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Algebraic Number Theory is the study of algebraic numbers, and is a topic at the forefront of research in modern pure mathematics. The topic grew from a desire to prove Fermat’s Last Theorem, conjectured by Pierre de Fermat, in 1637, and proved by Andrew Wiles, in 1995. This module introduces and examines classes of algebraic objects, including algebraic number fields, rings of algebraic integers, and the set ideals in a ring of algebraic integers.

Towards the end of the module, you will learn about the factorisation of ideals in rings of algebraic integers. The crowning glory of this module is the examination of the ideal class group of an algebraic number field. This object measures the extent to which a ring of algebraic integers fails to be a principal ideal domain.

Pre-requisite Module: MTH3038 Galois Theory, or equivalent

_{Please note that all modules are subject to change, please get in touch if you have any questions about this module.}