MATH 355: Honors Analysis 4

Winter 2011

Course web page:

  • MWF 11:30-12:30, Burnside 920
  • Lectures on January 5, 7, will be given by N. Dimitrov.
  • Lecture on February 2 will be given by I. Gorelyshev.
  • There will be a review lecture on Wednesday, April 13, from 17:40-19:40, Burnside 920.
  • Lecture notes, final version: pdf

  • Instructor: D. Jakobson
    Office: BH1220, Office Hours: Wednesday, 10:30-11:30 and 12:30-13:00, or by appointment
    Tel: 398-3828
    E-mail: jakobson AT
    Web Page:
    Markers: TBA

    Prerequisites: Math 354 or equivalent
    Text: Elements of the Theory of Functions and Functional Analysis, by A. Kolmogorov and S. Fomin, Dover Publications.
    Syllabus: Lebesque measure, integration and Fubini's theorem. Abstract measure and integration. Convergence theorems. Introduction to Hilbert spaces. L_2 spaces, Fourier series. Fourier integrals (if time permits).
    Assignments: There will be be several assignments. Due dates will be announced in class and on the course web page. Late assignments will not be accepted, except in cases of emergency. Depending on availability of TA and other factors, some problems may not be marked.
  • Assignment 1, due Friday, January 28: ps and pdf. In section 33, problems 3, 5, 6 are now all extra credit. In section 37, problems 3, 4 are now both extra credit. Solutions: pdf
  • Assignment 2, Please, bring all you can on Friday, February 4; and the rest on Monday, February 7: ps and pdf. In section 40, problem 5 is extra credit. In section 41, problem 5 is extra credit. Problem 11 is extra credit. Solutions: pdf
  • Hausdorff Measure problem set 1 (extra credit), due date TBA: ps and pdf.
  • Assignment 3, due Friday, February 11: ps and pdf. Extra credit problems: sec. 42, no. 3; sec. 43, no. 3; sec. 44, no. 3. Solutions: pdf.
  • Assignment 4, due Wednesday, march 16: ps and pdf. Part 2: ps and pdf. Solutions: ps and pdf.
  • Assignment 5, due Monday, March 28 (extended): ps and pdf. Solutions: ps and pdf.
  • Assignment 6, due Monday, April 4 (extended): ps and pdf. Solutions: ps and pdf.

  • Midterm
  • In-class Midterm: There will be an in-class midterm, held on Monday, February 14, in Leacock 26. The room is booked from 6-9pm, the test will be held from 18:20-19:50.
  • Missed midterm cannot be redone. If you miss the midterm for any reason, the weights for your mark will be: Assignments 20%, Final 80%.
  • Take-home Midterm: Take-home midterm will be due on Monday, February 28. ps and pdf.
  • You can attempt both in-class and take home midterms; both will be marked, and your mark will be the highest of the two marks.

  • Final:
  • There will be a three hour final exam. Date: April 28, 14:00-17:00, Leacock 14/15. See exam schedule
  • Practice problems: pdf and ps. Please, note that many of the problems are more difficult than the problems on the final.
  • Material to review for the final: pdf and ps.
  • Office hours during the week of the final: Tuesday, April 26, 14:00-15:00. Wednesday, April 27, 14:00-15:30. Thursday, April 28, 11:00-12:00.

  • Supplemental: There will be a supplemental exam, counting 100% of the supplemental grade. No additional work will be accepted for D, F, or J.
  • An elementary proof of Lusin's theorem, by P. Loeb and E. Talvila
  • A short note about summability kernels: pdf and ps.

  • Grading: Your final mark will be the largest of the following: [20% Assignments + 30% Midterm + 50% Final]; OR [20% Assignments + 80% Final].
    WebCT: Your scores on assignments, midterm, final, and your final mark will be posted on WebCT
    Course material from previous courses at McGill:
  • Prof. V. Jaksic: 2010 Math 355
  • I. Feige took these lecture notes of Jaksic's math 355 lectures.
  • Prof. V. Jaksic: 2009 Math 354
  • A. Tomberg took Lecture notes of Prof. Jaksic's lectures.
  • Prof. D. Jakobson: 2006 Math 354
  • Linear algebra review (D. Jakobson): A note about determinants, ps and pdf.
  • Material from old Math 265 Course Pak (Prepared by Taylor and Labute): Implicit Function Theorem pdf and ps
  • Sam Drury's lecture notes for MATH 354 and MATH 355

  • Conferences etc
  • 14 Colloque pan-quebecois des etudiants del'ISM, May 20-22, 2011, Universite de Montreal.

  • Web links in Analysis
  • Metric space, Topology glossary, Functional analysis in Wikipedia
  • Norm, Holder's inequality, Minkowski inequality, Lp 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 book
  • Yahoo group in Harmonic Analysis + a page with listings of conferences, successors to Terry Tao's old page on Harmonic analysis.
  • Terry Tao's blog
  • HELPDESK and their email:
    WEB LINKS in Calculus, Algebra, Geometry and Differential Equations.
    NOTICE: In accord with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded.
    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).