Professor Steve Alpern, COL 3.06

The course is primarily intended for students taking MSc Applicable Mathematics. Students on other MSc programmes may follow this course, provided they fulfil the pre-requisites.

A background in undergraduate mathematics, in particular linear algebra (for instance, at the level of MA201 Further Mathematical Methods (Linear Algebra)) and ordinary calculus (for example, at the level of MA200 Further Mathematical Methods (Calculus)), would be sufficient as a prerequisite. Some degree of mathematical maturity is expected.

This course aims at familiarizing the student with the basic concepts, principles and methods of functional analysis and its applications. The topics covered are: normed and Banach spaces, continuous linear transformations, inner product and Hilbert spaces, compact operators, applications to differential equations, numerical analysis, optimization, and approximation theory with illustrative examples.

20 lectures (MA412) and 10 seminars (MA412.A) in MT

Weekly exercises are set and marked.

Jean-Pierre Aubin, Applied Functional Analysis, Wiley, 2000; A.V. Balakrishnan, Applied Functional Analysis, Springer, 1981; Erwin Kreyszig, Introductory Functional Analysis with Applications, John Wiley, 1989; Nicholas Young, An Introduction to Hilbert Space, Cambridge University Press, 1988.

There will be a formal two-hour written examination in the ST (90%) and one piece of coursework to be completed in the middle of the MT (10%).