100 4th year Dr K. Ecker. double semester At least six one-semester lecture courses of 26 lectures (or equivalent seminars or guided reading), and project work as required. Attendance at departmental research seminars relevant to the areas of course work and project undertaken is also expected. The invitation of the Head of the Department is required. (See Note) To train mathematics graduates in advanced mathematics topics and to provide an opportunity for students to participate in mathematical 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 mathematics and related disciplines; an ability to work independently on advanced material; an insight into research techniques.
• Appreciate the sophistication and aesthetics of advanced mathematics; the interplay of different areas of mathematics required to solve problems; the special skills required at research level.

A Research Project plus six semester lecture courses (for details, see the Mathematics Honours entry in the Faculty of Science section of this Handbook). 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 Mathematics. Students averaging less than a grade of H3 across six third-year Mathematics subjects (or a smaller number of Mathematics subjects together with other subjects with substantial mathematical content) are unlikely to be invited into the subject. However students with fewer than six third-year Mathematics subjects, but a very high standard of prior achievement may still receive favourable consideration.