Introduction to Probability
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The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics.
The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.
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Dimitri P. Bertsekas undergraduate studies were in engineering at the National Technical University of Athens, Greece. He obtained his MS in electrical engineering at the George Washington University, Wash. DC in 1969, and his Ph.D. in system science in 1971 at the Massachusetts Institute of Technology.
Dr. Bertsekas has held faculty positions with the Engineering-Economic Systems Dept., Stanford University (1971-1974) and the Electrical Engineering Dept. of the University of Illinois, Urbana (1974-1979). From 1979 to 2019 he was with the Electrical Engineering and Computer Science Department of the Massachusetts Institute of Technology (M.I.T.), where he served as McAfee Professor of Engineering. In 2019, he was appointed Fulton Professor of Computational Decision Making, and a full time faculty member at the department of Computer, Information, and Decision Systems Engineering at Arizona State University (ASU), Tempe, while maintaining a research position at MIT. His research spans several fields, including optimization, control, large-scale computation, and data communication networks, and is closely tied to his teaching and book authoring activities. He has written numerous research papers, and eighteen books and research monographs, several of which are used as textbooks in MIT and ASU classes. Most recently Dr Bertsekas has been focusing on reinforcement learning, and authored a textbook in 2019, and a research monograph on its distributed and multiagent implementation aspects in 2020.
Professor Bertsekas was awarded the INFORMS 1997 Prize for Research Excellence in the Interface Between Operations Research and Computer Science for his book "Neuro-Dynamic Programming", the 2000 Greek National Award for Operations Research, the 2001 ACC John R. Ragazzini Education Award, the 2009 INFORMS Expository Writing Award, the 2014 ACC Richard E. Bellman Control Heritage Award for "contributions to the foundations of deterministic and stochastic optimization-based methods in systems and control," the 2014 Khachiyan Prize for Life-Time Accomplishments in Optimization, the SIAM/MOS 2015 George B. Dantzig Prize, and the 2022 IEEE Control Systems Award. In 2018, he was awarded, jointly with his coauthor John Tsitsiklis, the INFORMS John von Neumann Theory Prize for the contributions of the research monographs "Parallel and Distributed Computation" and "Neuro-Dynamic Programming". In 2001, he was elected to the United States National Academy of Engineering for "pioneering contributions to fundamental research, practice and education of optimization/control theory, and especially its application to data communication networks."
Dr. Bertsekas' recent books are "Introduction to Probability: 2nd Edition" (2008), "Convex Optimization Theory" (2009), "Dynamic Programming and Optimal Control," Vol. I, (2017), and Vol. II: (2012), "Abstract Dynamic Programming" (2018), "Convex OptimizationAlgorithms" (2015), "Reinforcement Learning and Optimal Control" (2019), and "Rollout, Policy Iteration, and Distributed Reinforcement Learning" (2020), all published by Athena Scientific.
John Tsitsiklis received the B.S. degree in Mathematics (1980), and the B.S. (1980), M.S. (1981), and Ph.D. (1984) degrees in Electrical Engineering, all from the Massachusetts Institute of Technology, Cambridge, Massachusetts, U.S.A.
Since 1984, he has been with the department of Electrical Engineering and Computer Science (EECS) at the Massachusetts Institute of Technology (MIT), where he is currently a Clarence J Lebel Professor of Electrical Engineering. At MIT, he has served as the director of the Laboratory for Information and Decision Systems (LIDS) and also as a co-director of the Operations Research Center (ORC).
His research interests are in the fields of systems, optimization, control, and operations research. He is a coauthor of Parallel and Distributed Computation: Numerical Methods (D. Bertsekas), Neuro-Dynamic Programming (with D. Bertsekas), Introduction to Linear Optimization (with D. Bertsimas), and Introduction to Probability (with D. Bertsekas). He is also a coinventor in seven awarded U.S. patents.
He is a member of the National Academy of Engineering "for contributions to the theory and application of optimization in dynamic and distributed systems." He is a Fellow of the IEEE (1999) and of INFORMS (2007). His distinctions include the ACM Sigmetrics Achievement Award (2016), the INFORMS John von Neumann Theory Prize (2018), and the IEEE Control Systems Award (2018). He holds honorary doctorates from the Université catholique de Louvain, (2008), the Athens University of Economics and Business (2018), and the Harokopio University (2019).
