Applied Probability Models with Optimization Applications: Studies in Logic and the Foundation of Mathematics
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Book Details:
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Publisher: Dover
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Author: Sheldon M. Ross
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Language: English
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Binding: Paperback
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Edition: Reprint
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ISBN: 9780486673141
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Number of Pages: 198
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Dimensions: 8.5 x 5.6 x 0.5 inches
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Release Date: 04-12-1992
About The Book:
"Introduction to Applied Probability" by Sheldon M. Ross offers a concise yet comprehensive introduction to the fundamental concepts of applied probability, making it an excellent resource for advanced undergraduate and beginning postgraduate students. The book focuses on the stochastic processes that are frequently encountered in applied probability, particularly in optimization models and decision processes.
Ross begins with an overview of basic probability theory and stochastic processes before delving into specific topics such as the Poisson process (including compound and nonhomogeneous versions), renewal theory, Markov chains, and more advanced processes like semi-Markov and regenerative processes. The book also covers practical applications, including inventory theory and continuous time optimization models like Brownian motion.
Each chapter is followed by a section of carefully chosen problems that reinforce the material and help students develop a deeper understanding of the concepts. The text is self-contained, making it accessible even to those with little prior knowledge of the subject. It’s especially suitable for a one-year course in applied probability.
Key Features:
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Clear and Concise: Written with clarity and precision, making the material accessible and understandable for students.
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Practical Focus: Emphasis on optimization models and decision processes, with real-world applications.
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Comprehensive Coverage: Topics include Poisson processes, renewal theory, Markov chains, inventory theory, and Brownian motion.
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Problem-Solving Approach: Each chapter is accompanied by a set of problems that complement the material and help with practice.
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Self-Contained: Requires little prior knowledge of applied probability, making it suitable for students at various levels.
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Useful References: Each chapter ends with a list of relevant references for further study.
Ideal for:
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Students: Ideal for advanced undergraduates or beginning postgraduates in applied probability or related fields.
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Educators: A suitable textbook for a one-year applied probability course, covering key topics in an accessible manner.
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Professionals: Useful for those in fields requiring knowledge of stochastic processes, optimization models, and decision-making methods.
Conclusion:
"Introduction to Applied Probability" by Sheldon M. Ross is a well-organized and accessible textbook that serves as an excellent introduction to applied probability and stochastic processes. By focusing on practical models like Poisson processes, Markov chains, and inventory theory, the book provides students with the tools to approach real-world problems in optimization and decision-making. With its clear explanations, practical problems, and relevant references, this book is a great resource for anyone seeking a solid foundation in applied probability.