MPS352 Combinatorics
Lecturer: Neil Strickland
Module information
Notes, problem sheets, solutions,
past papers and so on can be found on this page. There is also a
Blackboard page for the course,
with a discussion board etc.
Homework schedule
In Weeks 1, 3, 5, 8 and 10 there will be
online tests.
These will use the same system that was used for Algebra and Analysis
modules last year, so it should be familiar for most students.
I will also issue offline problem sheets to be submitted at the end of
weeks 2, 4, 6, 9 and 11.
Each of these will specify one or two problems that you can hand in to
be marked. I strongly prefer for you to hand in paper in the Friday lecture.
If that is not possible for some reason, then you can submit work by email.
If you send handwritten work by email, please make sure that it is a single
PDF file (not separate images) scanned using one of the university
printer/copier/scanner machines or a proper scanning app on your phone; do
not simply use your phone camera. Please also scan complete A4 pages, even
if some pages are nearly empty.
These problem sheets, and subsequently the solutions, will appear on this page.
Formal assessment will be based solely on the final exam.
Lecture notes
Both versions of the notes contain links to various interactive
demonstrations (described below) and videos.
You should attend lectures in person if at all possible. If you
cannot do that, I recommend that you work from the notes and embedded
videos and demonstrations. There is also
a lecture progress page where you can see
which sections of the notes have been covered in lectures.
Encore recordings do not work very well for this module.
Interactive demonstrations
There is a set of
interactive demonstrations
explaining many of the ideas in the course. I will talk through these
in lectures, there are attached YouTube videos, and you can try them
yourself at other times. These are experimental and under development. I
welcome comments about the extent to which they are comprehensible, useful
or interesting.
Polls
There will be some polls during the lectures. You will be asked to
visit the URL
https://aim.shef.ac.uk/sangaku
on your phone or some other device. Outside of the lectures you will
not see anything at that page, but during the lecture various questions
may be displayed there, with buttons that you can click to select an
answer. Answers will be counted but not tied to individual students.
Coding
Most of the ideas in this course can be implemented by computers.
Students who are interested in such things can find Python code
in a
Github repository. The Python code is partly translated from
the Javascript code that drives the interactive demonstrations.
That Javascript code is in
another Github repository. You can ignore all this if you
are not interested; I will at most make occasional comments about
it in lectures.
AI Tools
The situation with AI tools (such as
Google Gemini,
ChatGPT,
GitHub copilot
and so on) is quite new and changing very rapidly. For this module,
formal assessment is based solely on the final exam, for which you
will of course not have access to any such tools. You are welcome
to use AI throughout the semester if you think that it will help you
to develop your understanding. Currently available tools (in
September 2024) give answers to the homework problems that are
sometimes excellent, sometimes completely wrong, and usually somewhere
in between.
I would be interested to hear about your experiences with AI.
If you use it while doing the homework questions that you hand in,
please mention that on your homework.
Recommended books
The main recommended book is
Aspects of Combinatorics by
Victor Bryant
(
Amazon,
Google Books).
The author taught combinatorics in Sheffield for many years.
Another possibility is
A First Course in Combinatorial
Mathematics by Ian Anderson
(
Amazon,
Google Books).
Exam information
The format of the exam and the arrangements for taking it will
be as in 2023-24. You can find the 2023-24 exam and solutions
below. There will be about 10 questions of varying lengths, all
compulsory. Some questions will ask you to state definitions
or results from the notes, or reproduce proofs from the notes.
However, most questions will instead ask you to solve problems,
which will often require some creative modification of the
methods explained in the notes.
There is a document listing which definitions, results and proofs
you might need to reproduce in the exam:
Past exam papers
Office hours
Official office hours are 14:00-15:00 on Fridays. I will expect people
to come to my office (Hicks J26) by default, but you can email me to
arrange an online meeting if you prefer. If you find me in my
office at some other time, then I may well be able to talk to you, but
I do not guarantee it.
Contact details
Neil Strickland
N.P.Strickland@sheffield.ac.uk
Hicks Building, Room J26
https://strickland1.org