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. There will also be some ring theory.
Course description	· Group actions & Sylow Theorems · Homomorphisms, isomorphisms & factor groups · Group Presentations · Simple groups & Composition Series · Polynomial rings & finite fields · Classification of finite abelian groups · PIDs & their modules

Entry Requirements (not applicable to Visiting Students)
Pre-requisites	Students MUST have passed: Honours Algebra (MATH10069)	Co-requisites
Prohibited Combinations	Students MUST NOT also be taking Group and Galois Theory (MATH10078)	Other requirements	Students wishing to take both MATH10079 Group Theory and MATH10080 Galois Theory in the same academic session should register for the 20 credit course MATH10078 Group and Galois Theory.

Information for Visiting Students
Pre-requisites	None

Course Delivery Information

Academic year 2015/16, 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 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
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		2:00
Main Exam Diet S1 (December)	MATH10079 Group Theory (Semester 1 Visiting Students Only)		2:00

Academic year 2015/16, Part-year visiting students only (VV1)		Quota: 1
Course Start	Semester 1
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info)	Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment)	Coursework 20%, Examination 80%
Feedback	Not entered
No Exam Information

Learning Outcomes
1. 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. 2. Ability to manipulate composition series, through both the proof of abstract structural properties and the calculation of explicit examples. 3. Capacity to work with the classes of rings and fields appearing in the course, particularly specific calculations around finite fields and polynomials. 4. Be able to produce examples and counterexamples illustrating the mathematical concepts presented in the course. 5. Understand the statements and proofs of important theorems and be able to explain the key steps in proofs, sometimes with variation.

Reading List
Recommended : - T S Blyth and E S Robertson, Groups (QA171.Bly ) - J F Humphreys, A Course in Group Theory (QA177 Hum) - M A Armstrong, Groups and Symmetry (QA171 Arm ) - J J Rotman, The theory of groups: An introduction (QA171 Rot ) - J J Rotman, An introduction to the Theory of Groups (QA174.2 Rot )