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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

MATH2051Geometry of Curves and Surfaces

This module is mutually exclusive with

MATH3112Differential 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

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Delivery typeNumberLength hoursStudent hours
Example Class61.006.00
Lecture251.0025.00
Private study hours119.00
Total Contact hours31.00
Total hours (100hr per 10 credits)150.00

Opportunities for Formative Feedback

Regular problem sheets

Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information


Exams
Exam typeExam 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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