Undergraduate Course: Numbers & Rings (MATH10023)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 10 (Year 3 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | Specialist Mathematics & Statistics (Honours) |
| Course website |
https://info.maths.ed.ac.uk/teaching.html |
Taught in Gaelic? | No |
| Course description | Optional course for Honours Degrees involving Mathematics and/or Statistics. Syllabus summary: Factorisation theory of integers and polynomials in one variable over a field. Euclidean domains. Unique Factorisation Domains. Congruences and modular arithmetic. Ideals and quotient rings. Gauss's Lemma and the Eisenstein criterion for irreducibility of polynomials over the integers. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
| Not being delivered |
Summary of Intended Learning Outcomes
1. To be able to use the division algorithm and euclidean algorithm in appropriate settings.
2. To be able to apply the Eisenstein criterion for irreducibility of integer polynomials.
3. To understand the necessity for rigorous proofs, as exemplified by the confusions due to assuming unique factorisation is universally applicable.
4. To understand the idea of defining operations on sets defined by equivalence relations and to understand the notion of 'well-defined' for such definitions.
5. To understand the abstract notions of ideals and factor rings and to be able to work with these notions in elementary situations.
6. Given an irreducible polynomial over a field, to be able to construct an extension field that contains a root of the polynomial.
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Assessment Information
Examination only.
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Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Not entered |
| Transferable skills |
Not entered |
| Reading list |
http://www.readinglists.co.uk |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | NuR |
Contacts
| Course organiser | Dr Agata Smoktunowicz
Tel:
Email: A.Smoktunowicz@ed.ac.uk |
Course secretary | Dr Jenna Mann
Tel: (0131 6)50 4885
Email: Jenna.Mann@ed.ac.uk |
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