To introduce the concept of algebraic numbers, and study their existence and properties.
Module learning outcomes
At the end of this module you should be able to understand:
The concept (definition and significance) of algebraic numbers and algebraic integers.
How to factorise an algebraic integer into irreducibles.
How to find the ideals of an algebraic number ring.
The definition of the Class Group.
Module content
Syllabus
Algebraic Numbers, including bases, norm, trace, and the ring of integers.
Modules, Integral Dependence and Noetherian Domains.
Factorisation in rings of integers, discriminant, examples of uniqueness and non-uniqueness of factorisation.
Factorisation of ideals, the Class Group and the Class Number.
Assessment
Task
Length
% of module mark
Closed/in-person Exam (Centrally scheduled) Algebraic Number Theory
2 hours
100
Special assessment rules
None
Reassessment
Task
Length
% of module mark
Closed/in-person Exam (Centrally scheduled) Algebraic Number Theory
2 hours
100
Module feedback
Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Indicative reading
I Stewart & D Tall, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition Taylor & Francis (2015).