Introduction to Probability Models” by Sheldon M.ross.

According to Leo Breiman (1968), probability theory has a right and a left hand. The right hand refers to rigorous mathematics, and the left hand refers to 'proba­ bilistic thinking'. The combination of these two aspects makes probability theory one of the most exciting fields in mathematics. One can study probability as a purely mathematical enterprise, but even when you do that, all the concepts that arise do have a meaning on the intuitive level. For instance, we have to define what we mean exactly by independent events as a mathematical concept, but clearly, we all know that when we flip a coin twice, the event that the first gives heads is independent of the event that the second gives tails. Why have I written this book? I have been teaching probability for more than fifteen years now, and decided to do something with this experience. There are already many introductory texts about probability, and there had better be a good reason to write a new one. I will try to explain my reasons now.

This book introduces and studies a number of stochastic models of subsistence, communication, social evolution and political transition that will allow the reader to grasp the role of uncertainty as a fundamental property of our irreversible world. At the same time, it aims to bring about a more interdisciplinary and quantitative approach across very diverse fields of research in the humanities and social sciences.

From the reviews of the first printing, published as Volume 7 of the Encyclopaedia of Mathematical Sciences:
"…… In this volume, we find an introductory essay entitled "Remarkable Facts of Complex Analysis" by Vitushkin… This is followed by articles by G.M.Khenkin on integral formulas in complex analysis, by E.M.Chirka on complex analytic sets, by Vitushkin on the geometry of hypersurfaces and by P.Dolbeault, on the theory of residues in several variables. … In sum, the volume under review is the first quarter of an important work that surveys an active branch of modern mathematics. Some of the individual articles are reminiscent in style of the early volumes of the first Ergebnisse series and will probably prove to be equally useful as a reference; all contain substantial lists of references."
Bulletin of the American Mathematical Society, 1991 "… This remarkable book has a helpfully informal style, abundant motivation, outlined proofs followed by precise references, and an extensive bibliography; it will be an invaluable reference and a companion to modern courses on several complex variables."

Probability and Statistics are studied by most science students, usually as a second- or third-year course. Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real-life and using real data, the authors can show how the fundamentals of probabilistic and statistical theories arise intuitively. It provides a tried and tested, self-contained course, that can also be used for self-study.

The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise.

The theory of probability and mathematical statistics is becoming an indispensable discipline in many branches of science and engineering. This is caused by increasing significance of various uncertainties affecting performance of complex technological systems. Fundamental concepts and procedures used in analysis of these systems are often based on the theory of probability and mathematical statistics.