04424nam a22005775i 4500 978-1-0716-4172-9 DE-He213 20251030114606.0 cr nn 008mamaa 241207s2024 xxu| s |||| 0|eng d 9781071641729 978-1-0716-4172-9 10.1007/978-1-0716-4172-9 doi QA276-280 PBT bicssc MAT029000 bisacsh PBT thema Lange, Kenneth. author. aut http://id.loc.gov/vocabulary/relators/aut 88634 Applied Probability [electronic resource] / by Kenneth Lange. 3rd ed. 2024. New York, NY : Springer US : Imprint: Springer, 2024. XVII, 602 p. 18 illus., 1 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Texts in Statistics, 2197-4136 Basic Notions of Probability Theory -- Calculation of Expectations -- Convexity, Optimization, and Inequalities -- Combinatorics -- Combinatorial Optimization -- Poisson Processes -- Discrete-Time Markov Chains -- Continuous-Time Markov Chains -- Branching Processes -- Martingales -- Diffusion Processes -- Asymptotic Methods -- Numerical Methods -- Poisson Approximation -- Number Theory -- Entropy -- Appendix: Mathematical Review. Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. This third edition includes new topics and many worked exercises. The new chapter on entropy stresses Shannon entropy and its mathematical applications. New sections in existing chapters explain the Chinese restaurant problem, the infinite alleles model, saddlepoint approximations, and recurrence relations. The extensive list of new problems pursues topics such as random graph theory omitted in the previous editions. Computational probability receives even greater emphasis than earlier. Some of the solved problems are coding exercises, and Julia code is provided. Mathematical scientists from a variety of backgrounds will find Applied Probability appealing as a reference. This updated edition can serve as a textbook for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. Readers should have a working knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Statistics. 65982 Probabilities. 65724 Computer science Mathematics. 64041 Mathematical statistics. 67233 Mathematics Data processing. 65715 Statistical Theory and Methods. Probability Theory. 67428 Probability and Statistics in Computer Science. 67234 Computational Mathematics and Numerical Analysis. 66073 SpringerLink (Online service) Springer Nature eBook Printed edition: 9781071641712 Printed edition: 9781071641736 Printed edition: 9781071641743 Springer Texts in Statistics, 2197-4136 72551 https://doi.org/10.1007/978-1-0716-4172-9 ZDB-2-SMA ZDB-2-SXMS 65539 65539