MATH2050C - Mathematical Analysis I - 2019/20

Announcement

• Note that revised date and time for the final take-home test. It will be available at 9:30AM on May 8, 2020 and the submission deadline is 9:30AM on May 9, 2020.
• Problem Set 11, 12 are posted and the due dates are Apr 27 (Mon) and May 1 (Fri) respectively.
• Due to potential security issues, we have revised the passwords for all the ZOOM meetings. Please check you email to receive the new passwords.
• The online course and teaching evaluation (OCTE) will be available from Apr 24, 9:30AM. Please be reminded to submit your answers by Apr 25, 11:15AM.
• Problem Set 10 is posted and the due date is Apr 20 (Mon).
• Lecture Notes have been posted for revision purpose.
• Final Exam will be replaced by a take-home test conducted online via Blackboard, in a way similar to the midterm. It will be available on May 5, 2020 at 8:30AM May 8, 2020 at 9:30AM and the submission deadline will be May 6 at 8:30AM May 9 at 9:30AM.
  • Your submitted solution will be checked carefully to avoid plagiarism. Discussions amongst classmates are strictly prohibited.
  • Please note that some of you may be chosen to attend an oral interview (either online or in person) to explain his/her answers to the final exam and possibly answer additional questions from the instructor. If a student fails to demonstrate sufficient understanding of his/her own answers, there will be severe penalty towards his/her course grade.
  • The final test and midterm will be open-book and open-notes (allowing search on internet), but it has to be done absolutely by yourself without asking others in any format.
• Midterm will be conducted online using "Blackboard" as a "take-home midterm" with 24 hours limit. It will be available on April 15, 2020 at 8:30am and the deadline for submission (via "Blackboard") is April 16, 2020 at 8:30am.
  • It will cover topics in Chapter 2-4 of the textbook (except binary/decimal representations, limsup/liminf, 3.6, 3.7 and 4.3).
  • Due to the midterm, there will be no ZOOM tutorial/lecture on Apr 15.
  • Your submitted solution will be checked carefully to avoid plagiarism. Discussions amongst classmates are strictly prohibited.
• Note that there is no lectures or tutorials during from Mar 30 to Apr 3 due to Reading Week. Tutorials and lectures will resume on April 8.
• Problem Set 9 is posted and the due date is Apr 10 (Fri).
• Solutions to some difficult problems for Chapter 2 and 3 has been posted.
• Problem Set 8 is posted and the due date is Mar 27 (Fri).
• Problem Set 7 is posted and the due date is Mar 20 (Fri).
• A typo in the challenging exercises of Problem Set 5 is fixed (thanks to Jiaxin for pointing this out).
• Problem Set 6 is posted and the due date is Mar 13 (Fri).
• Problem Set 5 is posted and the due date is Mar 6 (Fri).
• From Feb 26 onwards, you can submit your completed classwork problems on Blackboard (the same way as for homework). Our TAs will give comments to your submissions.
• Problem Set 4 is posted and the due date is Feb 28 (Fri).
• The revised due date of Problem Set 3 is Feb 21 (Friday). Please try to submit your assignment through Blackboard well ahead of the due time so as to avoid possible delay caused by technical issues. Your submitted assignments will be marked with comments online through blackboard. You may also check your scores for problem sets under "My Grades".
• Special announcement on the course arrangements:
  • To reduce the risk of spreading the novel coronavirus, the university has announced to provide online teaching starting from 17 February until further notice.
  • Please keep checking the course webpage for any new updates about the course. We will be using a combination of (i) Course Webpage (for course materials); (ii) ZOOM (for lectures and appointments); (iii) Blackboard (for lecture videos, homework submission and Q&A).
  • Each lecture and tutorial will be a ZOOM "Meeting" hosted by the instructor and/or TAs, taking place during the same time as they have normally been scheduled. The particulars of the meetings are as follow:
    • Lecture (Wed 9:30-10:15AM) ID: 261-527-914
    • Lecture (Fri 9:30-11:15AM) ID: 515-260-839
    • Tutorial (Wed 8:30-9:15AM) ID: 862-987-175
    Alternatively, you can also click on the corresponding links under the "Useful Links" section below (using the same passwords as above). Please try your best to get familiar with various built-in functions (especially “Raise Hand”, “Chat” and “Private Message” functions) in ZOOM. Lectures will be recorded and uploaded to Blackboard in a folder under “Panopto Video”.
  • For homework assignments, please do NOT come to campus to submit your completed assignments. Instead, you can either type up your assignment or scan a copy of your written assignment into ONE PDF file and submit through CUHK Blackboard on/before the due date. Please remember to write down your name and student ID. You can refer to the webpage under "Useful Links" below about how to submit assignments through Blackboard.
  • We will suspend the rest of the quizzes. A new midterm date (likely in late March til mid April) will be announced later when the situation becomes clearer. The assessment scheme will be revised accordingly pending approval from the Department Chair.
  • If you have any questions, you can stay in the ZOOM meeting after class or you can email me to set up an appointment for a future ZOOM meeting. You are also highly encouraged to use the "Discussion Board" in Blackboard as well. Anyone of you are welcomed to ask and answer questions posted there, I will be regularly checking and replying some of the posts myself as well.
• If you are a student sitting in this course, please send me an email to let me know so that I can keep you updated about the course via emails.
• Quiz 1 will take place on Jan 22 (Wed) in class. It will cover topics from Section 2.1, 2.2 and 2.3.
• Problem Set 2 is posted and the due date is Jan 22 (Wed) at 9:15AM.
• Problem Set 1 is posted and the due date is Jan 15 (Wed) at 9:15AM.
• There is no tutorial in the first week. The first lecture will be on Jan 8 (Wed) from 9:30 to 10:15am at LPN LT.

