Algebraic structures and probability

the long version

In this text the authors have attempted to introduce a judicious blending of the set theoretical approach and the more traditional approach to the various topics. The set theoretical approach can be very useful in demonstrating relationships between apparently unrelated topics and, from this point of view, is a powerful mathematical tool. However, overindulgence in set theory simply for the sake of using sets may often cause basically simple ideas to appear much more complicated than they actually are. Study of Chapters 6, 7, and 8, may usefully be delayed until the authors companion volume entitled Vectors and Matrices has been studied. This is not essential since these chapters are complete in themselves, but a familiarity with Vectors and Matrices may enable the student to study these chapters more quickly. Definitions and key points in the various chapters have been printed in red. In addition some problems in certain exercises have been numbered in red. These tend to be more difficult than the other problems and might be omitted on a first reading...