Undergraduate Course: Group Theory (MATH10079)

Course Outline
School	School of Mathematics	College	College of Science and Engineering
Credit level (Normal year taken)	SCQF Level 10 (Year 4 Undergraduate)	Availability	Available to all students
SCQF Credits	10	ECTS Credits	5
Summary	This is a course in abstract algebra, although connections with other fields will be stressed as often as possible. It is a systematic study of the basic structure of groups, finite and infinite.
Course description	- Homomorphisms, isomorphisms, and factor groups - Group presentations and universal properties - Sylow theorems and applications - Simple groups and composition series - Classification of finite abelian groups and applications - Solvable groups and the derived series

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-requisites	Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
High Demand Course?	Yes

Course Delivery Information

Academic year 2024/25, 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 6, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 68 )
Assessment (Further Info)	Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment)	Coursework 20%, Examination 80%
Feedback	Not entered
Exam Information
Exam Diet	Paper Name		Hours & Minutes
Main Exam Diet S2 (April/May)	MATH10079 Group Theory		2:00

Academic year 2024/25, Part-year visiting students only (VV1)		Quota: None
Course Start	Semester 1
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 6, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 68 )
Assessment (Further Info)	Written Exam 75 %, Coursework 25 %, Practical Exam 0 %
Additional Information (Assessment)	Coursework 20%, Examination 80%
Feedback	Not entered
Exam Information
Exam Diet	Paper Name		Hours & Minutes
Main Exam Diet S1 (December)	Group Theory For Visiting Students Only		2:00

Learning Outcomes
On completion of this course, the student will be able to: Demonstrate facility with the Sylow theorems, group homomorphisms and presentations, and the application of these in order to describe aspects of the intrinsic structure of groups, both abstractly and in specific examples. Manipulate composition series, through both the proof of abstract structural properties and the calculation of explicit examples. Work with the classes of groups appearing in the course, particularly specific calculations involving abelian and solvable groups. Produce examples and counterexamples illustrating the mathematical concepts presented in the course. Understand the statements and proofs of important theorems and be able to explain the key steps in proofs, sometimes with variation.

Reading List
The course notes will be the main reference, although : M A Armstrong, Groups and Symmetry (QA171 Arm ) is a subsidiary reference. Other references include T S Blyth and E S Robertson, Groups (QA171.Bly) J F Humphreys, A Course in Group Theory (QA177 Hum) J J Rotman, The theory of groups: An introduction (QA171 Rot ) J J Rotman, An introduction to the Theory of Groups (QA174.2 Rot )

Additional Information
Graduate Attributes and Skills	Not entered
Keywords	GrTh

Contacts
Course organiser	Dr David Jordan Tel: (0131 6)50 7210 Email: D.Jordan@ed.ac.uk	Course secretary	Mrs Alison Fairgrieve Tel: (0131 6)50 5045 Email: Alison.Fairgrieve@ed.ac.uk