The Mathematical Foundations of Mixing the Linked Twist Maps as a Paradigm in Applications

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Mixing processes occur in many technological and natural applications, with length and time scales ranging from the very small to the very large. The diversity of problems can give rise to a diversity of approaches. Are there concepts that are central to all of them? Are there tools that allow for prediction and quantification? The authors show how a variety of flows in very different settings possess the characteristic of streamline crossing. This notion can be placed on firm mathematical footing via Linked Twist Maps (LTMs), which is the central organizing principle of this book. The authors discuss the definition and construction of LTMs, provide examples of specific mixers that can be analyzed in the LTM framework and introduce a number of mathematical techniques which are then brought to bear on the problem of fluid mixing. In a final chapter, they present a number of open problems and new directions. First book explaining new important ideas in our understanding of how fluids mix Authors are well-known book writers and leading researchers Starts with a broad, accessible and thought-provoking chapter, and ends with a collection of open problems

Big Data Science in Finance: Mathematics and Applications (1版)

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【簡介】 Explains the mathematics, theory, and methods of Big Data as applied to finance and investingData science has fundamentally changed Wall Street--applied mathematics and software code are increasingly driving finance and investment-decision tools. Big Data Science in Finance examines the mathematics, theory, and practical use of the revolutionary techniques that are transforming the industry. Designed for mathematically-advanced students and discerning financial practitioners alike, this energizing book presents new, cutting-edge content based on world-class research taught in the leading Financial Mathematics and Engineering programs in the world. Marco Avellaneda, a leader in quantitative finance, and quantitative methodology author Irene Aldridge help readers harness the power of Big Data.Comprehensive in scope, this book offers in-depth instruction on how to separate signal from noise, how to deal with missing data values, and how to utilize Big Data techniques in decision-making. Key topics include data clustering, data storage optimization, Big Data dynamics, Monte Carlo methods and their applications in Big Data analysis, and more. This valuable book: Provides a complete account of Big Data that includes proofs, step-by-step applications, and code samplesExplains the difference between Principal Component Analysis (PCA) and Singular Value Decomposition (SVD)Covers vital topics in the field in a clear, straightforward mannerCompares, contrasts, and discusses Big Data and Small DataIncludes Cornell University-tested educational materials such as lesson plans, end-of-chapter questions, and downloadable lecture slidesBig Data Science in Finance: Mathematics and Applications is an important, up-to-date resource for students in economics, econometrics, finance, applied mathematics, industrial engineering, and business courses, and for investment managers, quantitative traders, risk and portfolio managers, and other financial practitioners.

Mathematics in Architecture, Art, Nature, and Beyond (1版)

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【簡介】 There is little opportunity in classrooms today for teachers to explore the amazing applications of mathematics outside the curriculum. This book is intended to show how mathematics manifests itself in areas that most people are unaware of. One can even revel in the history of how our number system evolved and how that has enabled us to define the beauty in mathematics as well as in art, architecture, nature, and beyond.The first two chapters of this book introduce the Fibonacci numbers and investigate their amazing relationships and applications in our general environment. The following four chapters focus on the Golden Ratio and the Golden Rectangle, exploring how they manifest all around us, often hiding in plain sight: in everything from architectural wonders such as the Taj Mahal to coin design, and from Greek vases to petal formation. We conclude our enjoyable journey through these mathematical wonders by considering conic sections and how they explain many aspects of everyday life, such as radar dishes, headlight reflectors, and whispering halls. This exposure to aspects of mathematics that are usually bypassed in the school curriculum will provide high school students, teachers, and general readers with an opportunity to truly appreciate the power and beauty of mathematics.

Mathematics for Engineers Vol.2 (1版)

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【簡介】 This second volume in our series is intended primarily as a companion text for the second semester mathematics preliminaries for students and lecturers of electrical engineering and other engineering disciplines. In a clear and concise manner, and without too much abstraction, it introduces students to the topics covered in the basic mathematics lectures. Volume 2 also provides students at universities and applied universities with a largely accurate, but always illustrative, presentation as a practical aid to entry into higher mathematics. Mathematical concepts are clearly motivated, systematically equated and visualized in many animations. Mathematical proofs are almost completely avoided. Instead, many applications not only support the application of mathematics, but also contribute to a better understanding of mathematics. 【目錄】