David Abaas: De p-adiska talen

Abstract.

Although p-adic numbers play a crucial role in fields such as number theory, they are often not well known among undergraduate students in mathematics. This essay aims to illuminate the enigmatic nature of the p-adic numbers by building and explaining the underlying theory, as well as highlighting their applications in the context of Hensel’s lemma and the Newton-Raphson method. In addition, the theoretical discussion is supplemented with a concrete implementation in Python, which can enable a deeper understanding through practical examples and applications.