MATH3060 - Mathematical Analysis III - 2020/21

Course Year: 
2020/21
Term: 
1

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


Tutorial Notes


Assignments


Solutions


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: November 27, 2020 11:18:01