MA411 Half Unit
Probability and Measure
This information is for the 2025/26 session.
Course Convenor
Prof Peter Allen
Availability
This course is available on the MSc in Financial Mathematics, MSc in Mathematics and Computation and MSc in Quantitative Methods for Risk Management. This course is available with permission as an outside option to students on other programmes where regulations permit.
Requisites
Additional requisites:
Some background in real analysis is essential. Familiarity with basic probability (independence, expectation) will be helpful but not required.
Course content
The purposes of this course are (a) to explain the formal basis of abstract probability theory (measure theory), and the justification for basic results in the theory, and (b) to explore some applications.
The course will cover: Probability spaces and probability measures. Random variables. Expectation and integration. Convergence of random variables. Conditional expectation. The Radon-Nikodym Theorem. Martingales in discrete time. Markov chains. Large deviations.
Applications may include: Infection models. Dimension reduction in big data. Monte Carlo sampling. Randomised algorithms. Discrete time financial models.
Teaching
10 hours of seminars and 20 hours of lectures in the Autumn Term.
Formative assessment
Problem sets weekly
Written answers to set problems will be expected on a weekly basis.
Indicative reading
Full lecture notes will be provided. The following may prove useful: J S Rosenthal, A First Look at Rigorous Probability Theory; G R Grimmett & D R Stirzaker, Probability and Random Processes; D Williams, Probability with Martingales; M Caplinski & E Kopp, Measure, Integral and Probability; J Jacod & P Protter, Probability Essentials.
Assessment
Exam (90%), duration: 120 Minutes in the Spring exam period
Continuous assessment (10%) weekly
Key facts
Department: Mathematics
Course Study Period: Autumn Term
Unit value: Half unit
FHEQ Level: Level 7
CEFR Level: Null
Total students 2024/25: 10
Average class size 2024/25: 10
Controlled access 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
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills