MA411 Half Unit
Probability and Measure
This information is for the 2014/15 session.
Teacher responsible
Prof Graham Brightwell
Availability
This course is available on the MSc in Applicable Mathematics, MSc in Financial Mathematics and MSc in Risk and Stochastics. This course is available as an outside option to students on other programmes where regulations permit.
Pre-requisites
Some background in real analysis is essential.
Course content
The purposes of this course are (a) to explain the formal basis of abstract probability theory, and the justification for basic results in the theory, and (b) to explore those aspects of the theory most used in advanced analytical models in economics and finance. The approach taken will be formal. Probability spaces and probability measures. Random variables. Expectation and integration. Convergence of random variables. Conditional expectation. The Radon-Nikodym Theorem. Martingales. Stochastic processes. Brownian motion. The Itô integral.
Teaching
20 hours of lectures and 9 hours of seminars in the MT. 1 hour of seminars in the LT.
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 (100%, duration: 2 hours) in the main exam period.
Key facts
Department: Mathematics
Total students 2013/14: 23
Average class size 2013/14: 22
Controlled access 2013/14: No
Lecture capture used 2013/14: No
Value: Half Unit
Personal development skills
- Self-management
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills
