MAS334 Combinatorics 2016-2017

Lecturer: Prof Sarah Whitehouse


This is the 2016-2017 course web page for MAS334 Combinatorics. It will be updated as the module progresses. 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. Some of the problems have been set for homework and marked by me. Feedback has been given, in the form of written comments on individual homework and also general feedback in lectures on common problems. Homework problems are indicated below. Solutions are now all here.

Solutions to Example Sheet 1
Solutions to Example Sheet 2
Solutions to Example Sheet 3
Solutions to Example Sheet 4
Solutions to Example Sheet 5

Homework schedule

I expect to set 4 homeworks, with hand-in deadlines the Wednesday lecture in weeks 2, 5, 8 and 10. 

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 and 4. Due in: Wednesday lecture week 8.

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

Past Exam Papers

The last two years' exams are below, with solutions

Exam information sheet

Interesting Extras

Tetrahedral numbers (wikipedia) Relates to Examples 17, 18 in Chapter 1 (giving another point of view).

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 (as 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:  Monday 3-4 or by appointment.

Last updated: 6 December 2016