MA3F1 Introduction to topology
Term I 2017-2018
This module, MA3F1
(Introduction to topology) has the prerequisites MA222
(Metric spaces) and MA249
Topology is the study of shapes: the study of spaces forgetting all
notions of geometry. We begin by saying precisely what it means for
two spaces \(X\) and \(Y\) to be "the same" in the topological
setting. This done we investigate one of the most powerful
topological invariants: the fundamental group \(\pi_1(X)\). The
justly named fundamental group is related, inside topology, to
covering spaces and related, for example in number theory, to Galois
The material covered in this module is directly relevant to MA3H5
(Algebraic topology), and many others.
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 closely follow the first chapter of the book Algebraic
topology, by Allen
Hatcher. The book is available from Hatcher's website, and can
also be purchased from the university bookshop
Links to the Lecture Capture audio files, and to the discussion forum,
are on the module's Moodle page.
See the schedule for the example
In addition to the exercises prepared for this class, please note that
Hatcher's book contains many interesting exercises. He has also given
exercises. Here is the web-page
for this module as taught by Professor Mond in 2012.
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 five 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 one of the
three indicated exercises. These will be marked by a 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 14:00 on Thursdays. No late work will be accepted.
Please write your name, the date, and the module code (MA3F1) 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