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 09 (Year 3 Undergraduate) |
Credits |
10 |
Home subject area |
Mathematics |
Other subject area |
Specialist Mathematics & Statistics (Ordinary) |
Course website |
http://student.maths.ed.ac.uk |
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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. |
Course Delivery Information
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.
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Assessment Information
Coursework: 15%; Degree Examination: 85%.
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Please see Visiting Student Prospectus website for Visiting Student Assessment information |
Special Arrangements
Not entered |
Contacts
Course organiser |
Dr Bruce Worton
Tel: (0131 6)50 4884
Email: Bruce.Worton@ed.ac.uk |
Course secretary |
Mrs Katherine Mcphail
Tel: (0131 6)50 4885
Email: k.mcphail@ed.ac.uk |
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copyright 2010 The University of Edinburgh -
1 September 2010 6:18 am
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