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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2016/2017

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: MIGSAA Algebra 1 (MATH11172)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) AvailabilityNot available to visiting students
SCQF Credits15 ECTS Credits7.5
Summary*Only students of the MIGSAA CDT may take this course*
On this course you will study groups and commutative rings which are perhaps the most natural algebraic structures. We assume you are familiar with the most simple concepts of group theory as they are taught in compulsory algebra courses everywhere, and cover a standard set of topics in the structure theory especially of finite groups.
Course description In the commutative rings part we discuss both of the two classical motivations for studying commutative rings: number theory on the one hand and algebraic geometry on the other.

Groups (5 lectures)
¿ Simple groups, Jordan-Hölder Theorem, (semi) direct products
¿ Permutation representations and group actions
¿ Sylow Thorems and applications
¿ Abelian, soluble and nilpotent groups
¿ Free groups and presentations

Commutative rings (5 lectures)
¿ Modules: introduction
¿ Chain conditions and Hilbert's basis theorem
¿ Fields and numbers
¿ Affine algebraic geometry and Hilbert's Nullstellensatz
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Other requirements None
Course Delivery Information
Not being delivered
Learning Outcomes
Thorough understanding of groups and commutative rings.
Reading List
None
Additional Information
Graduate Attributes and Skills Not entered
Keywordsmigsaa,algebra
Contacts
Course organiserProf A Carbery
Tel: (0131 6)50 5993
Email: A.Carbery@ed.ac.uk
Course secretaryMs Isabelle Hanlon
Tel: (0131 6)50 5955
Email: i.hanlon@ed.ac.uk
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