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, takehome 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, 9:3011:00am, submission deadline 11:30am on Oct 23, 2020; takehome, 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 takehome 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 9:3010:15am ERB803; Fri 9:3011:15am ARC G03
 Tutorial: Wed 8:309:15am 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, StoneWeierstrass 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 Preclass 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
Preclass 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%  
Midterm (Oct 23, 2020, 9:3011:15am; takehome and/or oral)  40%  
Final (Dec 4. 2020, 9:3011:15am; takehome 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