What is Applied Mathematics and Statistics?
Applied statistics and mathematics focusses on studying practical problems from the real world. The problems could be from the worlds of engineering, physics, chemistry, economics, biology, medicine, social, or political studies … you name it!
The key step in applying mathematics or statistics to real life phenomena is the process of modelling: where models could be based on equations, or random variables, or even algorithms. Given this wide application it's not surprising that good modellers are in high demand within industrial and scientific institutions.
We have picked out four projects which give you an introduction to mathematical and statistical modelling as it is carried out in the real world (as opposed to the way it is carried out in textbooks!).
Projects
January Camp
The mathematics of encryption and communication
We are constantly transmitting private information, such as personal or work-related emails, or credit card information for online purchases. How can we ensure that such information is transmitted securely, so that no third-party can intercept and gain access to it? How can we ensure that encryption is efficient, so we can communicate as much information as we want privately without going through lengthy or complicated procedures? And how can we ensure that our information is received correctly, given that we might make a mistake when entering it, and that it might get garbled when transmitted? We will explore the mathematical principles and techniques governing encryption and error-detection/correction in communication.
July Camp
Classification and clustering
Classification and clustering are two very important problems in statistics and machine learning. Classification is for when we have some idea what we are looking for: is it a picture of a cat or a dog? What language is this document written in? Clustering is for when we are trying to find hidden groupings in the data, i.e. data exploration. Are there genes that always get expressed at the same time? Are there patterns in the way financial markets behave? We will explore the mathematics behind a number of methods for classification and clustering, design algorithms to implement them, and look at the important statistical principles needed to use these methods appropriately.