MT4515 Functional Analysis

Academic year

2024 to 2025 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 10

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

Not automatically available to General Degree students

Planned timetable

12.00 noon Mon (even weeks), Tue and Thu

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof M J Todd

Prof M J Todd
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Dr Spyridon Dimoudis

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This object of this module is to familiarise students with the basic notions of functional analysis, that is analysis on normed spaces and Hilbert space. The module will cover normed spaces, convergence and completeness, operators, Hilbert spaces and may include topics such as spectral theory and the Hahn-Banach theorem.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2501 AND PASS MT3502

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x 10 weeks) and 1 tutorial (x 10 weeks).

Intended learning outcomes

  • Appreciate the interplay between linear algebra and analysis that arises in many areas of mathematics
  • Understand how notions from linear algebra and real analysis can be extended to infinite dimensional spaces;
  • Understand the notion of normed spaces, operators on normed spaces and their norms
  • Understand completeness in normed spaces and its consequences
  • Be able to apply the general theory of normed spaces and operators to specific problems such as solutions of differential equations
  • Understand the spectral theorem for compact self-adjoint operators on Hilbert space