Level of study Third/Final year
Credit value 20
Semester Students may study either 1 or both.
Pre-requisite modules 22497,22507
Linear Analysis underpins much modern mathematics, from partial differential equations to probability theory. One half of this course introduces Hilbert space, Banach spaces, dual spaces, and linear operators, and explores the interaction between linear algebra and analysis in the study of infinite dimensional spaces. The other half examines integration in more detail, and develops the theory of measurability, measure and the Lebesgue integral on euclidean spaces. The concepts of measure and integral are then extended to the more abstract context of measure spaces, and the monotone and dominated convergence theorems for the Lebesgue integral are proved.