# Category Archives: Pure Mathematics

## The Inverted Pendulum

Why is it that a solid pendulum can be made to stand on its end when it’s other end is made to oscillate? This project will investigate the underlying mathematics

## Mondromy of Abelian Integrals

This project is related to the change in an complex integral as its defining parameters change. You will need to learn some theory about Riemann surfaces and integrals on them,

## Hilbert’s 10th Problem

How complicated can it be to find all the integer solutions to a set of polynomial equations? In fact, as complicated as you like! Given any output from a computer

## Algebraic Curves

We know that x2+y2=1 is the equation of a circle, but what happens when the degree of the equation is greater than two? In this project we investigate some of

## Symmetry Groups and Space

This project will look at the interplay between group theory and symmetry in different spaces. It is deliberately left open for you to explore the areas that you like best

## Studying varieties with computer algebra

A variety is the solution set of a system of polynomial equations, usually in several unknowns. For instance, some famous plane curves are described by one polynomial equation in x

## Integrability conditions and computer algebra

Various dynamical systems are described by differential equations. In control theoretic problems (e.g., in robotics), it is essential to determine and utilise the degrees of freedom of a system. The