Introduction to Markov Chains

Markov chains are one of the most elegant and powerful mathematical tools for modelling systems that evolve over time. They are widely used in computer science, data analysis, economics, decision-making, artificial intelligence, and countless applications where uncertainty plays a fundamental role. This course, Introduction to Markov Chains, has been designed to give you a clear, intuitive, and practical understanding of how these stochastic processes work and how you can apply them to real problems.

We begin by building a solid foundation: what stochastic processes are, how Markov chains are defined, and why the Markov property is so important. We explore transition matrices, state classifications, absorbing and recurrent states, and long-term behaviour. Every concept is introduced gently, using simple explanations, visual examples, and step-by-step reasoning.

As the course progresses, you will learn how to compute multi-step transitions, steady-state distributions, and long-run probabilities. These tools allow you to answer questions such as: What is the probability of the system being in a specific state after many transitions? Will the process stabilise over time? How can we model random events in a way that is both realistic and mathematically sound?

To make the theory applicable and engaging, the course includes numerous practical examples drawn from everyday scenarios: weather prediction, customer behaviour, queueing systems, board games, reliability models, and more. You will see how Markov chains can model situations where outcomes depend not on the full history, but on the current state — a simple yet incredibly powerful assumption.

By the end of the course, you will be able to model your own systems, construct transition matrices, classify states, compute long-term behaviour, and understand how Markov chains form the basis for more advanced topics such as Markov decision processes, PageRank, and stochastic simulations.

Whether you are a student, a data scientist, a programmer, or simply curious about how mathematical models can describe the world, this course gives you everything you need to confidently take your first steps into the world of Markov chains. No advanced mathematical background is required — just curiosity and a willingness to learn.

Join me and discover how Markov chains can transform the way you analyse and understand dynamic systems.