COURSE CONTENT:
This course is about the exploration and understanding of a wide variety of random phenomena and processes. It consists of two parts.In the first part we will review some results of elementary Probability Theory and put them in a more rigorous and mature framework. We will look at the modelling of random experiments via probability spaces and probability distributions. We will consider concepts such as conditioning and independence which are of great importance for modelling information (or the lack thereof) in a random experiment. We will discover famous theorems such as the Law of Large Numbers and the Central Limit Theorem.
In the second part of the course we will deal with various Stochastic Processes such as Markov chains, Poisson Processes and Markov processes. We will explore the properties of these processes and find out how they can be used to model random phenomena in engineering, biology, finance, computer science and physics.
WHERE IS IT USED:
The theory of stochastic processes is one of the fastest growing areas in probability and statistics. Markov and Poisson processes are used to model the (random) dynamics of animal populations, stock markets, telecommunication systems, vehicle traffic, production lines, DNA mutations and many more. Obviously, there is much cross-fertilisation between probability and statistics (statistical inference), but the field has connections to many other areas of both applied and pure mathematics. For example, certain complicated integrals can be easily evaluated by Monte Carlo simulation; randomised algorithms can be used to solve NP complete combinatorial problems; and stochastic processes can be used to solve certain (partial) differential equations.WHO IS INTERESTED:
This course is for anyone in mathematics, engineering, finance, physics, computer science, biology and other disciplines who is likely to encounter random processes in their study or future work, and for anyone who would like to use a thorough understanding of random processes to their advantage. The course is suitable for third and fourth year students.
WHAT DO I NEED:
There are no formal prerequisites for this course, but you should have an appreciation and basic knowledge of integration and linear algebra. A complete set of lecture notes with everything you need to know can be purchased from the Copy Shop of the university.
WHEN IS IT AVAILABLE:
The course is given every year, in Semester 2.