Unit name | Introduction to Geometry |
---|---|
Unit code | MATH20004 |
Credit points | 20 |
Level of study | I/5 |
Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
Unit director | Dr. Mackay |
Open unit status | Not open |
Pre-requisites |
MATH11005 Linear Algebra and Geometry, MATH10012 ODEs, Curves and Dynamics, and MATH10011 Analysis |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Unit Aims
The aim of this unit is to introduce fundamental concepts in geometry in a hands-on and rigorous way, focused on curves and surfaces, and to lay the foundations for more advanced courses in later years.
Unit Description
Geometry is central to mathematics, both as a subject in its own right and as an essential viewpoint on nearly every area of pure and applied mathematics. This course focuses on the geometry of curves and surfaces in R2 and R3, continuing on from calculus.
A key concept is the curvature of a surface, which describes locally how it bends, whether it is flat like Euclidean space, positively curved like a sphere, or, less-familiarly, negatively curved like a saddle. A major goal is to prove the Gauss-Bonnet theorem, which links the curvature of a surface to its overall shape.
Relation to Other Units
The unit complements MATH20901 Multivariable Calculus and MATH20006 Metric Spaces, and leads into later units in geometry such as MATH30018 Fields, Forms & Flows and MATH30001 Topics in Modern Geometry.
By the end of the course the students should
The unit will be taught through a combination of
90% Timed, open-book examination 10% Coursework
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.
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