University of St Andrews

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 9

Semester: 1

Planned timetable: 11.00 am Mon (even weeks), Tue & Thu

This module continues the study of analysis begun in the 2000-level module MT2502 Analysis. It considers further important topics in the study of real analysis including: integration theory, the analytic properties of power series and the convergence of functions. Emphasis will be placed on rigourous development of the material, giving precise definitions of the concepts involved and exploring the proofs of important theorems. The language of metric spaces will be introduced to give a framework in which to discuss these concepts.

Relationship to other modules

Pre-requisite(s): Before taking this module you must pass MT2502

Learning and teaching methods and delivery

Weekly contact: 2.5-hours of lectures and 1 tutorial.

Scheduled learning hours: 35

Guided independent study hours: 115

Assessment pattern

As used by St Andrews: 90% exam, 10% class test

As defined by QAA
Written examinations : 90%
Practical examinations : 0%
Coursework: 10%

Re-assessment: Oral examination = 100%

Personnel

Module coordinator: Professor M J Todd
Module teaching staff: Prof Kenneth Falconer
Module coordinator email m.todd@st-andrews.ac.uk

Intended learning outcomes

• Appreciate the differing cardinalities of infinite sets and be able to determine whether sets are countable or uncountable
• Understand the formal development of the Riemann integral and the proof of the fundamental theorem of the calculus
• Understand the utility of uniform convergence of sequences and series of functions leading to differentiation and integration of power series
• See how many ideas in analysis can readily be extended to the settings of metric and normed spaces