MAS334 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 MAS220 and MAS221 last year, so it should be familiar for most students.

In weeks 2, 4, 6, 9 and 11 I will issue offline problem sheets. 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.

Problem sheet 5 Solutions
Please hand in Exercises 5.1 and 5.7 by the end of Week 11.
Problem sheet 4 Solutions
Please hand in Exercises 4.1 and 4.4 by the end of Week 9.
Problem sheet 3 Solutions
Please hand in Exercises 3.1 and 3.2 by the end of Week 6.
Problem sheet 2 Solutions
Please hand in Exercises 2.1 and 2.5 by the end of Week 4.
Problem sheet 1 Solutions
Please hand in Exercises 1.1 and 1.3 by the end of Week 2.

Lecture notes

PDF download HTML version

Both versions of the notes contain links to various interactive demonstrations (described below) and videos.

The HTML version is relatively new. It should be better than the PDF for viewing on a phone, or for reading with a screen reader. I would welcome any comments on either of these use cases.

I strongly recommend that you should attend lectures in person if 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.

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.


Most of the ideas in this course can be implemented by computers. Students who are interested in such things can find code (in HTML+Javascript) for the interactive demonstrations in the combinatorics diagrams repository on GitHub. If you prefer Python, you can find some equivalent Python code in the combinatorics Python repository. I will probably translate more of the Javascript code to Python as the semester progresses. All of this is purely optional; I will say almost nothing about it in lectures, and it will not be examined.

AI Tools

The situation with AI tools (such as Google Bard, 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. I would be interested to hear about your experiences with that. If you use AI while doing the homework questions that you hand in, please mention that on your homework.

My assessment in September 2023 is as follows. If you ask ChatGPT4 (which is not free) to do the homework problems, it will typically give an answer that contains some good ideas and correct ingredients, but also contains a number of errors. Google Bard and the free version of ChatGPT are currently much less capable and often produce complete nonsense.

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 2022-23. You can find the 2022-23 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:
Examinable material: Short version Long version

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
Hicks Building, Room J26