Evolutionary relationships are key to modern understanding of biological systems. Phylogenetic search is the means by which these relationships are inferred. Phylogenetic search is NP-Hard. As such it is necessary to employ heuristic methods. This work proposes new methods based on viewing the relationships between species as sets of partitions. These methods produce more parsimonious phylogenies than current methods.

Title: Descriptive geometry applications in cartography Author: Jana Vlčková Department: Department of Mathematics Education Supervisor: RNDr. Vlasta Moravcová, Ph.D., Department of Mathematics Education Abstract: This thesis is focused on constructions of geographic nets in maps and serves as a base for studies and teaching for teachers and students of secondary schools or universities, which are focused on the cartography field. The thesis contains seven chapters, the first of which describes basic terms used in the thesis. Other chapters deal with the analysis of chosen cartography projections, whereas first three chapters concerns with the projection of the globe into a plane, another two chapters concerns with a cylindrical surface and the last one concerns with a conical surface. Constructive tasks, which serve for practising the subject matter, are enclosed for each chapter. Key words: cartographic projection, azimuthal projection, ortographic projection, gno- monic projection, stereographic projection, cylindrical projection, conical projection 1