Despite the fears of university mathematics departments, mathematics educat,ion is growing rather than declining. But the truth of the matter is that the increases are occurring outside departments of mathematics. Engineers, computer scientists, physicists, chemists, economists, statis- cians, biologists, and even philosophers teach and learn a great deal of mathematics. The teaching is not always terribly rigorous, but it tends to be better motivated and better adapted to the needs of students. In my own experience teaching students of biostatistics and mathematical bi- ogy, I attempt to convey both the beauty and utility of probability. This is a tall order, partially because probability theory has its own vocabulary and habits of thought. The axiomatic presentation of advanced probability typically proceeds via measure theory. This approach has the advantage of rigor, but it inwitably misses most of the interesting applications, and many applied scientists rebel against the onslaught of technicalities. In the current book, I endeavor to achieve a balance between theory and app- cations in a rather short compass. While the combination of brevity apd balance sacrifices many of the proofs of a rigorous course, it is still cons- tent with supplying students with many of the relevant theoretical tools. In my opinion, it better to present the mathematical facts without proof rather than omit them altogether.

The long-awaited revision of Fundamentals of Applied Probability and Random Processes expands on the central components that made the first edition a classic. The title is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self-study. - Demonstrates concepts with more than 100 illustrations, including 2 dozen new drawings - Expands readers' understanding of disruptive statistics in a new chapter (chapter 8) - Provides new chapter on Introduction to Random Processes with 14 new illustrations and tables explaining key concepts. - Includes two chapters devoted to the two branches of statistics, namely descriptive statistics (chapter 8) and inferential (or inductive) statistics (chapter 9).

Concise advanced-level introduction to stochastic processes that arise in applied probability. Poisson process, renewal theory, Markov chains, Brownian motion, much more. Problems. References. Bibliography. 1970 edition.

In this book, Feldman and Valdez-Flores present applied probability and stochastic processes in an elementary but mathematically precise manner, with numerous examples and exercises to illustrate the range of engineering and science applications for the concepts. The book is designed to give the reader an intuitive understanding of probabilistic reasoning, in addition to an understanding of mathematical concepts and principles. Unique features of the book include a self-contained chapter on simulation (Chapter 3) and early introduction of Markov chains.

Despite the fears of university mathematics departments, mathematics educat,ion is growing rather than declining. But the truth of the matter is that the increases are occurring outside departments of mathematics. Engineers, computer scientists, physicists, chemists, economists, statis- cians, biologists, and even philosophers teach and learn a great deal of mathematics. The teaching is not always terribly rigorous, but it tends to be better motivated and better adapted to the needs of students. In my own experience teaching students of biostatistics and mathematical bi- ogy, I attempt to convey both the beauty and utility of probability. This is a tall order, partially because probability theory has its own vocabulary and habits of thought. The axiomatic presentation of advanced probability typically proceeds via measure theory. This approach has the advantage of rigor, but it inwitably misses most of the interesting applications, and many applied scientists rebel against the onslaught of technicalities. In the current book, I endeavor to achieve a balance between theory and app- cations in a rather short compass. While the combination of brevity apd balance sacrifices many of the proofs of a rigorous course, it is still cons- tent with supplying students with many of the relevant theoretical tools. In my opinion, it better to present the mathematical facts without proof rather than omit them altogether.

Applied probability is a broad research area that is of interest to scientists in diverse disciplines in science and technology, including: anthropology, biology, communication theory, economics, epidemiology, finance, geography, linguistics, medicine, meteorology, operations research, psychology, quality control, sociology, and statistics. Recent Advances in Applied Probability is a collection of survey articles that bring together the work of leading researchers in applied probability to present current research advances in this important area. This volume will be of interest to graduate students and researchers whose research is closely connected to probability modelling and their applications. It is suitable for one semester graduate level research seminar in applied probability.

This 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables.

Introduction to Applied Probability provides a basis for an intelligent application of probability ideas to a wide variety of phenomena for which it is suitable. It is intended as a tool for learning and seeks to point out and emphasize significant facts and interpretations which are frequently overlooked or confused by the beginner. The book covers more than enough material for a one semester course, enhancing the value of the book as a reference for the student. Notable features of the book are: the systematic handling of combinations of events (Section 3-5); extensive use of the mass concept as an aid to visualization; an unusually careful treatment of conditional probability, independence, and conditional independence (Section 6-4); the resulting clarification facilitates the formulation of many applied problems; the emphasis on events determined by random variables, which gives unity and clarity to many topics important for interpretation; and the utilization of the indicator function, both as a tool for dealing with events and as a notational device in the handling of random variables. Students of mathematics, engineering, biological and physical sciences will find the text highly useful.

This book is an introductionary course in stochastic ordering and dependence in the field of applied probability for readers with some background in mathematics. It is based on lectures and senlinars I have been giving for students at Mathematical Institute of Wroclaw University, and on a graduate course a.t Industrial Engineering Department of Texas A&M University, College Station, and addressed to a reader willing to use for example Lebesgue measure, conditional expectations with respect to sigma fields, martingales, or compensators as a common language in this field. In Chapter 1 a selection of one dimensional orderings is presented together with applications in the theory of queues, some parts of this selection are based on the recent literature (not older than five years). In Chapter 2 the material is centered around the strong stochastic ordering in many dimen sional spaces and functional spaces. Necessary facts about conditioning, Markov processes an"d point processes are introduced together with some classical results such as the product formula and Poissonian departure theorem for Jackson networks, or monotonicity results for some re newal processes, then results on stochastic ordering of networks, re~~ment policies and single server queues connected with Markov renewal processes are given. Chapter 3 is devoted to dependence and relations between dependence and ordering, exem plified by results on queueing networks and point processes among others.