Discrete Fourier Analysis 2010/11 (Sandro Mattarei)

Contents

The main goal of the course is understanding the main ideas behind the many manifestations of the Fourier transform in mathematics. The starting point will be the study of the discrete Fourier transform (or DFT) on a finite abelian group, along with a selection of its applications. We will also see how this relates to the more analytic topic of Fourier series and the classical Fourier transform. Depending on time we may see an introduction to how these ideas generalize to the case of nonabelian groups.

Course material

Much of the material for the course will be taken from the textbook
A. Terras, Fourier Analysis on Finite Groups and Applications,
London Mathematical Society Student Texts 43, Cambridge University Press, 1999.
More sources will be specified (in the Day-to-day schedule) as we go along.

Problem sheets

Every one or two weeks I will hand you a problem sheet, which you can also download from here. Please just ask me if you want to discuss the solutions. There will be no more problem sheets.

Lecture schedule

The lectures take place in the second semester, as follows:
Monday 14:30-16:30 Room 109
Wednesday 10:30-11:30 Room 109
Office hours: will be agreed on request.
Day-to-day schedule: dvi, pdf

The exam

The exam will consist of a written and an oral part. The written part will consist of solving a set of problems similar to those assigned in the problem sheets.

Le exam sessions are as follows.
  • Written exam, 6 June 2011, at 14.00 in room 106. Oral exam, one of the next few days.
  • Written exam, 25 July 2011, at 14.00 in room 106. Oral exam, most likely on 29 July (to be confirmed at the written exam).
  • Written exam, 5 September 2011, at 9.00 in room 101. Oral exam, one of the next few days.
  • Written exam, 25 January 2012, at 9.00 in room 101. Oral exam, the following morning.