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General Information

Lecturer

• LI Man-chun Martin
  • Office: LSB 236
  • Tel: 3943-1851
  • Email:
  • Office Hours: by appointment

Teaching Assistant

• LO Chiu Hong
  • Office: LSB 228
  • Tel: 3943-7955
  • Email:
  • Office Hours: Wed 2:30-4:30PM
• WANG Gaoming
  • Office: LSB 222A
  • Tel: 3943-3575
  • Email:
  • Office Hours: Tue 2:00-4:00PM

Time and Venue

• Lecture: Wed 9:30-10:15AM at LPN LT; Fri 9:30-11:15AM at LSB LT3
• Tutorial: Wed 8:30-9:15AM at LPN LT

Course Description

This course is intended to provide conceptual understanding in the theory of functions of one variable. Topics include: real numbers, real valued functions, set notations; limits of sequences, convergence, Bolzano-Weierstrass; limits of functions, continuous functions, uniform continuity.

Textbooks

• "Introduction to Real Analysis" (4th edition) by R.G. Bartle and D.R. Sherbert, John-Wiley and Sons, NY, 2011

References

• "Principles of Mathematical Analysis" by W. Rudin, McGraw-Hill, 1976

Pre-class Notes

• Course outline (revised on Jan 8)

Lecture Notes

• Lecture on Feb 19
• Lecture on Feb 21
• Lecture on Feb 26
• Lecture on Feb 28
• Lecture on Mar 4
• Lecture on Mar 6
• Lecture on Mar 11
• Lecture on Mar 13
• Lecture on Mar 18
• Lecture on Mar 20
• Lecture on Mar 25
• Lecture on Mar 27
• Lecture on Apr 8
• Lecture on Apr 17
• Lecture on Apr 22
• Lecture on Apr 24
• Lecture on Apr 29

Tutorial Notes

• Tutorial notes 1 (Jan 15)
• Tutorial notes 2 (Jan 22)
• Tutorial notes 3 (Feb 19)
• Tutorial notes 4 (Feb 26)
• Tutorial notes 5 (Mar 4)
• Tutorial notes 6 (Mar 11)
• Tutorial notes 7 (Mar 18)
• Tutorial notes 8 (Mar 25)
• Tutorial notes 9 (Apr 8)
• Tutorial notes 10 (Apr 22)
• Tutorial notes 11 (Apr 29)

Assignments

• Problem Set 0 (no need to hand in)
• Problem Set 1 (due on Jan 15)
• Problem Set 2 (due on Jan 22)
• Problem Set 3 (due on Feb 21)
• Problem Set 4 (due on Feb 28)
• Problem Set 5 (due on Mar 6)
• Problem Set 6 (due on Mar 13)
• Problem Set 7 (due on Mar 20)
• Problem Set 8 (due on Mar 27)
• Problem Set 9 (due on Apr 10)
• Problem Set 10 (due on Apr 20)
• Problem Set 11 (due on Apr 27)
• Problem Set 12 (due on May 1)

Solutions

• .

Assessment Scheme

Assignments and Quizzes		20%
Midterm (available on Apr 15 at 8:30AM)		35%
Take-home final test (available on May 8 at 9:30AM)		45%

Useful Links

• Link to ZOOM meeting for Wed Lectures (if you are in Hong Kong)
• Link to ZOOM meeting for Fri Lectures (if you are in Hong Kong)
• Link to ZOOM meeting for Wed Tutorials (if you are in Hong Kong)
• Link to ZOOM meeting for Wed Lectures (if you are in mainland China)
• Link to ZOOM meeting for Fri Lectures (if you are in mainland China)
• Link to ZOOM meeting for Wed Tutorials (if you are in mainland China)
• How to submit assignments through CUHK Blackboard

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

http://www.cuhk.edu.hk/policy/academichonesty/

and thereby help avoid any practice that would not be acceptable.

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Assessment Policy

Last updated: January 11, 2022 10:40:27