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Constitutional Calculus

The Math of Justice and the Myth of Common Sense

Jeff Suzuki

How should we count the population of the United States? What would happen if we replaced the electoral college with a direct popular vote? What are the consequences of allowing unlimited partisan gerrymandering of congressional districts? Can six-person juries yield verdicts consistent with the needs of justice? Is it racist to stop and frisk minorities at a higher rate than non-minorities? These and other questions have long been the subject of legal and political debate and are routinely decided by lawyers, politicians, judges, and voters, mostly through an appeal to common sense and tradition. But mathematician Jeff Suzuki asserts that common sense is not so common, and traditions developed long ago in what was a mostly rural, mostly agricultural, mostly isolated nation of three million might not apply to a mostly urban, mostly industrial, mostly global nation of three hundred million. In Constitutional Calculus, Suzuki guides us through the U.S. Constitution and American history to show how mathematics reveals our flaws, finds the answers we need, and moves us closer to our ideals. From the first presidential veto to the debate over mandatory drug testing, the National Security Agency's surveillance program, and the fate of death row inmates, Suzuki draws us into real-world debates and then reveals how math offers a superior compass for decision-making. Relying on iconic cases, including the convictions of the Scottsboro boys, League of United Latin American Citizens v. Perry, and Floyd v. City of New York, Suzuki shows that more math can lead to better justice, greater fairness, and a more stable democracy. Whether you are fascinated by history, math, social justice, or government, your interest will be piqued and satisfied by the convincing case Suzuki makes.

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A Cooperative Species

Human Reciprocity and Its Evolution

Samuel Bowles

Why do humans, uniquely among animals, cooperate in large numbers to advance projects for the common good? Contrary to the conventional wisdom in biology and economics, this generous and civic-minded behavior is widespread and cannot be explained simply by far-sighted self-interest or a desire to help close genealogical kin.

In A Cooperative Species, Samuel Bowles and Herbert Gintis--pioneers in the new experimental and evolutionary science of human behavior--show that the central issue is not why selfish people act generously, but instead how genetic and cultural evolution has produced a species in which substantial numbers make sacrifices to uphold ethical norms and to help even total strangers.

The authors describe how, for thousands of generations, cooperation with fellow group members has been essential to survival. Groups that created institutions to protect the civic-minded from exploitation by the selfish flourished and prevailed in conflicts with less cooperative groups. Key to this process was the evolution of social emotions such as shame and guilt, and our capacity to internalize social norms so that acting ethically became a personal goal rather than simply a prudent way to avoid punishment.

Using experimental, archaeological, genetic, and ethnographic data to calibrate models of the coevolution of genes and culture as well as prehistoric warfare and other forms of group competition, A Cooperative Species provides a compelling and novel account of how humans came to be moral and cooperative.

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Croissance végétale et morphogénèse

Les fractions continues - Le treillis cylindrique - Spirales logarithmiques - La diffusion - Théories et modèles mathématiques - Épilogue : l'état de la question.

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The Cult of Pythagoras

Math and Myths

Alberto A. Martinez

Martínez discusses various popular myths from the history of mathematics. Some stories are partly true, others are entirely false, but all show the power of invention in history. Martínez inspects a wealth of primary sources, in several languages, over a span of many centuries. By exploring disagreements and ambiguities in the history of the elements of mathematics, The Cult of Pythagoras dispels myths that obscure the actual origins of mathematical concepts.

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The Cult of Statistical Significance

How the Standard Error Costs Us Jobs, Justice, and Lives

Stephen T. Ziliak and Deirdre N. McCloskey

“McCloskey and Ziliak have been pushing this very elementary, very correct, very important argument through several articles over several years and for reasons I cannot fathom it is still resisted. If it takes a book to get it across, I hope this book will do it. It ought to.” —Thomas Schelling, Distinguished University Professor, School of Public Policy, University of Maryland, and 2005 Nobel Prize Laureate in Economics “With humor, insight, piercing logic and a nod to history, Ziliak and McCloskey show how economists—and other scientists—suffer from a mass delusion about statistical analysis. The quest for statistical significance that pervades science today is a deeply flawed substitute for thoughtful analysis. . . . Yet few participants in the scientific bureaucracy have been willing to admit what Ziliak and McCloskey make clear: the emperor has no clothes.” —Kenneth Rothman, Professor of Epidemiology, Boston University School of Health The Cult of Statistical Significance shows, field by field, how “statistical significance,” a technique that dominates many sciences, has been a huge mistake. The authors find that researchers in a broad spectrum of fields, from agronomy to zoology, employ “testing” that doesn’t test and “estimating” that doesn’t estimate. The facts will startle the outside reader: how could a group of brilliant scientists wander so far from scientific magnitudes? This study will encourage scientists who want to know how to get the statistical sciences back on track and fulfill their quantitative promise. The book shows for the first time how wide the disaster is, and how bad for science, and it traces the problem to its historical, sociological, and philosophical roots. Stephen T. Ziliak is the author or editor of many articles and two books. He currently lives in Chicago, where he is Professor of Economics at Roosevelt University. Deirdre N. McCloskey, Distinguished Professor of Economics, History, English, and Communication at the University of Illinois at Chicago, is the author of twenty books and three hundred scholarly articles. She has held Guggenheim and National Humanities Fellowships. She is best known for How to Be Human* Though an Economist (University of Michigan Press, 2000) and her most recent book, The Bourgeois Virtues: Ethics for an Age of Commerce (2006).

