Stochastic Tools in Mathematics and Science (Texts in Applied Mathematics), by Alexandre J Chorin, Ole H Hald
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Stochastic Tools in Mathematics and Science (Texts in Applied Mathematics), by Alexandre J Chorin, Ole H Hald
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"Stochastic Tools in Mathematics and Science" covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. The topics covered include conditional expectations, stochastic processes, Brownian motion and its relation to partial differential equations, Langevin equations, the Liouville and Fokker-Planck equations, as well as Markov chain Monte Carlo algorithms, renormalization, basic statistical mechanics, and generalized Langevin equations and the Mori-Zwanzig formalism. The applications include sampling algorithms, data assimilation, prediction from partial data, spectral analysis, and turbulence. The book is based on lecture notes from a class that has attracted graduate and advanced undergraduate students from mathematics and from many other science departments at the University of California, Berkeley. Each chapter is followed by exercises. The book will be useful for scientists and engineers working in a wide range of fields and applications. For this new edition the material has been thoroughly reorganized and updated, and new sections on scaling, sampling, filtering and data assimilation, based on recent research, have been added. There are additional figures and exercises. Review of earlier edition: "This is an excellent concise textbook which can be used for self-study by graduate and advanced undergraduate students and as a recommended textbook for an introductory course on probabilistic tools in science." Mathematical Reviews, 2006
Stochastic Tools in Mathematics and Science (Texts in Applied Mathematics), by Alexandre J Chorin, Ole H Hald- Amazon Sales Rank: #9055480 in Books
- Published on: 2015-06-24
- Released on: 2015-06-24
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .51" w x 6.10" l, .68 pounds
- Binding: Paperback
- 200 pages
From the Back Cover
"Stochastic Tools in Mathematics and Science" covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. The topics covered include conditional expectations, stochastic processes, Brownian motion and its relation to partial differential equations, Langevin equations, the Liouville and Fokker-Planck equations, as well as Markov chain Monte Carlo algorithms, renormalization, basic statistical mechanics, and generalized Langevin equations and the Mori-Zwanzig formalism. The applications include sampling algorithms, data assimilation, prediction from partial data, spectral analysis, and turbulence.
The book is based on lecture notes from a class that has attracted graduate and advanced undergraduate students from mathematics and from many other science departments at the University of California, Berkeley. Each chapter is followed by exercises. The book will be useful for scientists and engineers working in a wide range of fields and applications.
For this new edition the material has been thoroughly reorganized and updated, and new sections on scaling, sampling, filtering and data assimilation, based on recent research, have been added. There are additional figures and exercises.
Review of earlier edition:
"This is an excellent concise textbook which can be used for self-study by graduate and advanced undergraduate students and as a recommended textbook for an introductory course on probabilistic tools in science."
Mathematical Reviews, 2006
About the Author Alexandre J. Chorin is a professor of mathematics at the University of California, Berkeley who works in applied mathematics. He is known for his contributions to the field of Computational fluid dynamics. Ole Hald is a professor of mathematics at the University of California, Berkeley.
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Most helpful customer reviews
5 of 5 people found the following review helpful. A great "user's guide" to stochastic calculus and its important applications By SeferTech This is an excellent user's guide to stochastic calculus and its important applications. I say excellent because it is well-written (clear and easy to read with a focus on the essentials as previous review said). I say "user's guide" because the author's get down to the nut's and bolt's of stochastic processes (concepts and related equations). I say "important applications" because they again focus on key "tools" such as Fokker-Planck equation and related stochastic differential equation, statistical mechanics, MCMC, turbulence, etc. - so there is something for everyone here e.g. physicists, financial "engineers", ME's and Aero's simulating turbulence (especially via PDF methods), etc. A few criticisms would be lack of "pixels" - they say a picture tell's a thousand words for a reason, hard to locate a term or definition or concept from index,...Overall, a very nicely priced/sized read and a must have reference for anyone working with stochastic processes seeking insight.
4 of 4 people found the following review helpful. The Essentials By Nicholas Hoell This book was written to fill in the gaps between what people learn in standard "pure" math trainings and what people use "in the field". The professors who wrote it come from a University where one can study math and never see topics from statistical sciences. They have attempted a very readable and clear exposition of some of the fundamentals behind the useful stochastic analysis in physics and economics. They use some formalism but largely skip long, difficult proofs, focusing instead on important examples. What I mean is they use the language of formal probability theory (measure theory), but keep the applications very concrete (differential equations, stochastic walks, etc). It cuts to the chase and is an exciting read for those like myself who get very turned off by overly formal probability theory, yet who are curious about some of the formalism. Short, paperback, good references, lively read.
3 of 3 people found the following review helpful. Fails half way between the math and the application By Litsios James I am sad to give this book only three stars as I am a fan of one of its authors, Prof. Chorin, and have read many of his articles on numerical methods in fluid dynamics. But... after having owned this book for some time now have having given it "my bedside attention"! I must conclude that this book fails what it tries to achieve. It tries to introduce mathematical stochastic tools without the rigor to a "broader" applied mathematician audience. But the feeling I get is the "mathematician" part of the authors cannot let go and the book still has too much rigor, and the scope of presentation still remains too constrained, not opening up the subject enough for its application. And so my three start only rating!
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