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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, ...
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.
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. $$\begin \tag* P (E^S) \leq P(E) \quad \text E \subset \mathbb^n. , and (see, for instance, Theorem 14.4 in ) is satisfied: ! and Mc Mullen P., Arcs with increasing chords, Proc. In such problems, it is of course important to choose an appropriate metric on the space of the probability measures. :-)) are scarce and buried in mathematical biology books and journals. 72(1972), 205--207 Studying the convergence properties of sequences of probability measures comes up in many applications (for example in the study of approximations of probability measures and stochastic inverse problems). This is only the case that the gap penalty is 0, but already the project can be only on the LCS. Eﬃcient algorithms computing optimal alignments and optimality regions (what are those? 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. 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). is a plane curve with the increasing chord property with length ! We will examine how to improve the above constant "!