MAS277 Vector Spaces and Fourier Theory

Spring Semester 2010-2011

Dr Sarah Whitehouse

This page is intended to supplement the main official module information with additional material. Here is the course front page.

Module information for 2010-2011

• Duration: 21 lectures: two lectures per week (except week 10, when there is a bank holiday Monday) and one tutorial every two weeks. There will be no lectures or tutorials in Week 12.
• Lecture times (Spring 2011): Monday at 10:00 in Hicks Lecture Theatre 7 and Friday at 11.10 in Hicks Lecture Theatre 7. 
• Lecturer: Dr Sarah Whitehouse, office J23, telephone extension: 23870
• Office hour: Wednesday 10-11
• Tutorial groups (Spring 2011): Weeks 1, 3, 5, 7, 9, 11.

To find your tutorial class for this course (and various others), go to the tutorials web page. Please attend the correct tutorial group; if you want to change groups, ask the lecturer.

Lecture notes

Here are notes for the course. Printed copies will be circulated in lectures. They contain definitions, statements of results and discussion. You need to take notes in lectures of proofs and worked examples.

• lecture notes
• appendix (on the proof of the L^2 convergence theorem; not examinable)
• hand-out with reminders on trig identities and their use in calculating integrals in Fourier theory

Tutorial and homework problems

Here is the problem booklet for this module. It contains the complete problem set, including tutorial and homework problems.

You are strongly advised to do these questions, as they will aid your understanding of the course, and some may resemble exam questions. On the other hand, they do not form part of your formal assessment.

In some lectures, a lecture question will be announced; this will be done on the board at the start of the next lecture, but possibly quite quickly, so that those who have tried them may find it useful, but others may not.

The tutorial questions are those which will be attempted in the tutorials in Weeks 1, 3, 5, 7, 9 and 11.

Details of homework will appear here.

Full solutions to all problems.

Exam

The August Supplementary paper is 9:00 - 11:00 on Friday 19 August in the Philadelphia Conference Centre.

For the benefit of those re-sitting, here is the main 2010-2011 paper,  the solutions and some feedback. 

The main exam was 9:00 - 11:00 on Tuesday 31 May in the Octagon Centre.

Some detailed exam information is here and has been circulated in lectures. 

The part of the notes 3.34 to 3.37 inclusive was not lectured and is not examinable. 

Two past papers and solutions are below.

Exam 2009-2010

Here is the paper from Spring 2010, and here are the solutions.

Exam 2008-2009

Here is the paper from Spring 2009, and here are the solutions.

Miscellaneous links which may be of interest

Some biographical notes on mathematicians mentioned in lectures:

• Cauchy
• Fourier
• Hermite                                                                                                                                                                                        
• Schwarz

                                                                                                                                          Sarah Whitehouse       27 July 2011