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Dynamic Programming Models Applied to Health, Risk, Employment, and Financial Stability
Individuals and families make key decisions that impact many aspects of financial stability and determine the future of the economy. These decisions involve balancing current sacrifice against future benefits. People have to decide how much to invest in health care, exercise, their diet, and insurance. They must decide how much debt to take on, and how much to save. And they make choices about jobs that determine employment and unemployment levels. Forward-Looking Decision Making is about modeling this individual or family-based decision making using an optimizing dynamic programming model.
Robert Hall first reviews ideas about dynamic programs and introduces new ideas about numerical solutions and the representation of solved models as Markov processes. He surveys recent research on the parameters of preferences--the intertemporal elasticity of substitution, the Frisch elasticity of labor supply, and the Frisch cross-elasticity. He then examines dynamic programming models applied to health spending, long-term care insurance, employment, entrepreneurial risk-taking, and consumer debt.
Linking theory with data and applying them to real-world problems, Forward-Looking Decision Making uses dynamic optimization programming models to shed light on individual behaviors and their economic implications.
Models and Applications
The 1918-19 influenza epidemic killed more than fifty million people worldwide. The SARS epidemic of 2002-3, by comparison, killed fewer than a thousand. The success in containing the spread of SARS was due largely to the rapid global response of public health authorities, which was aided by insights resulting from mathematical models. Models enabled authorities to better understand how the disease spread and to assess the relative effectiveness of different control strategies. In this book, Lisa Sattenspiel and Alun Lloyd provide a comprehensive introduction to mathematical models in epidemiology and show how they can be used to predict and control the geographic spread of major infectious diseases.
Key concepts in infectious disease modeling are explained, readers are guided from simple mathematical models to more complex ones, and the strengths and weaknesses of these models are explored. The book highlights the breadth of techniques available to modelers today, such as population-based and individual-based models, and covers specific applications as well. Sattenspiel and Lloyd examine the powerful mathematical models that health authorities have developed to understand the spatial distribution and geographic spread of influenza, measles, foot-and-mouth disease, and SARS. Analytic methods geographers use to study human infectious diseases and the dynamics of epidemics are also discussed. A must-read for students, researchers, and practitioners, no other book provides such an accessible introduction to this exciting and fast-evolving field.
The Physics of Winter Sports
As anyone from cold climates knows, frequently occurring ice and snow lead to a special appreciation of sports such as skiing, sledding, and skating. Prolific physics popularizer Mark Denny’s take on winter athletics lays out the physical principles that govern glaciated game play. After discussing the physical properties of ice and snow and how physics describes sliding friction and aerodynamic drag, Denny applies these concepts to such sports as bobsledding, snowboarding, and curling. He explains why clap skates would only hinder hockey players, how a curling rock curls, the forces that control luge speed, how steering differs in skiing and snowboarding, and much more. With characteristic accuracy and a touch of wit, Denny provides fans, competitors, and coaches with handy, applicable insight into the games they love. His separate section of technical notes offers an original and mathematically rigorous exploration of the key aspects of winter sports physics. A physics-driven exploration of sports played on ice and snow that is truly fun and informative, Gliding for Gold is the perfect primer for understanding the science behind cold weather athletics.
The Physics of Music
Why does a harpsichord sound different from a piano? For that matter, why does middle C on a piano differ from middle C on a tuning fork, a trombone, or a flute? Good Vibrations explains in clear, friendly language the out-of-sight physics responsible not only for these differences but also for the whole range of noises we call music. The physical properties and history of sound are fascinating to study. Barry Parker's tour of the physics of music details the science of how instruments, the acoustics of rooms, electronics, and humans create and alter the varied sounds we hear. Using physics as a base, Parker discusses the history of music, how sounds are made and perceived, and the various effects of acting on sounds. In the process, he demonstrates what acoustics can teach us about quantum theory and explains the relationship between harmonics and the theory of waves. Peppered throughout with anecdotes and examples illustrating key concepts, this invitingly written book provides a firm grounding in the actual and theoretical physics of music.
Every day, biologists in parkas, raincoats, and rubber boots go into the field to capture and mark a variety of animal species. Back in the office, statisticians create analytical models for the field biologists' data. But many times, representatives of the two professions do not fully understand one another's roles. This book bridges this gap by helping biologists understand state-of-the-art statistical methods for analyzing capture-recapture data. In so doing, statisticians will also become more familiar with the design of field studies and with the real-life issues facing biologists.
Reliable outcomes of capture-recapture studies are vital to answering key ecological questions. Is the population increasing or decreasing? Do more or fewer animals have a particular characteristic? In answering these questions, biologists cannot hope to capture and mark entire populations. And frequently, the populations change unpredictably during a study. Thus, increasingly sophisticated models have been employed to convert data into answers to ecological questions. This book, by experts in capture-recapture analysis, introduces the most up-to-date methods for data analysis while explaining the theory behind those methods. Thorough, concise, and portable, it will be immensely useful to biologists, biometricians, and statisticians, students in both fields, and anyone else engaged in the capture-recapture process.
L'univers de l'homme moderne, si pétri de rationalisme, si environné de technologies et d'artéfacts rassurants, est néanmoins imprégné de hasard, davantage que ne l'était celui de ses ancêtres. L'auteur traite des séries de nombres aléatoires, de leurs propriétés, leur test, leur génération, leur application dans l'estimation Monte Carlo, une méthode qui utilise massivement les capacités de calcul de l'ordinateur pour trouver des solutions numériques approximatives à des problèmes complexes.
History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions.
The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective.
The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.
What is the maximum number of pizza slices one can get by making four straight cuts through a circular pizza? How does a computer determine the best set of pixels to represent a straight line on a computer screen? How many people at a minimum does it take to guard an art gallery? Discrete mathematics has the answer to these—and many other—questions of picking, choosing, and shuffling. T. S. Michael's gem of a book brings this vital but tough-to-teach subject to life using examples from real life and popular culture. Each chapter uses one problem—such as slicing a pizza—to detail key concepts about counting numbers and arranging finite sets. Michael takes a different perspective in tackling each of eight problems and explains them in differing degrees of generality, showing in the process how the same mathematical concepts appear in varied guises and contexts. In doing so, he imparts a broader understanding of the ideas underlying discrete mathematics and helps readers appreciate and understand mathematical thinking and discovery. This book explains the basic concepts of discrete mathematics and demonstrates how to apply them in largely nontechnical language. The explanations and formulas can be grasped with a basic understanding of linear equations.
The Story of i [the square root of minus one] (Princeton Library Science Edition)
Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them.
In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times.
Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.
Some images inside the book are unavailable due to digital copyright restrictions.