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Probability and Statistics: The Science of Uncertainty / Edition 2

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Overview

The History of Mathematics is a six-volume set that examines the development of the science through discovery, innovation, collaboration, and experimentation. Designed to complement mathematics curricula, each volume covers a significant development in recent mathematical history as well as the subject's origins. The books represent a fascinating overview of the contributions that mathematical research has made to the physical world.

Probability and Statistics, Revised Edition details the evolution of these two disciplines and their relevance to the scientific and lay communities. Probability and statistics are two of the youngest branches of mathematics, having been discovered in the 17th and 18th centuries, respectively, yet in modern-day language and thinking, they have become omnipresent. The book discusses how probability and statistics pervade our world, from the nature of randomness to the role of statistics in developing vaccines. It also includes an exclusive interview with Dr. Michael Stamatelatos, director of the safety and assurance requirements division in the Office of Safety and Mission Assurance at NASA, who suggests how the use of probability in risk assessments leads to improved safety and reliability in space exploration.

The volume includes information on

the bell curve

the birth of modern statistics

credit default swaps

data analysis and precision

Edmund Halley

randomness

smallpox and public health

vaccinations and statistics

The book contains 40 color photographs and four-color line illustrations, sidebars, a chronology, a glossary, a detailed list of print and Internet resources, and an index. The History of Mathematics is essential for high school students, teachers, and general readers who wish to understand the contributions of the major branches of mathematics.

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Editorial Reviews

School Library Journal
Gr 10-Up-In uniform but independent volumes, Tabak offers sustained, meaty historical and methodological studies of the major branches of mathematics. Beginning, in some cases, with prehistoric evidence, he traces: developments in our very idea of what algebra is; the nature of ancient, projective (including non-Euclidian), and coordinate geometry; the uses of mathematics in finding precise ways to describe natural laws; the "invention" of rational, irrational and imaginary numbers, and the idea of infinity; and advances in probability theory and statistics. In each volume he analyzes the insights and accomplishments of many thinkers, ancient and modern, providing a generous array of illuminating demonstrations and examples while keeping extraneous biographical details-and, for that matter, illustrations-to a minimum, then closes with a time line, a specialized glossary, and annotated, multimedia reading lists. General readers may prefer to start with such single-volume histories as William Berlinghoff and Fernando Gouvea's Math through the Ages (Oxton House, 2002) or Ivor Grattan-Guinness's Rainbow of Mathematics (Norton, 2000), but for serious students of the subject, and collections supporting strong science programs, these make appropriate additions to both reference and circulating shelves.-John Peters, New York Public Library Copyright 2004 Reed Business Information.
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Product Details

  • ISBN-13: 9780816079414
  • Publisher: Facts on File, Incorporated
  • Publication date: 5/1/2011
  • Series: Facts on File History of Mathematics Series
  • Edition description: Revised
  • Edition number: 2
  • Pages: 272
  • Age range: 14 - 17 Years
  • Product dimensions: 6.10 (w) x 9.10 (h) x 0.80 (d)

Table of Contents

Preface x

Acknowledgments xvi

Introduction xvii

Part One: Probability 1

1 The Idea of Randomness 3

Randomness before the Theory of Probability 5

Early Difficulties in Developing a Theory of Randomness 10

Randomness and Religion Today in Burkina Faso 11

2 The Nature of Chance 14

Cardano's Mistake 16

Cardano on Luck and Math 17

Galileo Galilei 19

Pierre de Fermat and Blaise Pascal 22

The Division of Stakes, an Alternative Interpretation 26

Christiaan Huygens 27

Jacob Bernoulli 28

Abraham de Moivre 34

De Moivre on Math and Luck 36

The Bell Curve 39

3 Surprising Insights into Probability and Its Uses 41

Thomas Bayes and Inverse Probability 42

Buffon and the Needle Problem 46

Daniel Bernoulli and Smallpox 48

Jean le Rond d'Alembert and the Evaluation of Risk 53

Leonhard Euler and Lotteries 56

Smallpox, Probability, and the Public Health Revisited 59

4 Randomness in a Deterministic Universe 62

Simeon-Denis Poisson 69

The Poisson Distribution 71

5 Random Processes 74

James Clerk Maxwell 77

Brownian Motion Revisited 79

Markov Processes 82

A Markov Chain 84

6 Probability as a Mathematical Discipline 86

Theory and Practice 95

Probabilistic Risk Assessment 98

7 Probability and Risk, an Application 102

Credit Default Swaps 104

Information Asymmetries and Cdsss 109

Aig and the Worst Economic Crisis since the Great Depression 112

Part 2 Statistics 119

Introduction 121

The Age of Information 121

8 The Beginnings of Statistics 123

John Graunt 125

Edmund Halley 128

Breslau Mortality Table 131

Insurance 134

9 Data Analysis and the Problem of Precision 138

The Misuse of Statistics 142

10 The Birth of Modern Statistics 145

Karl Pearson 146

R. A. Fisher 152

11 The Theory of Sampling 160

The Problem 161

Walter Shewhart and Statistical Quality Control 164

William Edwards Deming 169

12 Statistics and Vaccinations 175

Vaccination Concepts 181

The Statistics of Vaccine Tests 183

Additional Studies 186

The National Vaccine Injury Compensation Program 190

Vaccines and Autism 193

Conclusion 195

Afterword: An Exclusive Interview with Dr. Michael Stamatelatos on the Quantification of Risk 197

Chronology 208

Glossary 225

Further Resources 229

Index 239

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