Algebraic Number Theory - MAT00029H
- Department: Mathematics
- Credit value: 10 credits
- Credit level: H
- Academic year of delivery: 2022-23
Related modules
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
None
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).