Chap1: Introduction -- Chap2: Basic Mathematical Preliminaries -- Chap3: Probability Theory -- Chap4: Random Variables -- Chap5: Characterization of Random Variables -- Chap6: Stochastic Process --  Chap7: Gaussian Distributions -- Chap8: Applications.

This book provides engineers with focused treatment of the mathematics needed to understand probability, random variables, and stochastic processes, which are essential mathematical disciplines used in communications engineering. The author explains the basic concepts of these topics as plainly as possible so that people with no in-depth knowledge of these mathematical topics can better appreciate their applications in real problems. Applications examples are drawn from various areas of communications. If a reader is interested in understanding probability and stochastic processes that are specifically important for communications networks and systems, this book serves his/her need. Narrows down probability, random variables, stochastic processes to an essential set of topics that communications systems engineers must understand; Presents difficult proofs of theories so that the reader can gain working level understanding of the subject as applied to communications networks and systems; Provides examples that the author encountered through his long experience in both teaching and industry; Provides a comprehensive review of the elements of complex variables, linear algebra and set theory -- pre-requisites for understanding the main topics of the book.