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Vol. 118 (1996) through current issue
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.
Ask a traditional mathematician the likely outcome of a coin-toss, and he will reply that no evidence exists on which to base such a prediction. Ask a Bayesian, and he will examine the coin, conclude that it was probably not tampered with, and predict five hundred heads in a thousand tosses; a subsequent experiment would then be used to refine this prediction. The Bayesian approach, in other words, permits the use of prior knowledge when testing a hypothesis. Long the province of mathematicians and statisticians, Bayesian methods are applied in this ground-breaking book to problems in cutting-edge physics. Joerg Lemm offers practical examples of Bayesian analysis for the physicist working in such areas as neural networks, artificial intelligence, and inverse problems in quantum theory. The book also includes nonparametric density estimation problems, including, as special cases, nonparametric regression and pattern recognition. Thought-provoking and sure to be controversial, Bayesian Field Theory will be of interest to physicists as well as to other specialists in the rapidly growing number of fields that make use of Bayesian methods.
Méthode et complexité
Les problèmes qui ont motivé la théorie et la pratique de la bioéthique dans les années 1960 et 1970 ont changé de nature. Les enjeux en bioéthique relèvent désormais de macro problèmes complexes, interreliés, qui touchent à la fois des populations entières et de nombreuses institutions sociales. L'auteure nous invite à une exploration méthodologique en bioéthique permettant de faire ressortir la complexité d'enjeux éthiques tels que l'euthanasie, le clonage et le commerce du gène et nous propose des moyens d'aborder cette complexité. Les écrits d'Edgar Morin sur la méthode et la complexité guident la réflexion.
Borges and Mathematics is a short book of essays that explores the scientific thinking of the Argentine writer Jorge Luis Borges (1899-1986). Around half of the book consists of two “lectures” focused on mathematics. The rest of the book reflects on the relationship between literature, artistic creation, physics, and mathematics more generally. Written in a way that will be accessible even to those “who can only count to ten,” the book presents a bravura demonstration of the intricate links between the worlds of sciences and arts, and it is a thought-provoking call to dialog for readers from both traditions. The author, Guillermo Martínez, is both a recognized writer, whose murder mystery The Oxford Murders has been translated into thirty-five languages, and a PhD in mathematics. Contents: Borges and Mathematics: First Lecture; Borges and Mathematics: Second Lecture; The Golem and Artificial Intelligence; The Short Story as Logical System; A Margin Too Narrow; Euclid, or the Aesthetics of Mathematical Reasoning; Solutions and Disillusions; The Pythagorean Twins; The Music of Chance (Interview with Gregory Chaikin); Literature and Rationality; Who’s Afraid of the Big Bad One?; A Small, Small God; God’s Sinkhole. This book was originally published in Spanish as Borges y la matemática (2003). It has been translated with generous support from the Latino Cultural Center at Purdue University. Key points: • Presents complex mathematical and literary concepts in a way that is accessible to non-specialists. • Promotes dialog between readers from both humanist and scientific traditions. • Expands understanding of the Argentine writer, Jorge Luis Borges, including presenting some never-before-translated work.
Challenging Physics Puzzlers
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.
Mathematics, Astronomy, and the Early History of Eclipse Reckoning
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.
Math and Myths
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.