Unit of study_

# Geometry and Topology - MATH3061

Year - 2020

The aim of the unit is to expand visual/geometric ways of thinking. The Geometry section is concerned mainly with transformations of the Euclidean plane (that is, bijections from the plane to itself), with a focus on the study of isometries (proving the classification theorem for transformations which preserve distances between points), symmetries (including the classification of frieze groups) and affine transformations (transformations which map lines to lines). The basic approach is via vectors and matrices, emphasising the interplay between geometry and linear algebra. The study of affine transformations is then extended to the study of collineations in the real projective plane, including collineations which map conics to conics. The Topology section considers graphs, surfaces and knots from a combinatorial point of view. Key ideas such as homeomorphism, subdivision, cutting and pasting and the Euler invariant are introduced first for graphs (1-dimensional objects) and then for triangulated surfaces (2-dimensional objects). Topics include the classification of surfaces, map colouring, decomposition of knots and knot invariants.

Classes
3x1-hr lectures; 1x1-hr tutorial/wk

Assessment
1 x Geometry assignment (5%); 1 x Topology assignment (5%); 1 x Geometry quiz (12%); 1 x Topology quiz (12%); 2-hr final exam (66%)

Assumed knowledge
Theory and methods of linear transformations and vector spaces, for example MATH2061, MATH2961 or MATH2022

Pre-requisites

12 credit points of Intermediate Mathematics

Prohibitions

MATH3001 or MATH3006

### Details

Faculty: Science

Semester 2

03 Aug 2020

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Aug 2020
Unit of study level: Senior
Credit points: 6.0
EFTSL: 0.125
Available for study abroad and exchange: Yes
Faculty/department permission required? No
Location
Camperdown
More details
Unit of Study coordinator: Dr Leo Tzou
HECS Band:
##### Courses that offer this unit

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