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For more information on any of these projects, please contact the project supervisor. Recommended modules: Measure and Integration, Perturbation theory and calculus of variations, Functional Analysis.
Key words: Isoperimetric Inequality, sets of finite perimeter.
We will give a rigorous proof of inequality (I), and we will consider interesting related problems. De Giorgi: Sulla proprietà isoperimetrica dell'ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita.
Several seminars will include presentations by members of the Department of Mathematics on proposed topics for dissertations that they would be interested in supervising.
Additional seminars will cover important aspects of writing a dissertation in mathematics, including: what plagiarism is and how to avoid it, the use of libraries for research, electronic research, general aspects of writing mathematics, and preparing a manuscript using mathematical text processing software (in particular, La Te X). Assessment is primarily based entirely on the Dissertation, three hard copies and one electronic copy of which must be submitted by early September (exact date to be specified later).
Students will be given support in the seminars on how to prepare, how to present and what is expected.
This page contains details for the topics available for final year dissertations for MMath students, and for projects for BSc students.
$$\begin \tag* P (E^S) \leq P(E) \quad \text E \subset \mathbb^n.
, and (see, for instance, Theorem 14.4 in ) is satisfied: !
10 hours of seminars and 3 hours of seminars in the MT. The ratio of lecture time and seminar time varies each week.
Seminars do not include personal supervision time, which is scheduled independently with student supervisors.