MA243 Geometry
Term I 2015-2016

Module Description

This module, MA243 (Geometry) has no offical prerequisites beyond the core. A keen appreciation of linear algebra will be be very helpful, however.

Geometry - literally "earth measurement" - is the mathematical study of shape using the tools of length and angle, area and volume. The geometry of a space can be especially beautiful when the space is highly symmetric. Examples here include spherical, euclidean, and hyperbolic geometry.

In the modern study of geometry, the notion of length can be abstracted away. This allows for ever larger symmetry groups and thus ever weaker (and so more general) invariants: aspect ratio, midpoints, parallelism, cross-ratio, and so on.

The material covered in this module is background for many of the third and fourth year modules in group theory, geometry, topology, and more.

Schedule

Instructor and TAs

Class meetings

Reference materials

We will follow the first five or six chapters of the book Geometry and Topology, by Miles Reid and Balázs Szendrői. The first six chapters may be purchased, in the form of lecture notes, from the front office at the Mathematics Institute. The book itself may be bought from the university bookshop or on-line.

Example sheets

See the schedule for the example sheets.

In addition to the exercises prepared for this class, please note that the book contains many interesting exercises. Here is the web-page for this module as recently taught by Professor Reid.

Exam

The exam will be 85% of your mark. The exam will be closed book. Here are the exam papers for this module from the last four years.

Assessed work

Assessed work will be 15% of your mark. Of this, 2% (at most) may be earned every week (starting the second week) by turning in the three required exercises. Exactly one of these will be marked by the TA (with a score of 0, 1, or 2). Please let me (Saul) know if any of the problems are unclear or have typos.

Homework solutions must be placed in the dropoff box (near the front office), by 15:00 on Mondays. No late work will be accepted.

Please write your name, the date, and the module code (MA243) at the top of the page. If you collaborate with other students, please include their names.

Solutions typeset using LaTeX are preferred. Each problem should require at most one side of one page. If you find you need more space then write out a complete solution and then rewrite with conciseness in mind.

Mistakes