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MATH40430

Academic Year 2024/2025

Measure Theory & Integration (MATH40430)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
4 (Masters)
Credits:
5
Module Coordinator:
Dr Michael Mackey
Trimester:
Autumn
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

Measure theory simply seeks to assign a measure, or quantity, to certain sets (typically in R^n) which is consistent, reasonably general, and agrees with our intuition in familiar situations. With this, one can develop the Lebesgue theory of integration which has several advantages over the rather limited Riemann integral. The material is fundamental to modern analysis, particularly stochastic processes and the mathematical models of financial markets.

About this Module

Learning Outcomes:

On successful completion of this module the student should appreciate the shortcomings in the Riemann integral and the necessity for the introduction of the Lebesgue integral; be familiar with the basic theory of sigma algebras,
measurable functions and integrable functions; know the conditions under which it is possible to swap limits and integration; be familiar with applications of measure theory to functional analysis, potential theory and other areas of mathematics.

Student Effort Hours:
Student Effort Type Hours
Lectures

30
Tutorial

6
Specified Learning Activities

24
Autonomous Student Learning

60
Total

120

Approaches to Teaching and Learning:
.

Requirements, Exclusions and Recommendations

Not applicable to this module.


Module Requisites and Incompatibles
Pre-requisite:
MATH10320 - Mathematical Analysis

Incompatibles:
MATH30360 - Measure Theory & Integration, MATH40790 - Measure Theory (online)

Additional Information:
Students should have completed a first course on mathematical analysis, such as MATH10320, which provides familiarity with concepts such as the completeness axiom, uniform convergence of functions, cardinality of sets and "epsilon-delta" arguments.


 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Assignment(Including Essay): Homework Week 3, Week 6, Week 9, Week 12 Standard conversion grade scale 40% No
20
 No
Exam (In-person): Final exam End of trimester
Duration:
2 hr(s)
 Standard conversion grade scale 40% No
80
 No

Carry forward of passed components
No
 

Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Feedback individually to students, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Fri 15:00 - 15:50
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Thurs 15:00 - 15:50
Autumn Lecture Offering 1 Week(s) - Autumn: All Weeks Tues 16:00 - 16:50
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