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: No
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Personal development skills

  • Self-management
  • Problem solving
  • Application of information skills
  • Communication
  • Application of numeracy skills
  • Specialist skills