Discrete Mathematics module (MA21003)

Discrete mathematics involves the study of structures that are either finite or have a form like the set of whole numbers. This module introduces several areas of discrete mathematics. Areas covered include difference equations, game theory, and combinatorics.

Difference equations are equations where the unknown is a function of a whole number instead of a decimal number. Recurrence relations are a type of difference equation.

Game theory is an area of maths that studies decision making where people interact with others. It is used to model and analyse when people have to make choices that depend on the choices of others.

Combinatorics is a branch of maths that deals with counting, arranging, and selecting objects. It is used to solve problems that involve finding the number of ways to choose or arrange objects in a set.

What you will learn

In this module, you will:

• learn the theory behind the solution structure of linear difference equations
• be introduced to game theory and its applications
• use recursive methods to find approximate solutions to equations
• be introduced to combinatorics

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

• solve linear second order difference equations
• find approximate solutions to nonlinear equations using iterative methods
• calculate steady states for Markov chains
• convert real-world problems into game theory notation
• find optimal strategies for problems in game theory
• solve simple problems using combinatorics

Assignments / assessment

• coursework (40%)
• final exam (60%)

Teaching methods / timetable

• four hours of lectures every week
  • course materials will be explained and discussed
  • lecture notes covering the full module content will be given before classes
• two hours of tutorials every week
  • solve problems individually and in groups
  • support with difficulties will be provided by your lecturer and peers