MA411 Half Unit
Probability and Measure
This information is for the 2021/22 session.
Teacher responsible
Dr Pavel Gapeev
Availability
This course is available on the MSc in Applicable Mathematics, MSc in Financial Mathematics and MSc in Quantitative Methods for Risk Management. 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
This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Michaelmas Term. This year, some or all of this teaching will be delivered through a combination of virtual classes and lectures delivered as online videos.
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 summer exam period.
Course selection videos
Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.
Important information in response to COVID-19
Please note that during 2021/22 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the differing needs of students in attendance on campus and those who might be studying online. For example, this may involve changes to the mode of teaching delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.
Key facts
Department: Mathematics
Total students 2020/21: 20
Average class size 2020/21: 11
Controlled access 2020/21: No
Value: Half Unit
Personal development skills
- Self-management
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills
