2008/09 Taught Postgraduate Module Catalogue

MATH5031M Differential Geometry 2

15 creditsClass Size: 30

Module manager: Professor R Bielawski
Email: rb@maths.leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

Pre-requisites

MATH2051

Geometry of Curves and Surfaces

This module is mutually exclusive with

MATH3112

Differential Geometry 1

This module is not approved as an Elective

Objectives

To further the study of curves and surfaces, in particular, to understand what properties of curves and surfaces are intrinsic, extrinsic, local, or global, and to give some applications. Some topics will be taken further than Differential Geometry 1 with extra proofs and mini-projects.

Syllabus

Plane curves: rotation index, isoperimetric inequality. Space curves: congruence, total curvature of a knot. Submanifolds of Euclidean spaces as level sets, Gauss map. Curves on a surface, geodesics. Transformations and map projections. Theorema Egregrium. Gauss-Bonnet theorem. Riemannian metrics on the plane. Introduction to abstract surfaces and higher-dimensional manifolds.

Teaching methods

Delivery type	Number	Length hours	Student hours
Example Class	6	1.00	6.00
Lecture	25	1.00	25.00
Private study hours			119.00
Total Contact hours			31.00
Total hours (100hr per 10 credits)			150.00

Opportunities for Formative Feedback

Regular problem sheets

Methods of assessment

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	3 hr	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 website

Last updated: 22/03/2010

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