Program Overview

Stochastic Processes Module

The Stochastic Processes module, coded as MA51005, is a comprehensive program designed to explore randomness and uncertainty through the study of Markov chains, Brownian motion, and probabilistic models. These concepts are fundamental across various disciplines, including science and finance.

Module Overview

This module is valued at 15 credits and is offered at level 5, during semester 1. It is part of the School of Science and Engineering, under the discipline of Mathematics. The program delves into the mathematical tools necessary for understanding and analyzing stochastic systems, which are prevalent in real-world scenarios such as stock markets, weather patterns, population dynamics, and particle movement through fluids.

What You Will Learn

In this module, students will:

• Study random variables, probability measures, and key theorems like the law of large numbers and central limit theorem.
• Explore Markov chains, including the Markov property, invariant measures, and first passage times.
• Learn about Brownian motion and how it arises from random walks.
• Be introduced to stochastic differential equations and Gaussian processes.
• Apply stochastic models to real-world problems in science, finance, and biology.

By the end of this module, students will be able to:

• Construct and analyse probabilistic models using rigorous mathematical methods.
• Solve problems involving random walks, Markov chains, and Brownian motion.
• Apply stochastic techniques to systems with uncertainty.
• Use analytical and numerical tools to explore randomness in practical settings.

Assignments / Assessment

The assessment for this module consists of:

• Coursework (100%), which includes written problem sets involving theoretical and applied questions. There is no final exam for this module.

Teaching Methods / Timetable

The teaching methods include:

• Lectures: Structured exploration of core theory and practical examples.
• Tutorials: Small-group problem-solving sessions.

Courses

This module is available on the following courses:

• Mathematics MMath (Hons)
• Mathematics and Physics MSci (Hons)
• Mathematics and Physics BSc (Hons)
• Mathematics BSc (Hons)
• Mathematical Biology BSc (Hons)

It is also part of the Physics courses, including Mathematics and Physics MSci (Hons) and Mathematics and Physics BSc (Hons).