This textbook on applied probability is intended for graduate students inapplied mathematics biostatistics computational biology computer sciencephysics and sta... » 

This textbook on applied probability is intended for graduate students inapplied mathematics biostatistics computational biology computer sciencephysics and statistics. It presupposes knowledge of multivariate calculuslinear algebra ordinary differential equations and elementary probabilitytheory. Given these prerequisites Applied Probability presents a unique blendof theory and applications with special emphasis on mathematical modelingcomputational techniques and examples from the biological sciences. Chapter 1reviews elementary probability and provides a brief survey of relevant resultsfrom measure theory. Chapter 2 is an extended essay on calculatingexpectations. Chapter 3 deals with probabilistic applications of convexityinequalities and optimization theory. Chapters 4 and 5 touch on combinatoricsand combinatorial optimization. Chapters 6 through 11 present core material onstochastic processes. If supplemented with appropriate sections from Chapters 1and 2 there is sufficient material here for a traditional semesterlong coursein stochastic processes covering the basics of Poisson processes Markovchains branching processes martingales and diffusion processes. FinallyChapters 12 and 13 develop the ChenStein method of Poisson approximation andconnections between probability and number theory. Kenneth Lange is Professorof Biomathematics and Human Genetics and Chair of the Department of HumanGenetics at the UCLA School of Medicine. He has held appointments at theUniversity of New Hampshire MIT Harvard and the University of Michigan.While at the University of Michigan he was the Pharmacia Upjohn FoundationProfessor of Biostatistics. TOCBasic Notions of Probability Theory.Calculation of Expectations. Convexity Optimization and Inequalities.Combinatorics. Combinatorial Optimization. Poisson Processes. DiscreteTimeMarkov Chains. ContinuousTime Markov Chains. Branching Processes.Martingales. Diffusion Processes. Poisson Approximation. Number Theory. «