Undergraduate Course: Group Theory (MATH10079)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | 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. |
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. |
| Additional Costs | None |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
|
| Delivery period: 2014/15 Semester 1, Available to all students (SV1)
|
Learn enabled: Yes |
Quota: None |
|
Web Timetable |
Web Timetable |
| Course Start Date |
15/09/2014 |
| Breakdown of 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 )
|
| Additional Notes |
|
| Breakdown of Assessment Methods (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| No Exam Information |
Summary of Intended 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. |
Assessment Information
| Coursework 20%, Examination 80% |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
· 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 |
| Transferable skills |
Not entered |
| 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 ) |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | GrTh |
Contacts
| Course organiser | Dr Susan Sierra
Tel: (0131 6)50 5070
Email: S.Sierra@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
|
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|
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