2015/16 Undergraduate Module Catalogue
MATH3071 Groups and Symmetry
15 creditsClass Size: 50
Module manager: Dr S Fryer
Email: S.Fryer@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2015/16
Pre-requisite qualifications
MATH2020This module is approved as a discovery module
Module summary
Informal description: The theory of groups is the mathematical theory of symmetry - not only of geometric figures but also symmetries of sets - that is permutations. The ultimate aim of the theory is to describe (the structure) of all groups. Applications of group theory range throughout mathematics, chemistry and physicsObjectives
On completion of this module, students should be able to:a) calculate the full symmetry groups of simple geometric figures;
b) represent such a group by permutations;
c) make use of direct products and Sylow's Theorems in determining the structure of special groups, including determinine when groups are simple;
d) prove (and be able to use) the homomorphism theorems;
e) find composition series of small groups.
Syllabus
- Preliminaries.
- Symmetries of plane and solid figures; Permutation groups.
- Groups acting on sets; Factor groups; Homomorphism theorems.
- Direct products.
- Sylow's theorems and applications.
- Simple groups and composition series.
- Orbit-Stabiliser theorem.
Teaching methods
Delivery type | Number | Length hours | Student hours |
Lecture | 33 | 1.00 | 33.00 |
Private study hours | 117.00 | ||
Total Contact hours | 33.00 | ||
Total hours (100hr per 10 credits) | 150.00 |
Private study
Studying and revising of course material.Completing of assignments and assessments.
Opportunities for Formative Feedback
Regular problem solving assignmentsMethods of assessment
Exams
Exam type | Exam duration | % of formal assessment |
Standard exam (closed essays, MCQs etc) | 2 hr 30 mins | 100.00 |
Total percentage (Assessment Exams) | 100.00 |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
The reading list is available from the Library websiteLast updated: 16/04/2015
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