Discrete Mathematics module (MA12007)

Discrete mathematics is the mathematics of patterns, choices, structures, and strategy. It underpins many of the ideas behind modern data science, cryptography, networks, decision-making, computing, and pure mathematics. In this module, you will explore how mathematics works when objects are counted, arranged, connected, or combined. 

You will study set theory and combinatorics, learning how to count possibilities and understand structures made from distinct objects. These ideas help answer questions such as: how many arrangements are possible, how can choices be organised, and how can complex counting problems be solved systematically? 

You will also explore game theory, where mathematics is used to analyse strategic decisions and learn how mathematical models can describe situations where outcomes depend on the choices of others. 

The module also introduces group theory, one of the central areas of pure mathematics. You will see how abstract structures capture ideas such as symmetry, operation, and pattern, giving you an insight into the kind of thinking used in more advanced algebra. 

By developing your ability to reason clearly, count systematically, analyse strategies, and recognise structure, this module builds powerful problem-solving skills for later study in mathematics and for careers involving logic, modelling, data, and decision-making.

What you will learn

In this module, you will:

• explore set theory and how mathematicians organise collections of objects 
• learn powerful counting methods, including permutations and combinations 
• investigate how complex arrangements and patterns can be counted systematically 
• analyse strategic decision-making using game theory, including ideas such as dominance and Nash equilibrium 
• study the mathematical structures behind operations, groups, subgroups, and symmetry

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

• solve counting problems using clear and systematic methods 
• use set theory to organise and analyse mathematical information 
• turn strategic situations into mathematical models 
• identify good strategies in simple games 
• recognise basic structures in group theory and symmetry 
• apply discrete mathematics to both abstract mathematical problems and real-world situations

Assignments / assessment

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

Teaching methods / timetable

You will learn through interactive seminars that introduce key mathematical ideas, methods, and worked examples in a supportive setting. 

Regular guided problem-solving will help you build confidence in choosing methods and applying them to new problems, with opportunities to work both individually and with other students. 

Clear online notes and resources will support your preparation, revision, and independent study, while ongoing feedback from lecturers will help you understand your progress and strengthen your problem-solving skills.