Course Details in

Module Title	Linear Analysis
School	Mathematics
Department	Mathematics
Module Code	06 22788
Module Lead	Michael Cowling
Level	Honours Level
Credits	20
Semester	Full Term
Pre-requisites	LI Linear Algebra & Linear Programming - (06 25765) LI Real & Complex Analysis - (06 25666) Real & Complex Analysis - (06 27146) LI Linear Algebra - (06 15552)
Co-requisites
Restrictions	none
Contact Hours	Lecture-46 hours Tutorial-10 hours Total: 56 hours
Exclusions
Description	One half of this course 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. The other half 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.
Learning Outcomes	By the end of the module the student should be able to: Understand the limitations of Riemann integration and how the Lebesgue integral overcomes many of these Manipulate abstract sets to prove results on measurability and measure Apply the main theorems on Lebesgue integration to solve problems of convergence of functions Work in infinite dimensional Hillbert and Banach spaces, finding bases of Hilbert space, and using different types of convergence Combine ideas from algebra and analysis to solve problems in functional analysis
Assessment	22788-01 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions	Assessments: 22788-01: Exam : Exam (CT) - Written Unseen (90%) Continuous Assessment : Coursework or class Tests (10%):
Other
Reading List