MATH3060 - Mathematical Analysis III - 2020/21
Announcement
- Zoom Class Link: https://cuhk.zoom.us/j/91029844539?pwd=d2RweHh6Q2VBbWhqS05KUmU0ME5CUT09
- Zoom Class info: Meeting ID: 910 2984 4539 Passcode: 004881
- Homework, take-home exams will be conducted via Gradescope (in the tool of Blackboard)
- Homework 1 (due on Sep 25, 2020 at 12:00noon, submit using Gradescope)
- Homework 2 (due on Oct 6, 2020 at 12:00noon, submit using Gradescope)
- Homework 3 (due on Oct 16, 2020 at 12:00noon, submit using Gradescope)
- Homework 4 (Revised, typo in Q3) (due on Thursday Oct 22, 2020 at 12:00noon, submit using Gradescope) (The deadline is a day earlier than usual since completing it before the midterm can help your study.)
- Midterm: Oct 23, 2020, 9:30-11:00am, submission deadline 11:30am on Oct 23, 2020; take-home, conducted via Gradescope; Open book; coverage: up to Minskowski inequality (Detailed guidelines will be sent to your @link account by emails early next week.)
- Plagiarism will be checked seriously. If necessary, an oral exam will be conducted, for those involved student(s), to supplement the take-home midterm result.
- Homework 5 (due on Nov 6, 2020 at 12:00noon, submit using Gradescope)
- Midterm Stat: Mean=59.06, SD=16.68, Median=59.75, Max=99. Min=32
- Homework 6 (due on Nov 13, 2020 at 12:00noon, submit using Gradescope)
- Homework 7, further revised (due on Nov 20, 2020 at 12:00noon, submit using Gradescope)
- Homework 8 (due on Dec 3, 2020 at 12:00noon, submit using Gradescope)
General Information
Lecturer
-
WAN, Yau Heng Tom
- Office: LSB 215
- Tel: 3943 37986
- Email:
Teaching Assistant
-
LI, Yan Lung Leon
- Office: AB1 505
- Tel: 3943 4298
- Email:
-
LEE, Yat Long Luca
- Office: AB1 505
- Tel: 3943 4298
- Email:
Time and Venue
- Lecture: Wed 9:30-10:15am ERB803; Fri 9:30-11:15am ARC G03
- Tutorial: Wed 8:30-9:15am ERB803
Course Description
This course is a continuation of MATH2060. It provides rigorous treatment on further topics in mathematical analysis. This course is essential for studying advanced mathematics, pure or applied, to the level beyond undergraduate. Topics include: Fourier series, pointwise and uniform convergence of Fourier series, $L^2$-completeness of Fourier series. Parseval's identity; metric spaces, open sets and continuity, completion of a metric space, contraction mapping principle; the space of continuous functions, Weierstrass approximation theorem, Stone-Weierstrass theorem, Baire category theorem, continuous but nowhere differentiable functions, equicontinuity and Ascoli's theorem; implicit and inverse function theorems, functional dependence and independence; fundamental existence and uniqueness theorem for differential equations, the continuous dependence of the solution on initial time and values.
References
- Lecture Notes of Prof KS Chou (see below in Pre-class Notes)
- Stein & Shakarchi, Fourier Analysis, An Introduction, Princeton Lectures in Analysis I, Princeton University Press
- Rudin, Principles of Mathematical Analysis, McGraw Hill
- Copson, Metric Spaces, Cambridge University Press
Pre-class Notes
- Lecture Notes of Prof KS Chou, Chapter 0
- Lecture Notes of Prof KS Chou, Chapter 1
- Lecture Notes of Prof KS Chou, Chapter 2
- Lecture Notes of Prof KS Chou, Chapter 3
- Lecture Notes of Prof KS Chou, Chapter 4
Lecture Notes
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
- Lecture 6
- Lecture 7
- Lecture 8
- Lecture 9
- Lecture 10 (Revised)
- Lecture 11
- Lecture 12
- Lecture 13
- Lecture 14
- Lecture 15
- Lecture 16
- Lecture 17
- Lecture 18
- Lecture 19
- Lecture 20
- Lecture 21
- Lecture 22
- Lecture 23
Tutorial Notes
- Tutorial 1 (16 Sep)
- Tutorial 2 (23 Sep)
- Tutorial 3 (30 Sep) (Q1 Remark 2 corrected)
- Tutorial 4 (7 Oct)
- Tutorial 5 (14 Oct)
- Tutorial 6 (21 Oct)
- Tutorial 7 (28 Oct)
- Tutorial 8 (4 Nov)
- Tutorial 9 (11 Nov)
- Tutorial 10 (18 Nov)
- Tutorial 11 (25 Nov)
- Tutorial 12 (2 Dec)
Assignments
- Homework 1 (due on Sep 25, 2020 12:00noon)
- Homework 2 (due on Oct 6, 2020 at 12:00noon)
- Homework 3 (due on Oct 16, 2020 at 12:00noon)
- Homework 4 (revised, typo in Q3) (due on Thursday Oct 22, 2020 at 12:00noon)
- Homework 5 (due on Nov 6, 2020 at 12:00noon)
- Homework 6 (due on Nov 13, 2020 at 12:00noon)
- Homework 7 (due on Nov 20, 2020 at 12:00noon) (further revised)
- Homework 8 (due on Dec 3, 2020 at 12:00noon)
Solutions
- Remark on HW Submission
- MATH3060 HW1 Solution (Corrected)
- MATH3060 HW2 Solution
- MATH3060 HW3 Solution
- MATH3060 HW4 Solution (Updated)
- MATH3060 HW5 Solution
- MATH3060 HW6 Solution
- MATH3060 HW7 Solution
- MATH3060 HW8 Solution
Assessment Scheme
| Homework | 10% | |
| Mid-term (Oct 23, 2020, 9:30-11:15am; take-home and/or oral) | 40% | |
| Final (Dec 4. 2020, 9:30-11:15am; take-home and/or oral) | 50% |
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.
Assessment Policy Last updated: December 03, 2020 12:18:14