MATH 564, Advanced Real Analysis I, Fall 2008

Course web page: http://www.math.mcgill.ca/jakobson/courses/math564-08.html

Lectures: MWF 9:30-10:30, Burnside 1205. Lectures start on September 3.
Tuesday, December 2, 9:30-10:30, Burnside 1205

Instructor: D. Jakobson
Office: BH1212, Office Hours: M 11:00-12:00, W 10:00-11:00 (may be adjusted), or by appointment
Tel: 398-3828
E-mail: jakobson AT math.mcgill.ca
Web Page: www.math.mcgill.ca/jakobson

Prerequisite: Math 354, 355 or equivalent

Marker: Tayeb Aissiou
Email: aissiou@math.mcgill.ca

Text

Required: W. Rudin, Real and Complex Analysis, McGraw-Hill.

Syllabus: Review of theory of measure and integration; product measures, Fubini's theorem; L^p spaces, basic principles of Banach spaces; Riesz representation theorem for C(X); Hilbert spaces; further material as time permits.

Tests

There will be a midterm that will count 30% of the grade. You can write a take-home midterm, in-class midterm or both. Your grade will be the maximum of the 2 scores.

Take-home midterm, due Friday, November 7, by 4pm: pdf and ps. Solution sketches: pdf and ps.

In-class midterm, Wednesday, November 12, 16:40-18:10, Burnside 1214. It is a closed-book exam.

There will be a final exam, which will count for 40% of the grade. You can write a take-home final, in-class final or both. Your grade will be the maximum of the 2 scores.

Take-home final, due December 15: pdf and ps

In-class final, Wednesday, December 10, 9:00-12:00, Room 1B24.

Grading: Your final mark will be the largest of the following: [30% Assignments + 30% Midterm + 40% Final]; OR [30% Assignments + 70% Final].

WebCT: Your scores on assignments, midterm, final, and your final mark will be posted on WebCT

Supplemental: There will be a supplemental exam, counting for 100% of the supplemental grade. No additional work will be accepted for D, F or J.

Homework will be assigned in class and will be due by 5pm by the specified deadline.

Assignments

Problem Set 1 (due Wednesday, September 17 by 5pm): ps and pdf.
Solutions: page 1, page 2, page 3, page 4, page 5, page 6

Problem Set 2 (due Wednesday, October 8): ps and pdf.
Solutions: page 1, page 2, page 3

Problem Set 3 (due date to be announced): ps and pdf.
Additional problems: ps and pdf. Solutions, part 1: pdf and ps. Solutions, part 2: pdf and ps. Solutions, part 3: pdf. Solutions, version 2: pdf and ps.

Problem Set 4 (due date to be announced): ps and pdf. Solutions (pdf): page 1, page 2, page 3

Problem Set 5 (due date to be announced): ps and pdf. Solutions: pdf, ps

Course material from previous courses at McGill:

Old Math 354 web page, D. Jakobson, Fall 2006

Sam Drury's lecture notes for MATH 354 and MATH 355

Old Math 366 web page, D. Jakobson, Fall 2007

Web links in Analysis

Metric space, Topology glossary, Functional analysis in Wikipedia

Norm, Holder's inequality, Minkowski inequality, L^p space, Hilbert space, Banach space, Cantor set, p-adic numbers in Wikipedia

Notes on differentiation of functions of several variables, implicit function theorem

Companion notes to Rudin's (undergraduate!) book

Harmonic Analysis page by Terry Tao (there is a lot of advanced stuff there)

HELPDESK and their email: helpdesk@math.mcgill.ca

NOTICE: McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see McGill web page on Academic Integrity for more information).