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, ...
The Dissertation in Mathematics is an individual, substantial project as an introduction to mathematical research methods.
The student will investigate and study an area of mathematical research or application of advanced mathematical techniques, and to write a report on their findings. The dissertation topic will normally be proposed by the Department. The seminars include a mixture of lecture time, presentations and discussion.
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.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. 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. 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. F., Optimal Lipschitz extensions and the infinity Laplacian, Calc. Miroslav Chlebik Presentation [PDF 309.98KB] Key words: Hausdorff dimension, Lipschitz mappings, rectifiable sets, fractals Recommended modules: Measure and Integration, Functional Analysis References: ! Falconer, K., Fractal geometry: Mathematical Foundations and Applications, John Wiley & Sons Ltd., 1990 if ! 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?