Probability and Measure - Michaelmas 2009

Notes and problems are available as a single pdf file, or by lecture number 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 and example sheet number 1, 2, 3, 4.


Schramm-Loewner evolutions - Lent 2010

Here are the notes for this year's course. There are also examples sheets (1, 2) and slides from the lectures ( 1, 2, 3, 4, 5/6, 7/8, 9, 10) You are advised not to print the slides.


Optimization and Control - Michaelmas 2007

Notes for the course can be downloaded a single file or in sections:

1. Controllable dynamical systems, 2. The dynamic optimality equation, 3. Finite-horizon dynamic optimization, 4. Dynamic optimization for non-negative rewards, 5. Dynamic optimization for discounted costs, 6. Dynamic optimization for non-negative costs, 7. Optimal stopping, 8. Dynamic optimization for long-run average costs. 9. Full controllability of linear systems, 10. Linear systems with non-negative quadratic costs, 11. Certainty-equivalent control, 12. LQG systems and the Kalman filter, 13. Observability, 14. The LQG model in equilibrium. 15. The Hamilton-Jacobi-Bellman equation, 16. Pontryagin's maximum principle, 17. Continuous-time stochastic systems, 18. Existence and uniqueness of solutions for differential equations.

Examples sheets are here: Examples Sheet 1, Examples Sheet 2, Examples Sheet 3. Supervisors of the course may wish to have an enhanced version of these sheets which is available from me on request.

Slides from the lectures are here:1, 2, 3, 4, 5-8, 9-10, 11-13, 14, 15, 16, 17.

Much of the material in the notes and examples sheets is derived from a previous version of the course given by Richard Weber.


Advanced Probability

Here are the notes from an old version of the course.


James Norris
Statistical Laboratory
University of Cambridge

Last modified: August 2011

Notes from courses given in past years