MAS334 Combinatorics 2017-2018

Lecturer: Prof Sarah Whitehouse


Welcome to the 2017-2018 course web page for MAS334 Combinatorics. This page will be updated as the module progresses. I do not use MOLE for this module - this webpage is the place to find course materials.

For official course information, including timetabling, please consult the list of current modules.

Course Information

The typed notes for the course consist of a booklet containing the statements of results and examples; proofs and solutions must be taken down by hand in the lectures. I will lecture the proofs and work through solutions to examples from hand-written notes and I do not plan to make any version of my notes generally available. (Of course, exceptions will be made for special cases and for lectures missed due to illness or special circumstances.)

The example sheets for the module are at the back of the lecture notes booklet. Copies of the printed booklet will be circulated in the first lecture. It can also be downloaded below. Also below is the course syllabus.


The exercise sheets for the course can be found at the back of the lecture notes. I would encourage you to attempt all of the problems on the sheets at some point. There are also some pointers to where you can find extra problems to practice if you wish.

Some of the problems will be set for homework and marked by me. Feedback will be given, in the form of written comments on individual homework and also general feedback in lectures on common problems. Homework problems will be indicated below. Solutions will appear here as the module progresses.


Solutions to Example Sheet 1          
 Feedback on homework 1
Solutions to Example Sheet 2
 Feedback on homework 2
Solutions to Example Sheet 3
 Feedback on homework 3
Solutions to Example Sheet 4
Solutions to Example Sheet 5
 Feedback on homework 4

Homework schedule

I expect to set 4 (non-assessed) homeworks, with hand-in deadlines the Wednesday lecture in weeks 2, 5, 8 and 10. Further details to appear below as the course progresses.

Homework 1: Example sheet 1, Questions 1, 3, 5. Due in: Wednesday lecture week 2.

Homework 2:  Example sheet 2, Questions 1, 3, 5. Due in: Wednesday lecture week 5.

Homework 3:  Example Sheet 3, Questions 1, 4. Due in: Wednesday lecture week 8.

Homework 4:  Example Sheet 4, Questions 2, 3 and Example Sheet 5, Question 2. Due in: Wednesday lecture week 10.

Past Exam Papers

The last two years' exams are below, with solutions.

Earlier exam papers can be obtained via the SoMaS webpage here.
Here is some further exam information.

Interesting Extras

Tetrahedral numbers (wikipedia) Relates to Examples 17, 18 in Chapter 1 (giving another point of view). And here, thanks to a chance encounter on the streets of Manchester, is more on some different approaches to Example 18, from former MAS334 student Rob Nicolaides.

Tetriminoes (wikipedia) Relates to Example 23 in Chapter 2, which is just one of  many such tiling problems.

The 7/5 Bridges of Königsberg/Kaliningrad

Maple worksheet on rook polynomials : this can be used to check your answers if you set yourself rook polynomial calculations.  [If your browser recognises Maple files, this should open in Maple on clicking. If not, you will need to download the file (probably by right clicking the link and then choosing “save link as…”) and then open it with Maple. Once you have the worksheet open in Maple, you should do "execute worksheet" to run all the commands. After that, you can play around with your own examples. Even if you have never used Maple before, this should be fairly easy to use.]

Colourful picture of 2 10x10  orthogonal Latin squares (probably to be seen in lecture 1 and relevant to chapter 5).

Contact Details

Prof Sarah Whitehouse
Room J6c, Hicks Building
Telephone: 0114 2223870  (internal extension: 23870)

Office Hour:  Tuesday at 4 or by appointment.

Last updated: 6 December 2017