G51MC2 Feedback 2004

This module went much better than last year, where the raw module average was 40%. This year the raw average was 48% indicating there is still some way to go before the module can be considered satisfactory but showing a marked improvement in the general understanding of the material. The biggest problem highlighted was confusion over mathematical induction with many student unable even to state a base case and step case for an inductive proof. This suggested that the cut back from the previous year in the amount of time spent on induction was unwise.

The Exam

Question 1

This was a compulsory short answer question covering the entire syllabus. The average mark was 12.5/20 which is a little on the low side. Since this question involved basic techniques this is disappointing. Particularly obvious was the student's inability to grasp even the basics of mathematical induction despite it being covered in both MCS and MC2.

Question 2

Matrices. This was the most popular on the paper. 137 students attempted the question and the average mark was 15 including a large number of firsts.

Question 3.

Graph Theory. 115 students attempted this question with an average mark of 12. Several were confused by the question and attempted to order the courses in the meal despite the fact they were not ordered in the description. However the majority of marks were lost because the students could not reproduce or apply the topological sort algorithm.

Question 4.

Probability. 112 students attempted this question and averaged 11/20. A few were confused by the question description and attempted to calculate probabilities for letters rather than fragments but in general marks were lost because people could not work with anything beyond the most basic combinations.

Question 5.

Program Correctness. 51 students attempted this question and the average mark was 8. On the whole this was not unexpected as questions involving proof generally have a bi-polar distribution with a lot of firsts and a lot of hard fails and this was no exception. However there was a significant number of thirds which was an improvement over the previous year - in general these students had grasped the basics of proof but were inclined to make errors in the actual application of proof rules.

Question 6.

General Proof. 46 students attempted this question and performance was uniformly poor with an average of 5 for the question. There seemed to be a tendency for the weaker students to attempt the question which was surprising given the challenging subject matter involved. None of the students were able to make any headway with the graph theory proof despite it being shown in lectures. Again a large part of the problem seemed to be an inability to even frame the beginnings of an inductive argument.