Welcome

Welcome to the Dundee mathematics pages. Are you enjoying mathematics at school and considering studying mathematics at University?

A mathematics degree enables you to become a logical numerate problem solver. Picking up from the mathematics that you have learned at school, you would:

Mathematics graduates have excellent career prospects. They tend to work across the economy (e.g. in finance, defence, computing, engineering, education, data science etc.).

The posts below have been developed in parallel with events that have been run by Dundee mathematics staff. The main aim is explore mathematical threads that you may have come across during school.

Modelling drug delivery

Calculus
Differential Equations
We can use calculus to study how to optimise drug delivery.

Monte Carlo Integration

integration
geometry
You may have previously come across definite integrals of the form

Roots of quadratic/cubic equations

Polynomials
Algebra
Consider the cubic equation \[ ax^3+bx^2+cx+d=0, \ \ \quad a,b,c, d \in \Re. \tag{1}\]

Cryptography

integration
geometry
Cryptography is the practice and study of techniques for securing communication and information against unauthorized access, modification, or forgery. It is used to protect…

Trigonometric equations and Fourier series

Trigonometry
Geometry
Fourier
Trigonometric functions appear throughout mathematics (e.g. geometry, calculus, differential equations, signal analysis). Here we explore some properties of trigonometric…

Recurrence relations and chaos

Recurrence relations
Discrete maths
Chaos
You might have previously encountered a recurrence relation of the form

D’Arcy Thompson and 2D mappings

Geometry
Growth and form
Mappings
In D’Arcy Thompson’s book ‘On Growth and Form’ he considers how the shapes of related species can be understood using mathematical maps.The underlying idea is that the…

Estimating pi

integration
geometry
Consider a circle of radius \(R\) centred at the origin.

Introduction to population dynamics

Population dynamics
Calculus
Differential Equations
We can use calculus to study how populations change in time. In the examples below we consider an illustrative model of population dynamics in a class room. The developed…

Affine transformations in the plane

Geometry
Growth and form
Mappings
An affine transformation is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles. Examples of affine…

Modelling the spread of infectious disease

Infectious diseases
Population dynamics
Calculus
Differential Equations
Infectious diseases can have severe health outcomes for individuals who contract them. They can also place an unmanageably large demand on the health service.

Second order ODEs

Differential Equations
Calculus
We can use calculus to study how quantities change in time. In the examples below we consider a second order linear ordinary differential equation (ODE) with constant…

Intersecting lines and linear algebra

Geometry
Algebra
Consider the equations of two straight lines given by \[ y=m_1x+c_1 \tag{1}\] and \[ y=m_2x+c_2, \tag{2}\] where \(m_1\), \(m_2\), \(c_1\) and \(c_2\) are constants.

Graduate employment

A mathematics degree will enable you to become a logical numerate problem solver. Over the course of your degree you will develop

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