Discrete Mathematics module (MA12007)

Discrete mathematics is the study of maths that deals with separate, distinct values. This is the kind of thinking behind algorithms, networks, puzzles, and many real-world systems. This module introduces you to a wide range of mathematical techniques used to model, analyse, and solve problems in probability, decision-making, and logic.

You’ll explore how systems change over time using difference equations and generating functions. You'll learn how to find approximate solutions to equations using iterative methods like Newton-Raphson, which are widely used in computer simulations. You'll also study Markov chains - models that describe systems that evolve step by step, from queues to genetics to games of chance.

In the second half of the module, you’ll discover how game theory is used to make strategic decisions and how combinatorics helps count possibilities in structured ways. This module will sharpen your logical reasoning and problem-solving skills.

What you will learn

In this module, you will:

• solve and analyse first- and second-order difference equations
• use iterative methods like Newton-Raphson to find approximate solutions
• study discrete-time Markov chains and explore their long-term behaviour
• learn basic game theory for modelling competitive decisions
• apply counting methods using permutations and combinations

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

• solve structured problems using discrete mathematical techniques
• apply iterative methods to approximate solutions of equations
• model and interpret Markov processes in a range of scenarios
• analyse simple games and determine optimal strategies
• use combinatorics to count outcomes and solve logical puzzles

Assignments / assessment

• Coursework (40%)
• Final written exam (60%)

Teaching methods / timetable

• lectures
  • These will introduce theory with examples, applications, and worked problems
• tutorials
  • These are small-group sessions to practise techniques and get feedback