THE UNIVERSITY of EDINBURGH

DEGREE REGULATIONS & PROGRAMMES OF STUDY 2017/2018

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Group Theory (MATH10079)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis 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-requisitesNone
High Demand Course? Yes
Course Delivery Information
Academic year 2017/18, 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)MATH100792:00
Main Exam Diet S1 (December)MATH10079 Group Theory (Semester 1 Visiting Students Only)2:00
Academic year 2017/18, 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 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 S1 (December)MATH10079 Group Theory (S1 Visiting Students Only)2:00
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 )
Additional Information
Graduate Attributes and Skills Not entered
KeywordsGrTh
Contacts
Course organiserDr Susan Sierra
Tel: (0131 6)50 5070
Email: S.Sierra@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk
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