Waves
Wave motion is found everywhere: sound waves, water waves, electromagnetic waves, traffic waves and Mexican waves are just some examples. The mathematical description of wave motion can be fairly straightforward,
Author Archives: David Graham
Chebychev Polynomials
In this project the aim is to study the mathematical properties of Chebychev polynomials and their role in numerical approximation. The concept of ‘good’ and ‘best’ numerical approximations and the
Particle methods for fluid dynamics
Particle-based numerical methods have been used extensively by Hollywood in modelling dramatic events such as floods or sinking ships. This project would investigate smoothed particle hydrodynamics (SPH) models or, possibly,
Numerical methods for PDE’s
Partial differential equations describe how the three/four dimensional world works. Solving such equations is the key to understanding the behaviour of many physical, chemical, biological or financial systems. A large
Pricing of American Options
An option is the right (but not the obligation) to buy, at or before an agreed expiry date, a share at a ‘strike price’ (agreed now). An American option allows
Multifractals in Finance
The standard mathematical model of random asset price variation is Geometric Brownian Motion – where the log of the asset price ‘return’ is normally distributed. However, this under-predicts the frequency
Mathematical Finance
Many topics in mathematical finance can make good project topics. The key to understanding lies in the modelling of the random behaviour seen in prices of shares, oil, foreign exchange