Math 142A: Introduction to Analysis

Winter 2020


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 Chapters 1-3 of the textbook. Topics covered in the course will include: the real number system, numerical sequences and series, limits of functions, continuity.


Hang Xu


Office Location: AP&M 6305

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

Course Assistant

Chengjie Huang


Office Location: AP&M 2000A

Office Hours: M 2:00-3:00 pm, Th 2:00-4:00 pm


MWF 3:00-3:50 pm at Peterson Hall 103

Discussion Sections

C01 F 5:00-5:50 pm at WLH 2209

C02 F 6:00-6:50 pm at WLH 2209


Your cumulative average will be the best of the following two 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:



















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 final exam is changed to be online. Here is the detailed instructions.

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 page 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.


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) 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 (1/6, 1/8, 1/10): The Real Number System

Read 1.1, 1.2, 1.3.
Homework 1: Chapter 1, problems 2.3, 2.5, 2.8, 4.6 (b), 4.7.
No homework is due.

Week 2 (1/13, 1/15, 1/17): The Completeness Theorem

Read 1.4, 1.5, 2.7.
Further reading: 1.6 on the Dedekind cuts.
Homework 2: Chapter 2, problems 8.1 (b) (c), 8.2 (a), 8.5, 8.8 (c), 8.9 (a), 8.10.
Homework 1 is due on 1/19.

Week 3 (1/22, 1/24): Limit of Sequences

Read 2.8, 2.9.
No class on Monday for the Martin Luther King, Jr. Holiday.
Homework 3: Chapter 1, problem 1.12; Chapter 2, problems 9.4, 9.6, 9.9 (a) (c), 9.10 (a), 9.12, 9.14.
Homework 2 is due on 1/26.

Week 4 (1/27, 1/29, 1/31): Limit Theorems for Sequences

Read 2.10.
1/31 is the last day to drop without ‘W’.
Homework 4: Chapter 2, problems 10.1, 10.2, 10.8, 10.10.
Homework 3 is due on 2/2.
Week 5 (2/3, 2/5, 2/7): Subsequences
Read 2.11.
Homework 5: Chapter 2, problems 10.5, 10.6, 10.7, 11.3, 11.6, 11.7, 11.8.
Midterm is on Wednesday in class.
Homework 4 is due on 2/9.

Week 6 (2/10, 2/12, 2/14): Series

Read 2.12, 2.14.
Homework 6: Chapter 2, problems 11.5, 11.10, 11.11, 12.1, 12.3 (d) (e) (f), 12.4, 12.11.
Homework 5 is due on 2/16.
2/14 is the last day to drop without ‘F’.

Week 6 (2/19, 2/21): Alternating Series and Integral Tests

No class on Monday for President’s Day.
Homework 7: Chapter 2, problems 12.2, 12.6, 12.10, 12.12, 12.14, 14.1, 14.4.
Homework 6 is due on 2/23.
Read 2.15.
Week 8 (2/24, 2/26, 2/28): Continuous Functions
Read 3.17.
Homework 8: Chapter 2, problems 14.6 (a), 14.8, 14.9, 15.1, 15.2, 15.3, 15.4 (b) (d), 15.6.
Homework 7 is due on 3/1.

Week 9 (3/2, 3/4, 3/6): Continuous Functions

Read 3.18.
Homework 9: Chapter 3, problems 17.9 (b) (c) (d), 17.10 (a) (b), 17.12, 17.13, 18.4, 18.5, 18.6, 18.10.
Homework 8 is due on 3/8.

Week 10 (3/9, 3/11, 3/13): Uniform Continuity

Read 3.19.
Homework 9 is due on 3/15.

Final Exam 3:00-6:00 pm on March 18