Unit name | Functional Analysis 34 |
---|---|

Unit code | MATHM6202 |

Credit points | 20 |

Level of study | M/7 |

Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |

Unit director | Dr. McGillivray |

Open unit status | Not open |

Pre-requisites |
MATH 20200 Metric Spaces 2 |

Co-requisites |
none |

School/department | School of Mathematics |

Faculty | Faculty of Science |

Unit aims

The unit aims to provide students with a firm grounding in the theory and techniques of functional analysis and to offer students ample opportunity to build on their problem-solving ability in this area. It also aims to equip students with independent self-study and presentation-giving skills.

General Description of the Unit

This unit sets out to explore some core notions in functional analysis. Functional analysis originated partly in the study of integral equations. It forms the basis of the theory of operators acting in infinite dimensional spaces. It is helpful in analysing trigonometric series and can be used to make sense of the determinant of an infinite-dimensional matrix. It has found broad applicability in diverse areas of mathematics (for example, spectral theory). Students will be introduced to the theory of Banach and Hilbert spaces. This will be followed by an exposition of four fundamental theorems relating to Banach spaces (Hahn-Banach theorem, uniform bounded-ness theorem, open mapping theorem, closed graph theorem). The unit may also include some discussion of the spectral theory of linear operators.

Relation to Other Units

This is a Level 7 version of the Level 6 unit Functional Analysis 3, and students may not take both units. See Assessment Methods for the differences.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

Learning Objectives

By the end of the unit, students will

- understand basic concepts and results in functional analysis;
- be able to solve routine problems;
- have developed skills in applying the techniques of the course to unseen situations;
- have acquired independent self-study skills through guided reading;
- have acquired presentation-giving skills.

Transferable Skills

Deductive thinking; problem-solving; mathematical exposition; presentation skills

Lectures (30), recommended problems, guided reading and presentation.

90% Examination and 10% Coursework.

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

The course will follow portions of the text Kreyszig, E., Introductory Functional Analysis with Applications, John Wiley & Sons (1989).

The following textbooks may also be useful,

W. Rudin, Functional Analysis

N. Young, An Introduction to Hilbert Space