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, 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
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Course Delivery Information
| Not being delivered |
Learning Outcomes
| Thorough understanding of groups and commutative rings.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | migsaa,algebra |
Contacts
| Course organiser | Prof A Carbery
Tel: (0131 6)50 5993
Email: |
Course secretary | Ms Isabelle Hanlon
Tel: (0131 6)50 5955
Email: |
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