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Algebraic Number Theory (MSc) - MAT00071H

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  • Department: Mathematics
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2022-23

Module summary

This module is for postgraduate students only.

Related modules

Pre-requisite modules

  • None

Co-requisite modules

  • None

Prohibited combinations


Additional information

Students should have seen a first course in Groups, Rings and Fields.

Module will run

Occurrence Teaching period
A Autumn Term 2022-23

Module aims

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.

Indicative assessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

Special assessment rules

Pass/fail

Indicative reassessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 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).


The information on this page is indicative of the module that is currently on offer. The University constantly explores ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary. In some instances it may be appropriate for the University to notify and consult with affected students about module changes in accordance with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.