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
Prerequisites  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 'welldefined' 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
Examination only.

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 

