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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Commutative Algebra (MATH10017)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis 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.
Course description Affine varieties
Polynomial rings
Euclidean algorithm
Gröbner bases
Hilbert Basis theorem
Buchberger algorithm
Applications to solving systems of polynomial equations
Elimination theory
Additional topics
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Algebra (MATH10069)
Co-requisites
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesNone
Course Delivery Information
Academic year 2015/16, Available to all students (SV1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 20%, Examination 80%
Feedback Not entered
No Exam Information
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.
Reading List
Cox, Little, O¿Shea: Ideals, Varieties and Algorithms. An introduction to computational Algebraic Geometry and Commutative Algebra

Reid: Undergraduate Commutative algebra
Additional Information
Course URL http://student.maths.ed.ac.uk
Graduate Attributes and Skills Not entered
KeywordsCoA
Contacts
Course organiserDr Martin Dindos
Tel:
Email:
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email:
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