# ST318: Probability Theory

###### Lecturer(s): Prof Vassili Kolokoltsov

*Prerequisite(s)**:* ST342 Mathematics of Random Events or MA359 Measure Theory.

* Commitment:* 3 lectures/week, 1 tutorial/fortnight. This module runs in Term 2.

*Content**:* Independence and conditioning, probability measures on metric spaces, types of probabilistic convergence, an introduction to martingales.

** Aims**: This course aims to give the student a rigorous presentation of some fundamental results in measure theoretic probability and an introduction to the theory of discrete time martingales. In so doing it aims to provide a firm basis for advanced work on probability and its applications.

** Objectives**: The objectives of the course are as follows: at the end of the course the student will:

- Understand the ideas relating to independence and zero-one laws and be able to apply these ideas in simple contexts.
- Understand the different modes of convergence for sequences of random variables (more generally random elements) and the relationship between these different modes.
- Be able to state and prove the Central Limit Theorem and understand how this result can be applied.
- Understand some basic results on discrete time martingales.

*Assessment**: *100% by* *2-hour examination.

** Course Material: **Lecture notes, example sheets, and other module material are to be found at the Module Resources page. Note that lecture notes are made available progressively throughout the module.