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Algebraic Number Theory (MSc) - MAT00071H

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• Department: Mathematics
• Module co-ordinator: Dr. Evgeniy Zorin
• Credit value: 10 credits
• Credit level: H
• Academic year of delivery: 2022-23
  • See module specification for other years: 2021-22

Module summary

This module is for postgraduate students only.

Related modules

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.

Assessment

Task	Length	% of module mark
Closed/in-person Exam (Centrally scheduled) Algebraic Number Theory	2 hours	100

Special assessment rules

Pass/fail

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).