Principal original sources of the material for the project should be consulted as far as possible, in addition to accounts that may be found in textbooks or surveys. All sources that have been used should be explicitly noted in the report. The status of the results in the project, whether they are new and obtained by the student or whether they are obtained by others, should be stated.

A student, in consultation with the supervisor, should write a summary of about 300 words on the nature and scope of the project. The summary should be bound with the project report. It should contain a statement highlighting the contributions made by the student.

The statement should include, if any,

- the student's own ideas, own results, own proof, own interpretations, own examples or counterexamples, own computer programmes which he/she does not obtain from other sources. The relevant parts of the written thesis which contain such contributions should be explicitly stated.
- improvements made by the students on existing theorems, proofs, etc. found in books or papers. The sources from which the results are improved upon should be mentioned explicitly.

A suggested format for the summary is appended below. Some examples of the Statement of the author’s contributions are also included.

SUMMARY
(Nature and scope of the written report)
........
(Statement of the author's contributions)
Example 1.
Theorem 3.5 is new and is a partial converse of the Buck-Cai Theorem ([2], page 124). Theorem 4.1 is a slight generalization of Theorem 1.6 in Bukhill ([3], page 96), and the proof is modelled on Bukhill's proof.
Example 2.
In [5] it is stated, without proof, that the converse of Theorem 3.2 is false, and this is substantiated by a counterexample, see Example 5.3. In the proof of Theorem 4.2, I have made use of a perturbation technique which avoids the lengthy calculations used in ([5], page 135, and [8], page 436).
Example 3.
I have obtained a new representation (Theorem 3.2) for the multivariate B-splines which is analogous to the divided difference representation in the one-dimensional case. A comparison of the computational efficiency of the methods available for the evaluation of multivariate B-splines and their integrals is studied in Section 3. Two computer programmes have been written and they are included in the Appendix. |