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"Mathematics-History"
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Count us in : how to make maths real for all of us
\"Mathematics, like language, is a universal experience. Every society counts and is empowered by its ability to count and to measure. The mathematical processes developed within various cultures differ widely, and Count Us In explores these cultural links, drawing examples from the author's personal experiences. The process of counting, like the process of communicating with words, is common to all societies worldwide but, just as there is a rich variety of languages, so too is there a rich variety in methods of counting and of recording numbers methods that have developed over centuries to meet the needs of various groups of people. The narrative of this book takes the form of a collection of short stories based on the author's personal experience, linked together by a number of sub-themes\" --page 4 of cover.
Book
Lecturas de historia de las matemáticas
En este libro se describe un panorama general del desarrollo histórico de las matemáticas en un periodo relativamente largo: desde la Antigüedad griega hasta inicios del siglo XXI. Las temáticas del texto giran en torno a la búsqueda de un corpus teórico mediante el cual especificar, de manera cuantitativa, las actividades de medir, contar, ordenar y estructurar. Se parte de la hipótesis de que todos los desarrollos matemáticos, por abstractos que parezcan, hunden sus raíces en los problemas de cuantificación que plantearon los antiguos griegos. Esto parece contraponerse con el carácter formal, simbólico y, sobre todo, variado que fueron adquiriendo las matemáticas a partir del siglo XIX, dada la enorme cantidad de disciplinas matemáticas que han proliferado en todas las latitudes. Esta eclosión de ramificaciones ha hecho que la actividad matemática haya evolucionado paulatinamente tanto en su metodología como en sus formas de representación, dando lugar a mundos complejos que parecen clausurar los vínculos con la intuición y el mundo empírico. Si bien existe una gran diferencia entre el carácter de las matemáticas antiguas, sustentadas por la aritmética y la geometría, las matemáticas modernas, fundadas por la geometría analítica, el álgebra y el análisis, y las matemáticas contemporáneas, establecidas en el álgebra universal, la teoría de conjuntos y la teoría de categorías, un análisis histórico de la evolución de las matemáticas permite identificar la existencia de vasos comunicantes con las actividades de medir, contar, ordenar y estructurar. Se han abordado algunos aspectos específicos del desarrollo histórico de las matemáticas. No puede ser de otra manera, dada la copiosa producción de nociones y procedimientos matemáticos que se han asentado durante más de 2500 años en todas las latitudes.
eBook
The secret lives of numbers
From building rockets to the handheld technology that governs our day-to-day lives, we are all in debt to the mathematical geniuses of the past. But the history of mathematics is warped; it looks like a sixteenth-century map that enlarges Europe at the expense of Africa, Asia and the Americas. This book introduces readers to a new group of mathematical boundary-smashers, those who have been erased by history because of their race, gender or nationality. Kitagawa and Revell bring to vivid life the stories and struggles of mathematicians from every continent: from the brilliant Arabic scholars of the ninth century 'House of Wisdom'; to the pioneering African-American mathematicians of the twentieth century; the first female mathematics professor (from Russia); and the 'lady computers' around the world who revolutionised our knowledge of the night sky.
Book
Newton's Dream
This lively collection of lectures presented at the symposium by prominent scholars was collected and edited by Marcia Stayer with the assistance of Boris Castel. The chapters outline the influence of the \"Principia\" on the work of Newton's contemporaries - such as Adam Smith - and on many areas of present-day science: particle physics, optics, astronomy, and non-mechanical fields such as computer theory. Contributors include A.P. French, Werner Israel, W.H. Newton-Smith, David Raphael, Stephen Smale, Steven Weinberg, Richard S. Westfall, and Denys Wilkinson. This book will be of interest to both general readers and students of science.
eBook
When Computers Were Human
Before Palm Pilots and iPods, PCs and laptops, the term \"computer\" referred to the people who did scientific calculations by hand. These workers were neither calculating geniuses nor idiot savants but knowledgeable people who, in other circumstances, might have become scientists in their own right. When Computers Were Human represents the first in-depth account of this little-known, 200-year epoch in the history of science and technology. Beginning with the story of his own grandmother, who was trained as a human computer, David Alan Grier provides a poignant introduction to the wider world of women and men who did the hard computational labor of science. His grandmother's casual remark, \"I wish I'd used my calculus,\" hinted at a career deferred and an education forgotten, a secret life unappreciated; like many highly educated women of her generation, she studied to become a human computer because nothing else would offer her a place in the scientific world. The book begins with the return of Halley's comet in 1758 and the effort of three French astronomers to compute its orbit. It ends four cycles later, with a UNIVAC electronic computer projecting the 1986 orbit. In between, Grier tells us about the surveyors of the French Revolution, describes the calculating machines of Charles Babbage, and guides the reader through the Great Depression to marvel at the giant computing room of the Works Progress Administration. When Computers Were Human is the sad but lyrical story of workers who gladly did the hard labor of research calculation in the hope that they might be part of the scientific community. In the end, they were rewarded by a new electronic machine that took the place and the name of those who were, once, the computers.
eBook
Reverse mathematics : proofs from the inside out
\"This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the \"right axioms\" to prove fundamental theorems--and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the \"right axiom\" to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics. \"-- Provided by publisher.
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The Theory That Would Not Die
Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok.
In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years-at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing's role in breaking Germany's Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security.
Drawing on primary source material and interviews with statisticians and other scientists,The Theory That Would Not Dieis the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.
eBook
Sourcebook in the mathematics of medieval Europe and North Africa /
Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments providing results on the conchoid--a curve previously unknown in medieval Europe; Levi ben Gershon's use of mathematical induction in combinatorial proofs; Al-Muʹtaman Ibn Hūd's extensive survey of mathematics, which included proofs of Heron's Theorem and Ceva's Theorem; and Muhyī al-Dīn al-Maghribī's interesting proof of Euclid's parallel postulate. This book includes a general introduction, section introductions, footnotes, and references. The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics. -- Inside jacket flap.
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Plato's ghost
Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions.
eBook