MATH39001, Combinatorics and Graph Theory
Here is the syllabus.
What is examinable?
The past 3 years' examination papers are available in blackboard together with the solutions to and the generic feedback on the January 2017 paper.
I am happy to look at your solutions to past examination questions or
to any of the questions on the problem sheets to provide individual feedback.
There are also some additional problems grouped by topic in the "Practice problems" item.
The test, the solutions and the generic feedback are available in
blackboard in the folder "Coursework test".
Graph theory notes in one file, or in separate chapters:
Here is the link to the textbook for the second half of the course:
Generating functions notes in one file, or in separate chapters:
Homework and solutions
Handouts and related material
Squared squares and rectangles
Interactive Ford–Fulkerson algorithm demonstrations:
16 October, 1st example,
16 October, 2nd example and
Remember that the colouring is only there to help you, it is not part of the algorithm. You
may do it if you like it,
but it is not a substitute
for writing all the numbers on the edges.
- The example
of the Ford–Fulkerson algorithm done on paper on 16 October. This is how you should do it in an examination.
A summary of formal power series
A list of useful power series
Examples of cards, decks, hands type problems
You can also download and experiment with the original
Save it, then open it with Mathematica.
article about partitions in the Notices of the American Mathematical Society.
- The excursion ticket problem and a link
to the Dudeney's book, the excursion ticket problem is number 32.
Interactive Ford–Fulkerson algorithm
Go to All Programs → MATH39001 → FlowDemo on any of the computers in the ATB ground floor cluster. (The first time you may have to a wait a long time for Mathematica to download. You will probably need to scroll down each time to see the latest graph, this is the result of an undocumented change from Mathematica 7.)
There are HELM (Helping Engineers Learn Mathematics) modules covering
1st order ODE's and
2nd order ODE's, which you may find useful if your knowledge of calculus has become a bit rusty.
66 combinatorial problems involving the Catalan numbers and
Squared squares and rectangles:
Numberphile video about squaring the square and
some extra footage.
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