MATH40370 Differential Geometry

Academic Year 2020/2021

Module Descriptor for 5 credit module ‘Differential Geometry’ for Science students, year 4.

This module will introduce the modern theory of curves and surfaces. Topics covered will be taken from the following list:

CURVES: reparametrisations and arc-length, curvature, the Frenet-Serret theorem and the fundamental theorem of curves.

SURFACES: Simple surface, tangent plane, tangent space, co-ordinate transformation and definition of a general surface. Level sets as surfaces. The first and second fundamental forms and Gaussian curvature. Minimal surfaces

Introduction to Topololgical Manifolds.

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Curricular information is subject to change

Learning Outcomes:

Students must be able to calculate the quantities inherent in the course: tangent vector, tangent line, tangent space, unit-speed reparametrisations etc.. They must be able to state the theorems proved in the course and reproduce some elements of proof. They must demonstrate an understanding of the concepts involved.

More generally students should be able to do the following:

WRITE MATHEMATICS: Students should be able to recognise, read and correctly use standard mathematical symbols and notation, to correctly write a mathematical statement and to recognise when such a statement is not correctly written.

QUESTION: Students should be able to ask pertinent questions themselves, to decide which questions are most relevant, which questions are answerable, which questions they should start with, etc.

UNDERSTAND: Students must be able to understand the reasoning behind any methods or procedures they use and be able to demonstrate that understanding.

PRODUCE EXAMPLES: Students must be able to produce examples themselves, to illustrate a definition, to show a method, to test boundaries of an idea.

Student Effort Hours: 
Student Effort Type Hours
Lectures

18
Small Group

6
Tutorial

10
Autonomous Student Learning

70
Total

104
Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning. 
Requirements, Exclusions and Recommendations

Not applicable to this module.


Module Requisites and Incompatibles
Incompatibles:
MST30070 - Differential Geometry


 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Continuous Assessment: Assignment or class-based tests. Throughout the Trimester n/a Standard conversion grade scale 40% No

50
Examination: final exam 2 hour End of Trimester Exam Yes Standard conversion grade scale 40% No

50

Carry forward of passed components
No
 
Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.