The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.

Does a glass of ice water filled to the brim overflow when the ice melts? Does the energy inside a sauna increase when you heat it up? What's the best way to cool your coffee—adding the creamer first or last? These and other challenging puzzlers provide a fresh—and fun—approach to learning real physics. Presenting both classic and new problems, Brainteaser Physics challenges readers to use imagination and basic physics principles to find the answers. Göran Grimvall provides detailed and accessible explanations of the solutions, sometimes correcting the standard explanations, sometimes putting a new twist on them. He provides diagrams and equations where appropriate and ends each problem by discussing a specific concept or offering an extra challenge. With Brainteaser Physics, students and veteran physicists alike can sharpen their critical and creative thinking—and have fun at the same time.

Lunar and solar eclipses have always fascinated human beings. Digging deep into history, Clemency Montelle examines the ways in which theoretical understanding of eclipses originated and how ancient and medieval cultures shared, developed, and preserved their knowledge of these awe-inspiring events. Eclipses were the celestial phenomena most challenging to understand in the ancient world. Montelle draws on original research—much of it derived from reading primary source material written in Akkadian and Sanskrit, as well as ancient Greek, Latin, and Arabic—to explore how observers in Babylon, the Islamic Near East, Greece, and India developed new astronomical and mathematical techniques to predict and describe the features of eclipses. She identifies the profound scientific discoveries of these four cultures and discusses how the societies exchanged information about eclipses. In constructing this history, Montelle establishes a clear pattern of the transmission of scientific ideas from one culture to another in the ancient and medieval world. Chasing Shadows is an invitingly written and highly informative exploration of the early history of astronomy.

A monumental accomplishment in the history of non-Western mathematics, The Chinese Roots of Linear Algebra explains the fundamentally visual way Chinese mathematicians understood and solved mathematical problems. It argues convincingly that what the West "discovered" in the sixteenth and seventeenth centuries had already been known to the Chinese for 1,000 years. Accomplished historian and Chinese-language scholar Roger Hart examines Nine Chapters of Mathematical Arts—the classic ancient Chinese mathematics text—and the arcane art of fangcheng, one of the most significant branches of mathematics in Imperial China. Practiced between the first and seventeenth centuries by anonymous and most likely illiterate adepts, fangcheng involves manipulating counting rods on a counting board. It is essentially equivalent to the solution of systems of N equations in N unknowns in modern algebra, and its practice, Hart reveals, was visual and algorithmic. Fangcheng practitioners viewed problems in two dimensions as an array of numbers across counting boards. By "cross multiplying" these, they derived solutions of systems of linear equations that are not found in ancient Greek or early European mathematics. Doing so within a column equates to Gaussian elimination, while the same operation among individual entries produces determinantal-style solutions. Mathematicians and historians of mathematics and science will find in The Chinese Roots of Linear Algebra new ways to conceptualize the intellectual development of linear algebra.

“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).

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.

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.

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.

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.

Revving engines, smoking tires, and high speeds. Car racing enthusiasts and race drivers alike know the thrill of competition, the push to perform better, and the agony—and dangers—of bad decisions. But driving faster and better involves more than just high horsepower and tightly tuned engines. Physicist and amateur racer Chuck Edmondson thoroughly discusses the physics underlying car racing and explains just what’s going on during any race, why, and how a driver can improve control and ultimately win. The world of motorsports is rich with excitement and competition—and physics. Edmondson applies common mathematical theories to real-world racing situations to reveal the secrets behind successful fast driving. He explains such key concepts as how to tune your car and why it matters, how to calculate 0 to 60 mph times and quarter-mile times and why they are important, and where, when, why, and how to use kinematics in road racing. He wraps it up with insight into the impact and benefit of green technologies in racing. In each case, Edmondson’s in-depth explanations and worked equations link the physics principles to qualitative racing advice. From selecting shifting points to load transfer in car control and beyond, Fast Car Physics is the ideal source to consult before buckling up and cinching down the belts on your racing harness.