Aims and Outcomes

**Education Aims**

This module forms part of the Analysis Pathway within Pure Mathematics, providing an introduction to some of the principal theorems of linear functional analysis. Basic properties of Banach spaces are covered enabling students to combine linear and metric topological ideas for proving theorems and exploring examples.

**Learning Outcomes**

A student who completes this module successfully should be able to:

*Knowledge and understanding*

- define and state some of the main concepts and theorems of functional analysis;
- apply these in the investigation of examples;
- prove basic propositions concerning functional analysis.

*Intellectual skills*

- apply complex ideas to familiar and to novel situations;
- work with abstract concepts and in a context of generality;
- reason logically and work analytically;
- perform with high levels of accuracy;
- transfer expertise between different topics in mathematics.

*Professional skills*

- select and apply appropriate methods and techniques to solve problems;
- justify conclusions using mathematical arguments with appropriate rigour;
- communicate results using appropriate styles, conventions and terminology.

*Transferable skills*

- communicate with clarity;
- work effectively, independently and under direction;
- analyse and solve complex problems accurately;
- adopt effective strategies for study.