MA3MTINU-Measure Theory and Integration

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:6
Semesters in which taught: Semester 1 module
Pre-requisites: MA1RA2NU Real Analysis II and MA2CANU Complex Analysis
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Current from: 2022/3

Module Convenor: Dr Nikos Katzourakis
Email: n.katzourakis@reading.ac.uk

Type of module:

Summary module description:

This module provides an introduction to measure theory and integration.

The Module lead at NUIST isÌýto be confirmed.

Aims:

The course gives an introduction to the general measure theoretical approach to integration. A unified approach to the concepts of length, area and integral is given.

Assessable learning outcomes:

By the end of the course, students are expected to be able:

to understand the concept of measure, measurability and integral construction for general measures;

to handle limits of integrals rigorously.

Additional outcomes:

Students should develop an understanding of the concepts of area, length and general measure theory. They should reflect on the difference, advantages and disadvantages of Riemann versus Lebesgue integration.

Outline content:

Measurable sets, measure, construction of measures, measure zero sets, measurable functions, construction of the integral, properties which hold almost everywhere, and limit theorems.

Brief description of teaching and learning methods:

Lectures supported by problem sheets.

Contact hours:

Ìý	Semester 1	Semester 2
Lectures	20
Guided independent study:	Ìý	Ìý
Ìý Ìý Wider reading (independent)	50
Ìý Ìý Wider reading (directed)	20
Ìý Ìý Exam revision/preparation	10
Ìý	Ìý	Ìý
Total hours by term	100	0
Ìý	Ìý	Ìý
Total hours for module	100

Summative Assessment Methods:

Method	Percentage
Written exam	100

Summative assessment- Examinations:

2 hours

Summative assessment- Coursework and in-class tests:

One examination paper.

Formative assessment methods:

Problem sheets.

Penalties for late submission:

The Support Centres will apply the following penalties for work submitted late:

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

The University policy statement on penalties for late submission can be found at:
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:

A mark of 40% overall.

Reassessment arrangements:

One examination paper of 2 hours duration in August/September only.

Additional Costs (specified where applicable):

Last updated: 29 March 2022