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Measure theory and measure-theoretic probability are fascinating subjects. Proofs describing profound ways to reason lead to results that are frequently startling, beautiful, and useful. Measure theory and probability also play roles in the development of pure and applied mathematics, statistics, engineering, physics, and finance. Indeed, it is difficult to overstate their importance in the quantitative disciplines. This book traces an eclectic path through the fundamentals of the topic to make the material accessible to a broad range of students. A Ramble through Probability: How I Learned to Stop Worrying and Love Measure Theory brings together the key elements and applications in a unifie...
This text places the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer.
This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.
Porous media are broadly found in nature and their study is of high relevance in our present lives. In geosciences porous media research is fundamental in applications to aquifers, mineral mines, contaminant transport, soil remediation, waste storage, oil recovery and geothermal energy deposits. Despite their importance, there is as yet no complete understanding of the physical processes involved in fluid flow and transport. This fact can be attributed to the complexity of the phenomena which include multicomponent fluids, multiphasic flow and rock-fluid interactions. Since its formulation in 1856, Darcy’s law has been generalized to describe multi-phase compressible fluid flow through ani...
Arnold Schoenberg was a polarizing figure in twentieth century music, and his works and ideas have had considerable and lasting impact on Western musical life. A refugee from Nazi Europe, he spent an important part of his creative life in the United States (1933-1951), where he produced a rich variety of works and distinguished himself as an influential teacher. However, while his European career has received much scholarly attention, surprisingly little has been written about the genesis and context of his works composed in America, his interactions with Americans and other émigrés, and the substantial, complex, and fascinating performance and reception history of his music in this countr...
The proceedings represent the state of knowledge in the area of algorithmic differentiation (AD). The 31 contributed papers presented at the AD2012 conference cover the application of AD to many areas in science and engineering as well as aspects of AD theory and its implementation in tools. For all papers the referees, selected from the program committee and the greater community, as well as the editors have emphasized accessibility of the presented ideas also to non-AD experts. In the AD tools arena new implementations are introduced covering, for example, Java and graphical modeling environments or join the set of existing tools for Fortran. New developments in AD algorithms target the ef...
The 1947 paper by John von Neumann and Herman Goldstine, OC Numerical Inverting of Matrices of High OrderOCO ( Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book is a unique collection of contributions by researchers who have lived through this evolution, testifying about their personal experiences and sketching the evolution of their respective subdomains since the early years. Sample Chapter(s). Chapter 1: Some pioneers of extrapolation methods (323 KB). Contents: Some Pioneers of Extrapolation Methods (C Brezinski); Very Basic Multidimensional Extrapolation Quadratu...
On this leg of the journey youll explore the scariest spots in the Sunshine State. Author David Lapham visits more than 30 legendary haunted places, all of which are open to the public-so you can test your own ghost hunting skills, if you dare. Join David as he visits each site, snooping around eerie rooms and dark corners, talking to people who swear to their paranormal experiences, and giving you a first-hand account. Enjoy Ghost hunting Florida from the safety of your armchair or hit the road, using the maps, ''Haunted Places ''travel guide with 50 more spooky sites and ''Ghostly Resources. ''Buckle up and get ready for the spookiest ride of your life.
This book provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership. It presents an outline of the underlying convergence and stability theory while avoiding technical details. Key ideas are illustrated with numerous computational examples and computer code is listed at the end of each chapter. The authors include 150 exercises, with solutions available online, and 40 programming tasks. Although introductory, the book covers a range of modern research topics, including Itô versus Stratonovich calculus, implicit methods, stability theory, nonconvergence on nonlin...
This tale of political suspense was one of the Seattle Times’s Top Ten Thrillers of the Year: “I couldn’t put it down” (Vince Flynn). Author of House Witness, 2019 Edgar Award Finalist for Best Novel There has been an assassination attempt on the president. He is only wounded—but his best friend and a Secret Service Agent have been killed. As it turns out, the attack wasn’t without warning. Gen. Andrew Banks, Secretary of Homeland Security, received a note that the president was in danger, and even more alarming, that Secret Service agents guarding the president had been compromised. General Banks is reluctant to tell the FBI about the note, partly for self-serving political reas...