Singularities of some functions's in 4 – dimensional Galilean space

This thesis consists of five chapters. In the first chapter, a short summary of literature about the Galilean Geometry and 4-dimensional Galilean space is given.Secondly, fundemental knowledge and some theorems which are used in this thesis are given as general information chapter. In the third chapter, material and method, the singularities theory is met shortly. The fourth chapter, findings chapter, consists of four sections. In the First and second section, height function and distance function in the 4-dimensional Galilean space are defined for applying singularity theory. Necessary derivatives are computed to find singularity order of singular points of these functions. Thirdly, being versal unfolding and (p)-versal unfolding situations which have important roles in singularity theory are expressed for these functions. In the results and suggestions chapter, short evaluations are given. The last the results and suggestions chapter chapters contain a list of references and short autobiograpy of the author, respectively.