Resources for MATH3969: Measure Theory and Fourier Analysis (Advanced)

This page contains links to tutorial and assignment sheets and other handouts (no hard copies will be distributed).

Also look at the Unit Information Sheet.

Lecture Notes

Lecture Notes are available as a PDF

• Partial notes (typeset version, partially completed) I hope to be able to complete the notes during the semester, but will not promise for sure. Please report any typos or other shortcomings in person or by email.
• Notes from 2011 (handwritten, scanned PDF 35MB)
• I managed to typeset the complete notes.

What's New

Important announcements will be posted here.

• Pre exam consultations: you can see me any time. If you want to be sure I am in send a brief e-mail.

• >>> Look at the Exam Information:

  Check the official exam timetable and information for the time and date of the exam.

  Only material covered in lectures and tutorials will be tested. The exam will also contain questions on the theory and proofs, and not just problems to solve.

  You can look at the 2009 exam (solutions) and the 2011 exam (solutions).

• Quiz 2 has been returned in the lecture on Tuesday 30 October. Those who have not picked theirs up can get it from the lecturer (Carslaw Room 715) any time. Solutions are available.
• The assignment has been returned in the lecture on 23 October. Solutions are available.
• Quiz 2 takes place on Wednesday 24 October during the tutorial 9-10am. The material covered is
  • limit theorems (monotone/dominated convergence, continuity and differentiability of integrals)
  • Theory of \(L^p\)-spaces (main properties, Hölder, Jensen , Minkowski inequality)
  • Theory and application of convolution and approximate identities
  • Fourier transform on \(L^1\) and \(L^2\) including Plancherel's theorem

  Tested will be the definitions, main theorems and the ability to apply and verify these in simple examples.

  You can look at last year's quiz

  Note that all rules regarding special consideration apply.

• >>> If you plan to do honours next year consider attending the AMSI Summer School. You may get credit for some units (approval by the honours coordinator needed.)
• A forth installment of the typeset notes is now available. Some corrections have been made to the other two installments. You can also get the complete version.
• A third installment of the typeset notes is now available. Some corrections have been made to the other two installments.
• The Assignment is available. It is due 12 October. (posted 29 September) Note \(M\) should be \(S\) in Question 2(a).
• Quiz 1 has been returned in the lecture on Wednesday 5 September. Those who have not picked theirs up can get it from the lecturer (Carslaw Room 715) any time. Solutions are available.
• Applications for Vacation Scholarships 2012-2013 are now open. Consider applying if you plan to do Honours next year.
• A second installment of the typeset notes is now available.
• Thanks to all those who provided corrections for the typeset lecture notes! I have updated the PDF.

• Quiz 1 takes place on Wednesday 29 August during the tutorial 9-10am. Material covered is up to and including the definition of the Lebesgue integral of non-negative functions and the monotone convergence theorem (Section 12 in the typeset notes). Tested will be the definitions, main theorems and the ability to apply and verify these in simple examples.

  You can look at last year's quiz

  Note that all rules regarding special consideration apply.

Schedule

Tutorial and assignment sheets and solutions are available as PDF files. If you have problems printing the PDF files look at the PDF Help Page