Postgraduate Course: Basic Algebra 1 (MATH11125)

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	20	ECTS Credits	10
Summary	Only Postgraduate Taught students on Mathematics Degree Programmes and Undergraduate MMath Year 5 students may take this course, and selection requires the approval of the Programme Director. Basic concepts in group theory, including definitions and examples; constructions of groups; generators and relations;simple groups; the Jordan-Holder theorem; soluble groups; group actions; conjugation; Sylow theorems and applications; free groups and presentations. (12 hours) Basic concepts in ring and module theory; chain conditions; Hilbert Basis Theorem; these ideas illustrated by examples in number theory and algebraic geometry. (8 hours)
Course description	Not entered

Entry Requirements (not applicable to Visiting Students)
Pre-requisites		Co-requisites
Prohibited Combinations	Students MUST NOT also be taking Jewels of Algebra (MATH10050)	Other requirements	None

Course Delivery Information
Not being delivered

Learning Outcomes
On completion of this course, the student will be able to: Thoroughly understand the basics of group theory, group actions, ring theory and elementary module theory. Apply ring theory and elementary module theory to rings arising in number theory and algebraic geometry.