As opposed to direct problems in which a given cause determines an effect, in inverse problems the situation is reversed, i.e. given an observable effect can we 
find uniquely the cause that generated that effect? Through this project, I will learn and perform research in the new subject of Inverse Problems for integral 
and differential equations, accompanied by achieving a distinguished level of research expertise in core subjects such as Mathematical Analysis and Algebra. 
Fundamental questions such as ‘Can one hear the shape of a drum?’ (i.e., to infer information about the shape of the drumhead from the sound it makes, i.e., 
from the list of overtones, via the use of mathematical theory), or ‘How to detect (size, shape and conductivity) a breast tumour or a landmine located deep 
inside a specimen based on surface skin/ground measurements?’ could be answered based on the research undertaken over the summer period.

Each week, I will investigate some research material, e.g. article, chapter in a book, manuscript, to read and research, in order to gain insight into the 
subject of inverse problems for integral equations, ODEs and the new techniques for solving them. I will aim to synthesise the material and realise 
the connection with the teaching material covered in courses currently taken and beyond the standard curriculum. In addition, in order to develop and enhance 
the my mathematical skills and background I will have to attempt to solve a series of 5-10 selected problems mainly in mathematical analysis and 
algebra. Some of these problems may involve some unseen material beyond textbook and occasionally, will have some research material attached to it, e.g. 
writing a literature review, reading and understanding a research article, presenting the subject in a coherent and logical manner, etc. At the weekly supervisory 
meetings, solutions attempted and other aspects of research will be analysed and discussed in detail.