Scattered spaces and eggs in finite projective spaces Topics in Finite Geometry

This book is concerned with Galois Geometry or Finite Geometry, quite a young area in Mathematics that dates back to around 1950 with the work of the celebrated Italian mathematician Beniamino Segre who studied n-dimensional projective spaces over finite fields and substructures of these spaces. Since then Finite Geometry has received more and more attention due to its close links with other areas of mathematics such as Group Theory and Algebra, as well as its many applications in Coding Theory and Cryptography. The topics treated in this book play a key role in Finite Geometry and can serve as an introductory text for mathematicians who are interested to work in this area or who want to get a flavor of the subject. It is particularly useful for mathematicians who want to become adept at the various techniques used in finite geometry, such as polynomials over finite fields or techniques in higher dimensional projective spaces. This work can be seen as consisting of two main parts, and together with the preliminaries both of these parts can serve a as basic text for a one-term postgraduate level in Finite Geometry.