2015/16 Undergraduate Module Catalogue
MATH3232 Transformation Geometry
15 creditsClass Size: 50
Module manager: Dr K Houston
Email: K.Houston@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2015/16
Pre-requisite qualifications
MATH2020 or MATH2080, or equivalent.This module is approved as a discovery module
Module summary
Two-dimensional Euclidean geometry is the study of isometries of the plane. Extending the group of transformations leads us first to affine geometry, and then to projective geometry and Poincaré's disc model of non-Euclidean geometry. A basic idea is to use appropriate transformations to turn a complicated geometrical problem to a simple special case. In this way we give proofs of some classical geometrical theorems due to Ceva, Desargues, Menelaus, Pascal and Pappus.Objectives
To develop abstract ideas of geometry based on considering the transformations that respect the various geometrical constructs.On completion of this module, students should be able to:
a) use affine transformations to prove appropriate theorems of Euclidean Geometry.
b) use projective coordinates to prove theorems of projective geometry.
c) express a conic in standard form for affine, Euclidean and projective geometry.
d) do calculations using inversion and Moeobius transformations.
e) do calculations either in Poincaré's disc model or in spherical geometry.
Syllabus
1. The Kleinian view of geometry.
2. Isometries and Euclidean geometry.
3. Affine transformations, affine geometry, Ceva's Theorem, Menelaus' Theorem, affine classification of conics.
4. Projective geometry, projective coordinates for the plane, projective transformations, Desargues' Theorem, Pappus' Theorem, Pascal's Theorem, projective conics, cross ratio.
5. Inversions in circles, Mobius transformations of the extended complex plane, either Poincaré's disc model of non-Euclidean geometry or, an introduction to spherical geometry.
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
Coursework
Assessment type | Notes | % of formal assessment |
In-course Assessment | * | 10.00 |
Total percentage (Assessment Coursework) | 10.00 |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Exams
Exam type | Exam duration | % of formal assessment |
Standard exam (closed essays, MCQs etc) | 2 hr 30 mins | 90.00 |
Total percentage (Assessment Exams) | 90.00 |
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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- Undergraduate module catalogue
- Taught Postgraduate module catalogue
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- Taught Postgraduate programme catalogue
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