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 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 |
Individual written feedback on hand-ins, as in a traditional course. There will also be a course Piazza page. |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | MATH10079 Group Theory | 2:120 | |
|
| 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 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 |
Individual written feedback on hand-ins, as in a traditional course. There will also be a course Piazza page. |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S1 (December) | Group Theory For Visiting Students Only | 2:120 | |
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 Jonathan Pridham
Tel: (0131 6)50 3300
Email: J.Pridham@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
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