MAT571S Linear Analysis, 2008-09

Announcement

• 17 Oct.: At the request of some student, I am attaching a file of Lecture Notes I - V and the Supplementary Notes (I missed p. V.11). Please amend it as follows: at the end of Cor on p.III.4, add "provided X_j \neq \emptyset, j=1,2.", at the end of the first sentence in the Cor. on p.III.9, add "and C \neq \emptyset". [Download file]
• 20 Oct.: Please return your Assignment 1 paper (but keep a xerox copy for your own reference) to me.
• 7 Nov.: Herewith attached is the scanned amended p.VI.13/14. [Download file]
• 14 Nov.: You should have read Sections 1, 3, 5 of Chapter 4 of the textbook by 25 Nov. 2008.
• 21 Nov.: A set of additional exercises is poste herewith for your consideration. [Download file]
• 21 Nov.: The amended p.VII.20 is posted herewith. [Download file]
• 25 Nov.: In the last part of our last lecture class on 27 Nov. 2008, we will do some revision work and talk about the final exam.
• 3 Dec.: Please note the date, time and venue of the final exam (posted below). The exam will be close-books and close-notes (as announced long ago, before the mid-term test took place), with scope covering pp.I.1 -- VIII.6 of the lecture notes, including the two sets of supplementary notes (pp.1 - 5, pp.2.S.1 - 2.S.7), i.e. Chapter 1, Chapter 2 and the first section of Chapter 3 of the lecture notes, and the corresponding material in the textbook. The main focus is on convergence, completeness and compactness. In the exam, you are not expected to do complicated calculations, but if you think you may need to use a pocket calculator, you should bring along yours (no sharing of calculators will be allowed). If your calculator is not of the types approved for usage in HKCEE, you must seek our approval first; in general, calculators in which you can input new programs will NOT be allowed. If in your revision, you need my help in connection to understanding the lecture notes, the model answers of the assignments, etc., you may write me an email with your specific problems, or to make an appoinment for an interview. As for solutions to the additional exercises, my impression is that students haven't spent enough effort to learn from the model answers of both assignments and examples in the lecture notes, nor our comments on the solution papers. In order to avail maximum benefit to those who do put in their own effort, I would like to propose that students may try to work out their own solutions, and send them to me via email, then I'll input some comments and further help.
• 4 Dec. I plan to be in my office from 10:30am to 4:30pm this Saturday 6 Dec. so that you can come to ask questions. If you do plan to come, please let me know by emailing me before 10:30pm this Friday 5 Dec.

General Information

Course Description

The course will be an introduction to linear structures and various concepts of limits/convergence in analysis especially in the context of Euclidean /Banach/Hilbert spaces (including the Lebesgue Integration Spaces). We will cover most of Chapters One to Four of the textbook, supplementing with material on Hilbert spaces and other topics.

Textbooks

• C. C. Pugh, Real Mathematical Analysis, Springer 2002.

References

• 1. D. S. Bridges, Foundation of Real and Abstract Analysis, Springer, 1998.
• 2. K. R. Davidson, A. P. Donsig, Real Analysis with Real Applications, Prentice Hall, 2002.

Lecture Notes

• Insert to Lecture Notes of 2 Oct. 2008
• Lecture Notes for 30 Oct. 2008 (please note the amendment of p.VI.13-14 filed in the announcement section above)
• Lecture Notes of 13 Nov. 2008
• Lecture Notes for 20 Nov. 2008 (Part 1) (please note the amendment on p.VII.20 posted in the announcement)
• Lecture Notes for 20 Nov. 2008 (Part 2)
• Lecture Notes for 27 Nov. 2008

Assignments

• Suggested Solutions of Assignment 1 (with Correction Comment added for Prob. VI)
• Suggested Solutions of Assignment 2

Solutions

• Model Solution of the Mid-term Test

Assessment Scheme

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:

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