Postgraduate Course: MIGSAA Algebra 1 (MATH11172)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 11 (Postgraduate) 
Availability  Not available to visiting students 
SCQF Credits  15 
ECTS Credits  7.5 
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, JordanHölder 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)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  None 
Course Delivery Information
Not being delivered 
Learning Outcomes
Thorough understanding of groups and commutative rings.

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  migsaa,algebra 
Contacts
Course organiser  Prof A Carbery
Tel: (0131 6)50 5993
Email: A.Carbery@ed.ac.uk 
Course secretary  Ms Isabelle Hanlon
Tel: (0131 6)50 5955
Email: i.hanlon@ed.ac.uk 

