Dear all,
Marks for the recent 20% coursework are now available.
In general the work was of high quality.
Note that if your work was submitted on time then your score will be a multiple of 10 (if not then you may have been deducted a multiple of 5 marks).
The feedback gives a score out of 10 (which was then multiplied by 10 to give a percentage score).
There were 3 marks per question, and a bonus mark awarded (very rarely) for submissions which pointed out some deliberate ambiguity in question 2.
Nobody scored above 90, but there were many submissions scoring 70, 80 and 90.
In general question 1 was done well.
For question 2, full marks were given for stating, with reasons, that the fixed point was neither attracting nor repelling.
But in a sense that was not the whole story, as the question (deliberately) omitted the domain of definition of f; for example if f was considered as part of the logistic family, defined as a map from [0,1] to itself, then the fixed point would be attracting.
And if you really wanted, it could be defined as a self-map of the non-positive numbers, in which case the fixed point is repelling.
The bonus marks were awarded for the (very few) students who pointed out the ambiguity in this question.
Question 3 was done quite well, with many people giving lots of details of points/orbits of low period, and some discussion of the implications of Sharkovskii's theorem.
However full marks were reserved for those who pointed out, and properly discussed, the possibility of topological conjugacy (which can be done but is not completely straightforward since there is no homeomorphism between [0,1] and the real numbers).
Please let me know if you have any queries about these marks.
Best wishes,
Oliver
