University of St Andrews

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 11

Semester: 1

Planned timetable: 11am Monday (odd weeks), Wednesday, Friday

This module introduces some of the powerful techniques and ideas of modern mathematical analysis that are important both in analysis in its own right and in its many applications in mathematics. The module will include topics such as: measure theory, integration theory and differentiation theory of measures. Mathematical analysis and the use of measure theory in analysis is one of the active research areas within the School, and the choice of topics will reflect current activity.

Relationship to other modules

Pre-requisite(s): Before taking this module you must pass MT3502

Anti-requisite(s): You cannot take this module if you take MT5825

Learning and teaching methods and delivery

Weekly contact: 2.5 lectures (x 10 weeks), 1 tutorial (x 9 weeks)

Scheduled learning hours: 34

Guided independent study hours: 119

Assessment pattern

As used by St Andrews: 2-hour Written Examination = 100%

As defined by QAA
Written examinations : 100%
Practical examinations : %

Re-assessment: Oral examination = 100%

Personnel

Module coordinator: Professor L O R Olsen
Module teaching staff:
Module coordinator email lo@st-andrews.ac.uk

Intended learning outcomes

• Understand the notion of a sigma-algebra and a measure
• Understand the definition of the Lebesgue integral
• Understand and appreciate the convergence results associated with the Lebesgue integral, including, the monotone convergence theorem and the dominated convergence theorem
• Understand the definition and the theory of the Lebesgue spaces L^p
• Understand the construction of product measures
• Understand Radon-Nikodym’s theorem