Explore UCD

UCD Home >

MATH40790

Academic Year 2024/2025

Measure Theory (online) (MATH40790)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
4 (Masters)
Credits:
5
Module Coordinator:
Dr Conor Finnegan
Trimester:
Autumn
Mode of Delivery:
Online
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
Specified Learning Activities

24

Autonomous Student Learning

60

Online Learning

36

Total

120


Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning.

Requirements, Exclusions and Recommendations
Learning Requirements:

A first course in Mathematical Analysis equal or equivalent to MATH10320 is required.

Learning Recommendations:

It is recommended that students have taken first courses in Calculus and Metric Spaces, equal or equivalent to MATH10350 and MATH30090, respectively.


Module Requisites and Incompatibles
Incompatibles:
MATH30360 - Measure Theory & Integration, MATH40430 - Measure Theory & Integration


 

Assessment Strategy  
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Exam (Online): 2 Hour Final Online Exam Week 14 Standard conversion grade scale 40% No

80

No
Assignment(Including Essay): Exercise sheet problems submitted during the semester Week 6, Week 8, Week 10, Week 12 Standard conversion grade scale 40% No

20

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

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Name Role
Dr Conor Finnegan Lecturer / Co-Lecturer