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.
3x1-hr lectures; 1x1-hr tutorial/wk
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%)
Theory and methods of linear transformations and vector spaces, for example MATH2061, MATH2961 or MATH2022
12 credit points of Intermediate MathematicsProhibitions
MATH3001 or MATH3006