Topology and Non-Euclidean Geometry

Course Overview

The last one hundred and fifty years have seen a revolution in the way mathematicians think about geometry, moving beyond the ideas that had been at its core since the Ancient Greeks. On this course, aimed at bright Year 11s and A-Level students, we will learn about some of these developments, absent from school curricula. By the end of the programme, students will have acquired a broadened awareness of the scope of mathematics, and familiarity with topics not studied at school, an increased appreciation of the logical structure of mathematical theories, an understanding of generalisations of familiar geometric notions to unfamiliar contexts, such as curved surfaces, an understanding of novel geometric notions, such as curvature, an ability to work quantitatively in two, three, and, arbitrarily, many dimensions and an introduction to Einstein's theory of gravity. The time spent on various topics may vary according to a student's understanding and interest; any topic can be elaborated on if the student wishes. There are illustrated course notes and short optional pieces of homework.