MA301-6-SP-CO:
Group Theory
2019/20
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Undergraduate: Level 6
Current
Monday 13 January 2020
Friday 20 March 2020
15
01 October 2019
Requisites for this module
MA114 and MA201 and MA204
(none)
(none)
(none)
(none)
The module continues the study of abstract algebra by further developing the theory of groups. The theory will be illustrated through examples in settings that students will already have encountered.
The module aims:
To continue the study of groups and to teach how an extensive and important theory can be developed by logical deductions from a small number of axioms.
On completion of the course, students should:
1. have a systemic understanding of key definitions in the theory of groups and critical awareness of how they interact and support each other
2. select and apply relevant theorems to examples
3. construct arguments to prove properties of groups
4. solve problems involving homomorphisms between pairs of groups
5. formulate counterexamples to statements
6. understand the concept of a group presentation
7. recognise and work with cyclic, dihedral, Fibonacci, and triangle groups,
8. deploy methods learned to distinguish pairs of groups defined by presentations or to prove they are isomorphic
9. apply geometric techniques to obtain and illustrate algebraic properties of particular groups
Syllabus
Homomorphisms, isomorphisms, automorphisms. Cosets, normal subgroups, quotient groups, abelianization and derived subgroup. Lagrange's theorem, isomorphism theorems. Free groups, group presentations (definition and examples), Tietze transformations, Cayley Diagrams, Van Kampen diagrams.
Lectures and classes plus revision lectures.
- (2014-09-01) Representation Theory: Springer.
- Fraleigh, John B. (©2014) A first course in abstract algebra: Pearson.
- Joseph A. Gallian. (2017) Contemporary Abstract Algebra, Boston, MA: Cengage Learning.
The above list is indicative of the essential reading for the course. The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students. Further reading can be obtained from this module's reading list.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Problem set 1 |
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| Coursework |
Problem set 2 |
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| Exam |
Main exam: 24hr during Summer (Main Period)
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Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Jesus Martinez-Garcia, email: jesus.martinez-garcia@essex.ac.uk.
Dr Jesus Martinez- Garcia, email jesus.martinez-garcia@essex.ac.uk
Dr Jesus Martinez-Garcia (jesus.martinez-garcia@essex.ac.uk)
Yes
No
No
No external examiner information available for this module.
Available via Moodle
Of 91 hours, 29 (31.9%) hours available to students:
62 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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