In general we know that the fixed point locus of a 1-dimensional additive linear algebraic group,G_{a}, action over a complete nonsingular variety is connected. In thesis, we explicitly identify a subset of the G_{a}-fixed locus of the punctual Hilbert scheme of the d points,Hilb^{d}(P^{2} / 0),in P^{2}. In particular we give an other proof of the fact that Hilb^{d}(P^{2} / 0) is connected.

The aims of this study were to investigate the effects of two different methods of dynamic geometry based computer instruction on seventh grade students&rsquo / attitudes towards geometry, attitudes toward mathematic and technology and spatial abilities compared to traditional textbook based instruction and to get the students&rsquo / views related to the effects of computer based instruction on their learning. The sample consisted of 57 seventh grade students from a private elementary school in Kayseri. The study was conducted in the 2006-2007 academic year, lasting 14 lesson hours (two weeks). The data were collected through spatial ability test, mathematics and technology attitude scale, geometry attitude scale, and interviews. The quantitative analyses were carried out by using multivariate covariance analyses. The results revealed that two different methods of dynamic geometry based computer instruction didn&rsquo / t have a significangt effect on students&rsquo / spatial abilities compared to traditional textbook based instruction. The results also indicated that two different methods of dynamic geometry based instruction had a significant effect on students&rsquo / attitudes toward geometry, mathematics and technology compared to traditional textbook based instruction. The results of the interviews indicated that computers created a dynamic learning environment which supported students&rsquo / development and computers also helped students to explore mathematic in a far more meaningful way.

On the tangent bundle of a Riemannian manifold the most natural choice of metric tensor field is the Sasaki metric. This immediately brings up the question of infinitesimal symmetries associated with the inherent geometry of the tangent bundle arising from the Sasaki metric. The elucidation of the form and the classification of the Killing vector fields have already been effected by the Japanese school of Riemannian geometry in the sixties. In this thesis we shall take up the conformal vector fields of the Sasaki metric with the help of relatively advanced techniques.