MA321 Half Unit
Measure Theoretic Probability
This information is for the 2025/26 session.
Course Convenor
Prof Graham Brightwell
Availability
This course is available on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Data Science, BSc in Mathematics with Economics, Erasmus Reciprocal Programme of Study and Exchange Programme for Students from University of California, Berkeley. This course is freely available as an outside option to students on other programmes where regulations permit. It does not require permission. This course is available with permission to General Course students.
Requisites
Pre-requisites:
Students must have completed MA203 before taking this course.
Course content
This is a first course in measure-theoretic probability. It covers the following topics. Abstract probability spaces: sample spaces, sigma-algebras, probability measures, examples. Borel sigma-algebra, Lebesgue measure. Random variables: distribution functions, discrete and absolutely continuous distributions, examples. Expectation and the Lebesgue integral: convergence theorems and properties. Different modes of convergence of random variables. Conditional expectation: definition, properties, examples. Changes of probability measure, Bayes' theorem.
Teaching
20 hours of lectures and 10 hours of classes in the Autumn Term.
Formative assessment
Written answers to set problems will be expected on a weekly basis.
Indicative reading
Comprehensive lecture notes will be provided.
The following books may prove useful:
D Williams, Probability with Martingales.
J. Jacod & P. Protter, Probability Essentials; A. Klenke Probability Theory. A Comprehensive Course
Assessment
Exam (100%), duration: 120 Minutes in the Spring exam period
Key facts
Department: Mathematics
Course Study Period: Autumn Term
Unit value: Half unit
FHEQ Level: Level 6
CEFR Level: Null
Total students 2024/25: 23
Average class size 2024/25: 12
Capped 2024/25: NoCourse selection videos
Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.
Personal development skills
- Self-management
- Problem solving
- Communication
- Application of numeracy skills
- Specialist skills