Undergraduate Course: Numbers & Rings (Ord) (MATH09017)
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 9 (Year 3 Undergraduate) |
Credits |
10 |
| Home subject area |
Mathematics |
Other subject area |
Specialist Mathematics & Statistics (Ordinary) |
| Course website |
http://student.maths.ed.ac.uk
|
Taught in Gaelic? |
No |
| Course description |
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
The following are the learning objectives for the Honours version, MAT-3-NuR; for this (Ordinary) version there is more emphasis on the technical, rather than conceptual elements, which will be reflected by a different examination.
1. To be able to use the division algorithm and euclidean algorithm in apppropraiate 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.
|
Assessment Information
Coursework: 15%; Degree Examination: 85%.
|
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Not entered |
| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords |
Not entered |
Contacts
| Course organiser |
Dr Bruce Worton
Tel: (0131 6)50 4884
Email: Bruce.Worton@ed.ac.uk |
Course secretary |
Mrs Kathryn Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk |
|
|
University Homepage