# Maths Dissertation

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. In order to give a rigorous meaning to inequality (I), one has to clarify what we mean by [3], which is a very useful tool in geometric variational problems.

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).

$$v\bigm|_=u\bigm|_ \qquad \implies \qquad \|\nabla u\|_\leq \|\nabla v\|_.$$!

is absolutely minimizing if and only if it is the solution of the infinity Laplacian, which is the (highly degenerate) Euler-Lagrange equation for the prototypical problem in the calculus of variations in ! Recommended modules: Functional Analysis, Partial Differential Equations References: !

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. is a plane curve with the increasing chord property with length ! We will examine how to improve the above constant "! Each student will be assigned a supervisor who will monitor their progress and provide appropriate guidance thorough the LT, ST, and over the summer. The report may include some software relating to the project.Detailed information about the required format for this submission will be provided during the Seminars. 2, 123--139 Hausdorff dimension is the principal notion of dimension in the context of fractal sets in ! We will examine some of these and their inter-relationship. However, other definitions are in widespread use, for example, packing dimension, upper and lower box-counting dimension, upper and lower Minkowski dimension, ... At the end of summer term, each student will give a presentation to an audience of two members of staff on the topic of their dissertations.This will be graded and worth 10% of the course grade.For full information on the BSc and MMath Final Year Projects, please see this page. These topics are also offered to students in MSc Mathematics.

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