters 4-6 of the textbook. Topics covered in the course will include: sequences and series of functions, uniform convergence, differentiation, integration.

Instructor and TAs

Hang Xu


Office Location: AP&M 6305

Office Hours: MW 4:00-5:30 pm via Zoom

Gongping Niu


Office Location: AP&M 6414

Office Hours: ThSa 2:00-3:00 pm and F 6:00-7:00 pm via Zoom

Lecture (delivered via Zoom)

MWF 3:00-3:50 pm

Discussion Sections (delivered via Zoom)

C01 F 5:00-5:50 pm

C02 F 6:00-6:50 pm


Your cumulative average will be:

We will have three exams in total and each exam will be 50 minutes long. You can take it at your convenient time within a given 24 hours time window. We will examine your starting time and submission time on Canvas and Gradescope. Here are the exam schedules:

Follow-up AI checks via Zoom: Our TA will look for any possible signs of academic misconduct during grading the exam. Any student may be asked to a follow-up Zoom meeting in which they will be asked to justify their work on the exam and show that it was their own work. If the follow-up is unconvincing, or the student is unable or unwilling to engage, their exam will be forwarded to the AI Office for a potential violation.

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



















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.

The detailed online exam instructions are available on Canvas.

Gradescope homework

The homework should be submitted directly to Gradescope through Canvas by 8:00 pm on Sundays.

Guidelines for submission through Gradescope:

Course policies

Resources for assistance

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. You can find our class registration page and class homepage.

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.


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. We will make every effort to arrange for whatever accommodations are stipulated by the OSD. For more information, see here.

Academic Integrity

Academic dishonesty is considered a serious offense at UCSD. Students caught cheating will face an administrative sanction which may include suspension or expulsion from the university. It is in your best interest to take pride in your work maintain your academic integrity. (Click here for more information.)

Noise and common courtesy: When class/section begins, please stop your conversations. Wait until class/section is over before putting your materials away in your backpack, standing up, or talking to friends. 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: Please do not use devices (such as cell phones, laptops, tablets, iPods, smart watches) for non-class-related matters while in class/section. No visual or audio recording is allowed in class/section without prior permission of the instructor (whether by camera, cell phone, or other means).

Tentative schedule (will be updated as the course progresses)

Homework will be posted by every Wednesday and due 8:00 pm on the next Sunday.

Week 1 (3/30, 4/1, 4/3): uniform continuity, limits of functions, power series.

Read 3.19, 3.20, 4.23.
Homework 1: problems 19.4, 19.7, 20.1, 20.2, 20.11, 20.18, 23.2, 23.6.
No homework is due.

Week 2 (4/6, 4/8, 4/10): uniform convergence.

Read 4.24.
Homework 2: problems 23.3, 23.4, 23.5, 23.7, 23.8, 23.9, 24.1, 24.2.
Homework 1 is due on 4/12.

Week 3 (4/13, 4/15, 4/17): more on uniform convergence.

Read 4.25.
Homework 3: problems 24.9, 24.10, 24.11, 24.12, 24.13, 24.15, 24.17, 25.2.
Homework 2 is due on 4/19.

Week 4 (4/20, 4/22, 4/24): differentiation and integration of power series.

Read 4.26.
Homework 4: problems 25.3, 25.5, 25,6, 25.8, 25.10, 26.2, 26.4, 26.6.
Homework 3 is due on 4/26.
Week 5 (4/27, 4/29, 5/1): basic properties of the derivatives.
Read 5.28.
Exam I is on Monday.
5/1 is the last day to drop without ‘W’.
Homework 5: problems 25.7, 25.9, 28.2 (c) (d), 28.3 (b) (c), 28.4, 28.5, 28.14, 28.16.
Homework 4 is due on 5/3.

Week 6 (5/4, 5/6, 5/8): the mean value theorem.

Read 5.29.
Homework 6: problems 29.2, 29.3, 29.4, 29.5, 29.7, 29.9, 29.12, 29.14.
Homework 5 is due on 5/10.

Week 7 (5/11, 5/13, 5/15): Taylor’s theorem.

Read 5.30.
5/15 is the last day to drop without ‘F’.
Homework 7: problems 29.16, 29.17, 29.18, 31.1, 31.2.
Homework 6 is due on 5/17.
Week 8 (5/18, 5/20, 5/22): the Riemann integral.
Read 6.32.
Exam II is on Monday.
Homework 8: problems 32.1, 32.2, 32.3, 32.6, 32.7, 33.4, 33.5.
Homework 7 is due on 5/24.

Week 9 (5/27, 5/29): properties of the Riemann integral.

Read 6.33.
No class on Monday for Memorial Day observance.
Homework 9: problems 32.8, 33.6, 33.7, 33.8, 33.9, 33.13, 34.3, 34.12.
Homework 8 is due on 5/31.

Week 10 (6/1, 6/3, 6/5): fundamental theorem of calculus.

Read 6.34.
Homework 9 is due on 6/7.
6/5 is the last day to change to P/NP grade (update: this is extended to week 11).

Exam III is on Wednesday 6/10.