Welcome to the Functional Analysis (MT4515) course webpage (this is an old page, put here to give some idea of what the 2025 version will be like, but is subject to changes). Most of the information on this course, tutorial sheets etc., can be downloaded from MySaint. The official description of this course is here.
Lectures: Tue, Thur, Even Mon 12pm-1pm
Tutorials: TBC (likely Thursday 2pm-3pm)
Contact Information
Lecturer: Mike Todd
Office: 320, Mathematical Institute
Email: m.todd -at- st-andrews.ac.uk
Course webpage: http://www.mcs.st-and.ac.uk/~miket/MT4515.html
Tutorial Questions
There will be tutorial questions assigned every week. These are not assessed, but if you would like feedback you will be able to hand in work for that, starting in week 2.
Recording
In line with University policy, and technology permitting, recordings of lectures and tutorials will be made available.
Topics covered
Bounded linear operators on normed spaces.
The operator norm.
Finite dimensional spaces.
Spaces of continuous functions.
Banach spaces.
Inner product spaces and Hilbert spaces.
The spectrum of a bounded linear operator.
Compact operators.
The spectral theorem for compact self-adjoint operators.
Assessment
100% by two hour examination
Textbooks
Rynne, B.P. & Youngson, M.A., Linear Functional Analysis, Springer, 2nd Ed 2007.
Young, N., An Introduction to Hilbert Space, Cambridge University Press, 1988.
Griffel, D.H., Applied Functional Analysis, Dover, 2nd Ed 2002.
Bollobas, B, Linear Analysis: An Introductory Course, Cambridge University Press, 2nd Ed 1999.