Undergraduate Course: Commutative Algebra (MATH10017)
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 4 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | Specialist Mathematics & Statistics (Honours) |
| Course website |
http://student.maths.ed.ac.uk |
Taught in Gaelic? | No |
| Course description | This course will be an introduction to commutative algebra, mainly focusing on methods to work with polynomial rings. The students will learn practical methods for solving systems of polynomial equations, as well as important theoretical results, for example, Hilbert's basis theorem. An important branch of algebra in its own right, commutative algebra is an essential tool to explore several other areas of mathematics, such as algebraic geometry, number theory, Lie theory, and non-commutative algebra. |
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Honours Algebra (MATH10069)
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
| Additional Costs | None |
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. Gain familiarity with the polynomial ring and be able to perform basic operations with both elements and ideals.
2. Master some computational tools to work with the polynomial ring, especially Gröbner bases.
3. Be able to apply the Buchberger algorithm to compute a Gröbner basis.
4. Use these computational tools to solve problems in polynomial rings, for example the ideal membership problem, or finding solutions to polynomial equations.
5. Be able to produce examples illustrating the mathematical concepts learnt in the class.
6. Understand the proofs of important theorems and be able to explain key steps in the proof. |
Assessment Information
| Coursework 20%, Examination 80% |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Affine varieties
Polynomial rings
Euclidean algorithm
Gröbner bases
Hilbert Basis theorem
Buchberger algorithm
Applications to solving systems of polynomial equations
Elimination theory
Additional topics |
| Transferable skills |
Not entered |
| Reading list |
Cox, Little, O¿Shea: Ideals, Varieties and Algorithms. An introduction to computational Algebraic Geometry and Commutative Algebra
Reid: Undergraduate Commutative algebra |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | CoA |
Contacts
| Course organiser | Dr Martin Dindos
Tel:
Email: M.Dindos@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
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