2005/06 Undergraduate Module Catalogue
MATH3232 Transformation Geometry
15 creditsClass Size: 100
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2005/06
Pre-requisitesMATH2200 or MATH2080 or equivalent.
This module is approved as an Elective
ObjectivesTo develop some basic geometrical ideas used in applications as diverse as navigation and relativity. On completion of this module, students should be able to: a) use transformations to obtain projective theorems from particular cases of Euclidean theorems; b) calculate and use cross-ratios; c) compute time contraction in relativity; d) compute navigational problems using spherical geometry; e) express a conic in standard form for affine, Euclidean and projective geometry.
This module uses linear algebra to develop the geometry of groups of transformations and their invariants. A basic idea is to transform a complicated geometrical problem to a simple special case such that the essential features of the problem are invariant under the transformation. Affine, Euclidean, projective, Lorentz and spherical geometries will be studied. The topics covered are: 1. Transformation groups and invariants. 2. Affine group and ratio. 3. Euclidean group and Euclidean distance, congruent triangles. 4. Orthogonal group acting on S2 , area of spherical triangles. 5. Projective group, duality, Desargues? Theorem, cross-ratio. 6. Classification of conics for affine, Euclidean and projective geometries. 7. Lorentz group and light lines.
Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for informationLectures: 26 hours. 7 examples classes.
Methods of assessment
Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for informationOne 3 hour examination at end of semester (100%).
Reading listThe reading list is available from the Library website
Last updated: 13/05/2005
Browse Other Catalogues
- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue
Errors, omissions, failed links etc should be notified to the Catalogue Team.PROD