Studies in pure mathematics are heavily focused on analyzing particular problems in the field through research that is often based on proofs. This kind of analysis can help students understand how to effectively solve problems in their everyday lives.

The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom and Britain, is a sovereign state located off the north-western coast of continental Europe.The two most famous (and oldest) universities are Oxford and Cambridge (often referred to as Oxbridge by many Britons) England also has several other world-class institutions, including several in London (notably Imperial College, the London School of Economics, University College London and King's College London, all are part of London University)

The PhD is a doctoral degree, specifically called a "doctor of philosophy" degree. This is misleading because PhD holders are not necessarily philosophers (unless they earned their degree in philosophy!). That said, PhD recipients are able to engage in thought experiments, reason about problems, and solve problems in sophisticated ways.

Part-time learning allows one to obtain a degree or qualification even if one cannot attend school on a full-time basis. One can learn at one's own pace, gradually accumulating credits that count towards a final qualification.