100 4th year Dr K. Ecker (Mathematics) and Dr K. Sharpe (Statistics). Double semester. As approved by the coordinators, usually comparable to that required for 618-440. The invitation of the Heads of both departments is required. (See Note) To train mathematical sciences graduates in advanced topics and to provide an opportunity for students to participate in research. On completion of this subject, students should:

• Comprehend in some depth and detail the theory and techniques associated with a number of advanced topics.
• Have developed skills to master advanced and abstract material and the ability to apply it to other areas of the mathematical sciences and related disciplines; an ability to work independently on advanced material; an insight into research techniques.
• Appreciate the sophistication and aesthetics of advanced mathematical sciences; the interplay of different areas of mathematical sciences required to solve problems; the special skills required at research level.

As approved by the coordinators, usually comparable to that required for 618-440. Research project 25%; Course work 75%. Students will not be invited to enrol in this subject without a suitably high level of previous achievement in Mathematical Sciences. Students averaging less than a grade of H3 across six third-year Mathematics or Statistics subjects are unlikely to be invited into the subject. However students with fewer than six third-year Mathematics or Statistics subjects, but a very high standard of prior achievement may still receive favourable consideration.