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Does Measurement Measure Up?

How Numbers Reveal and Conceal the Truth

John M. Henshaw

There was once a time when we could not measure sound, color, blood pressure, or even time. We now find ourselves in the throes of a measurement revolution, from the laboratory to the sports arena, from the classroom to the courtroom, from a strand of DNA to the far reaches of outer space. Measurement controls our lives at work, at school, at home, and even at play. But does all this measurement really measure up? Here, John Henshaw examines the ways in which measurement makes sense or creates nonsense. Henshaw tells the controversial story of intelligence measurement from Plato to Binet to the early days of the SAT to today's super-quantified world of No Child Left Behind. He clears away the fog on issues of measurement in the environment, such as global warming, hurricanes, and tsunamis, and in the world of computers, from digital photos to MRI to the ballot systems used in Florida during the 2000 presidential election. From cycling and car racing to baseball, tennis, and track-and-field, he chronicles the ever-growing role of measurement in sports, raising important questions about performance and the folly of comparing today's athletes to yesterday's records. We can't quite measure everything, at least not yet. What could be more difficult to quantify than reasonable doubt? However, even our justice system is yielding to the measurement revolution with new forensic technologies such as DNA fingerprinting. As we evolve from unquantified ignorance to an imperfect but everpresent state of measured awareness, Henshaw gives us a critical perspective from which we can "measure up" the measurements that have come to affect our lives so greatly.

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Elementary Set Theory, Part I

K.T. Leung ,Doris Lai-chue Chen

This book provides students of mathematics with the minimum amount of knowledge in logic and set theory needed for a profitable continuation of their studies. There is a chapter on statement calculus, followed by eight chapters on set theory.

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Elementary Set Theory, Part I/II

K.T. Leung ,Doris Lai-chue Chen

This book provides students of mathematics with the minimum amount of knowledge in logic and set theory needed for a profitable continuation of their studies. There is a chapter on statement calculus, followed by eight chapters on set theory.

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Equations from God

Pure Mathematics and Victorian Faith

Daniel J. Cohen

Throughout history, application rather than abstraction has been the prominent driving force in mathematics. From the compass and sextant to partial differential equations, mathematical advances were spurred by the desire for better navigation tools, weaponry, and construction methods. But the religious upheaval in Victorian England and the fledgling United States opened the way for the rediscovery of pure mathematics, a tradition rooted in Ancient Greece. In Equations from God, Daniel J. Cohen captures the origins of the rebirth of abstract mathematics in the intellectual quest to rise above common existence and touch the mind of the deity. Using an array of published and private sources, Cohen shows how philosophers and mathematicians seized upon the beautiful simplicity inherent in mathematical laws to reconnect with the divine and traces the route by which the divinely inspired mathematics of the Victorian era begot later secular philosophies.

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The Essential John Nash

John Nash

When John Nash won the Nobel prize in economics in 1994, many people were surprised to learn that he was alive and well. Since then, Sylvia Nasar's celebrated biography A Beautiful Mind, the basis of a new major motion picture, has revealed the man. The Essential John Nash reveals his work--in his own words. This book presents, for the first time, the full range of Nash's diverse contributions not only to game theory, for which he received the Nobel, but to pure mathematics--from Riemannian geometry and partial differential equations--in which he commands even greater acclaim among academics. Included are nine of Nash's most influential papers, most of them written over the decade beginning in 1949.

From 1959 until his astonishing remission three decades later, the man behind the concepts "Nash equilibrium" and "Nash bargaining"--concepts that today pervade not only economics but nuclear strategy and contract talks in major league sports--had lived in the shadow of a condition diagnosed as paranoid schizophrenia. In the introduction to this book, Nasar recounts how Nash had, by the age of thirty, gone from being a wunderkind at Princeton and a rising mathematical star at MIT to the depths of mental illness.

In his preface, Harold Kuhn offers personal insights on his longtime friend and colleague; and in introductions to several of Nash's papers, he provides scholarly context. In an afterword, Nash describes his current work, and he discusses an error in one of his papers. A photo essay chronicles Nash's career from his student days in Princeton to the present. Also included are Nash's Nobel citation and autobiography.

The Essential John Nash makes it plain why one of Nash's colleagues termed his style of intellectual inquiry as "like lightning striking." All those inspired by Nash's dazzling ideas will welcome this unprecedented opportunity to trace these ideas back to the exceptional mind they came from.

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