MATH3060  Mathematical Analysis III  2021/22
Announcement
 No tutorial in the 1st week
 Facetoface classes, midterm, and final exam. However, homework will be assigned and collected using Gradescope (in the tool of Blackboard)
 Homework 1 (due on Sep 24, 2021, 12:00noon, submit via Gradescope system)
 Homework 2 (due on Oct 8, 2021 at 12:00noon, submit via Gradescope system)
 Homework 3 (due on Oct 15, 2021 at 12:00noon, submit via Gradescope system)
 Homework 4 (due on Thursday Oct 21, 2021 at 12:00noon, submit via Gradescope system)
 Midterm exam next Friday Oct 22, 2021 during class (9:3011:00am), covers material up to Oct 15 and homework 4.
 Homework 5 (due on Wednesday Nov 10, 2021 at 12:00noon, submit via Gradescope system)
 Midterm statistics: average=48.97, SD=18.33, Max=90, Min=7
 Homework 6 (due on Nov 19, 2021 at 12:00noon, submit via Gradescope system)
 Homework 7 (due on Nov 26, 2021 at 12:00noon, submit via Gradescope system)
 Homework 8 (No need to handin, solution will be posted on Dec 8, 2021)
 Final exam: 18:3020:30, Dec 16, 2021, University Gym; covers all materials with emphasis on those after the midterm exam
General Information
Lecturer

Tom Yauheng Wan
 Office: LSB 215
 Tel: x 37986
 Email:
Teaching Assistant

Chan Ki Fung
 Office: AB1 505
 Tel: 394 34298
 Email:
Time and Venue
 Lecture: Wed 9:3010:15am ERB703; Fri 9:3011:15am WMY305
 Tutorial: Wed 08:3009:15am ERB703
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.
(Basic knowledge of (continuous) functions and sequences of (continuous) functions are expected including convergence, uniform convergence, differentiability, and integrability)
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
 B. Thomson, J Bruckner, & A Bruckner, Elementary Real Analysis, Prentice Hall
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
 Lecture 11
 Lecture 12
 Lecture 13
 Lecture 14
 Lecture 15
 Lecture 16
 Lecture 17
 Lecture 18
 Lecture 19
 Lecture 20 (revised)
 Lecture 21
 Lecture 22
Tutorial Notes
 15 Sept
 29 Sept
 6 Oct
 Solution of a tutorial question
 20 Oct
 Solutions to some of questions of Tutorial 4
 27 Oct
 3 Nov
 Supplement to tutorial 6
 10 Nov
 17 Nov
 24 Nov
 1 Dec (corrected some typos)
 Solution to 1st Dec Q4
Assignments
 Homework 1 (due on Sep 24, 2021, 12:00noon)
 Homework 2 (due on Oct 8, 2021 at 12:00noon)
 Homework 3 (due on Oct 15, 2020 at 12:00noon)
 Homework 4 (due on Thursday Oct 21, 2021 at 12:00noon)
 Homework 5 (due on Wednesday Nov 10, 2021 at 12:00noon)
 Homework 6 (due on Nov 19, 2021 at 12:00noon)
 Homework 7 (due on Nov 26, 2021 at 12:00noon)
 Homework 8 (No need to handin, solution will be posted on Dec 8, 2021))
Solutions
 Assignment 1
 Assignment 2
 Assignment 3
 Assignment 4
 Assignment 5 (updated Q3)
 Assignment 6
 Assignment 7
 Assignment 8(updated Q4)
Assessment Scheme
Homework  10%  
Midterm (Oct 22, 2021, 9:3011:15am)  40%  
Final (18:3020:30, Dec 16, 2021 University Gym)  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 08, 2021 18:38:45