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Quantitative finance is a field that has risen to prominence over the last few decades. It encompasses the complex models and calculations that value financial contracts, particularly those which reference events in the future, and apply probabilities to these events. While adding greatly to the flexibility of the market available to corporations and investors, it has also been blamed for worsening the impact of financial crises. But what exactly does quantitative finance encompass, and where did these ideas and models originate? We show that the mathematics behind finance and behind games of chance have tracked each other closely over the centuries and that many well-known physicists and mathematicians have contributed to the field.
MATHEMATICS / Applied. --- Finance --- Applied mathematics. --- Mathematical models.
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"In highly mathematical courses, it is a truism that students learn by doing, not by reading. Tamara Todorova's Problems Book to Accompany Mathematics for Economists provides a life-line for students seeking an extra leg up in challenging courses. Beginning with college-level mathematics, this comprehensive workbook presents an extensive number of economics-focused problem sets, with clear and detailed solutions for each one. By keeping the focus on economic applications, Todorova provides economics students with the mathematical tools they need for academic success"--
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Basic Sciences. Mathematics -- Applied Mathematics. --- Electromagnetism --- Geophysics --- Mathematics. --- Mathematics.
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This book provides a comprehensive introduction to the techniques, tools and methods for inverse problems and data assimilation, and is written at the interface between mathematics and applications for students, researchers and developers in mathematics, physics, engineering, acoustics, electromagnetics, meteorology, biology, environmental and other applied sciences. Basic analytic questions and tools are introduced, as well as a wide variety of concepts, methods and approaches to formulate and solve inverse problems. OCTAVE /MATLAB codes are included, which serve as a first step towards simulations and more sophisticated inversion or data assimilation algorithms.
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"Invisible in the Storm is the first book to recount the history, personalities, and ideas behind one of the greatest scientific successes of modern times--the use of mathematics in weather prediction. Although humans have tried to forecast weather for millennia, mathematical principles were used in meteorology only after the turn of the twentieth century. From the first proposal for using mathematics to predict weather, to the supercomputers that now process meteorological information gathered from satellites and weather stations, Ian Roulstone and John Norbury narrate the groundbreaking evolution of modern forecasting. The authors begin with Vilhelm Bjerknes, a Norwegian physicist and meteorologist who in 1904 came up with a method now known as numerical weather prediction. Although his proposed calculations could not be implemented without computers, his early attempts, along with those of Lewis Fry Richardson, marked a turning point in atmospheric science. Roulstone and Norbury describe the discovery of chaos theory's butterfly effect, in which tiny variations in initial conditions produce large variations in the long-term behavior of a system--dashing the hopes of perfect predictability for weather patterns. They explore how weather forecasters today formulate their ideas through state-of-the-art mathematics, taking into account limitations to predictability. Millions of variables--known, unknown, and approximate--as well as billions of calculations, are involved in every forecast, producing informative and fascinating modern computer simulations of the Earth system. Accessible and timely, Invisible in the Storm explains the crucial role of mathematics in understanding the ever-changing weather"--
MATHEMATICS / History & Philosophy. --- MATHEMATICS / Calculus. --- MATHEMATICS / Differential Equations. --- NATURE / Weather. --- MATHEMATICS / Applied. --- SCIENCE / Earth Sciences / Meteorology & Climatology. --- Climatology --- Meteorology --- Climate --- Climate science --- Climate sciences --- Science of climate --- Atmospheric science --- Mathematical models. --- Data processing.
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