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Unit information: Functional Analysis 3 in 2018/19

Please note: you are viewing unit and programme information for a past academic year. Please see the current academic year for up to date information.

Unit name Functional Analysis 3
Unit code MATH36202
Credit points 20
Level of study H/6
Teaching block(s) Teaching Block 2 (weeks 13 - 24)
Unit director Dr. Hassannezhad
Open unit status Not open
Pre-requisites

MATH 20200 Metric Spaces 2.

Co-requisites

none

School/department School of Mathematics
Faculty Faculty of Science

Description

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.

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 6 version of the Level 7 unit Functional Analysis 34, and students may not take both units.

Additional unit information can be found at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html

Intended learning outcomes

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.

Transferable Skills

Deductive thinking; problem-solving; mathematical exposition.

Teaching details

Lectures (30) and recommended problems.

Assessment Details

90% Examination and 10% Regular homework questions.

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.

Reading and References

Reading and references are available at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html

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