Term I 2015-2016
This module, MA243
(Geometry) has no offical prerequisites beyond the core. A keen
appreciation of linear algebra will be be very helpful, however.
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
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
The schedule has a planned list of
topics, organized by lecture. We will change the schedule as
necessary, as we work through the material. Links to example sheets
will be posted week-by-week.
Instructor and TAs
We will follow the first five or six chapters of the book Geometry and
Topology, by Miles Reid
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
See the schedule for the example
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.
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 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.
Please tell me in person, or via email, about any errors on this
website or made in class. I am especially keen to hear about
mathematical errors, gaffes, or typos made in lecture or in the