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 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.

Problem sheet 5
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.

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:
Examinable material: Short version Long version

Past exam papers

2023-24ExamSolutions
2022-23ExamSolutions
2021-22ExamSolutions
2020-21ExamSolutions
2019-20ExamSolutions
2018-19ExamSolutions
2017-18ExamSolutions
2016-17ExamSolutions
2015-16ExamSolutions

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