turning points in the history of mathematics compact textbooks in mathematics

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Turning Points In The History Of Mathematics

Author : Hardy Grant
ISBN : 9781493932641
Genre : Mathematics
File Size : 43. 74 MB
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This book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation. Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the “wedding,” via analytic geometry, of algebra and geometry; the “taming” of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor’s creation of transfinite set theory. The origin of each turning point is discussed, along with the mathematicians involved and some of the mathematics that resulted. Problems and projects are included in each chapter to extend and increase understanding of the material. Substantial reference lists are also provided. Turning Points in the History of Mathematics will be a valuable resource for teachers of, and students in, courses in mathematics or its history. The book should also be of interest to anyone with a background in mathematics who wishes to learn more about the important moments in its development.

Bernhard Riemann 1826 1866

Author : Detlef Laugwitz
ISBN : 9780817647773
Genre : Mathematics
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The name of Bernard Riemann is well known to mathematicians and physicists around the world. His name is indelibly stamped on the literature of mathematics and physics. This remarkable work, rich in insight and scholarship, is addressed to mathematicians, physicists, and philosophers interested in mathematics. It seeks to draw those readers closer to the underlying ideas of Riemann’s work and to the development of them in their historical context. This illuminating English-language version of the original German edition will be an important contribution to the literature of the history of mathematics.

The History Of Mathematics

Author : Roger L. Cooke
ISBN : 9781118030240
Genre : Mathematics
File Size : 74. 63 MB
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This new edition brings the fascinating and intriguing historyof mathematics to life The Second Edition of this internationally acclaimed text hasbeen thoroughly revised, updated, and reorganized to give readers afresh perspective on the evolution of mathematics. Written by oneof the world's leading experts on the history of mathematics, thebook details the key historical developments in the field,providing an understanding and appreciation of how mathematicsinfluences today's science, art, music, literature, andsociety. In the first edition, each chapter was devoted to a singleculture. This Second Edition is organized by subject matter: ageneral survey of mathematics in many cultures, arithmetic,geometry, algebra, analysis, and mathematical inference. This neworganization enables students to focus on one complete topic and,at the same time, compare how different cultures approached eachtopic. Many new photographs and diagrams have been added to thisedition to enhance the presentation. The text is divided into seven parts: The World of Mathematics and the Mathematics of the World,including the origin and prehistory of mathematics, culturalsurveys, and women mathematicians Numbers, including counting, calculation, ancient numbertheory, and numbers and number theory in modern mathematics Color Plates, illustrating the impact of mathematics oncivilizations from Egypt to Japan to Mexico to modern Europe Space, including measurement, Euclidean geometry,post-Euclidean geometry, and modern geometrics Algebra, including problems leading to algebra, equations andmethods, and modern algebra Analysis, including the calculus, real, and complexanalysis Mathematical Inference, including probability and statistics,and logic and set theory As readers progress through the text, they learn about theevolution of each topic, how different cultures devised their ownsolutions, and how these solutions enabled the cultures to developand progress. In addition, readers will meet some of the greatestmathematicians of the ages, who helped lay the groundwork fortoday's science and technology. The book's lively approach makes it appropriate for anyoneinterested in learning how the field of mathematics came to be whatit is today. It can also serve as a textbook for undergraduate orgraduate-level courses. An Instructor's Manual presenting detailedsolutions to all the problems in the book is available upon requestfrom the Wiley editorial department.

Consumption And The World Of Goods

Author : John Brewer
ISBN : 9781136157608
Genre : History
File Size : 83. 92 MB
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The study of past society in terms of what it consumes rather than what it produces is - relatively speaking - a new development. The focus on consumption changes the whole emphasis and structure of historical enquiry. While human beings usually work within a single trade or industry as producers, as, say, farmers or industrial workers, as consumers they are active in many different markets or networks. And while history written from a production viewpoint has, by chance or design, largely been centred on the work of men, consumption history helps to restore women o the mainstream. The history of consumption demands a wide range of skills. It calls upon the methods and techniques of many other disciplines, including archaeology, sociology, social and economic history, anthropology and art criticism. But it is not simply a melting-pot of techniques and skills, brought to bear on a past epoch. Its objectives amount to a new description of a past culture in its totality, as perceived through its patterns of consumption in goods and services. Consumption and the World of Goods is the first of three volumes to examine history from this perspective, and is a unique collaboration between twenty-six leading subject specialists from Europe and North America. The outcome is a new interpretation of the seventeenth and eighteenth centuries, one that shapes a new historical landscape based on the consumption of goods and services.

History Of Topology

Author : I.M. James
ISBN : 0080534074
Genre : Mathematics
File Size : 39. 61 MB
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Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards. As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

Featured Reviews In Mathematical Reviews 1997 1999

Author : Donald G. Babbitt
ISBN : 0821896709
Genre : Mathematics
File Size : 83. 58 MB
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This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.

The History Of Mathematics

Author : David M. Burton
ISBN : 0697111962
Genre : Mathematics
File Size : 42. 27 MB
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This text is designed for the junior/senior mathematics major who intends to teach mathematics in high school or college. It concentrates on the history of those topics typically covered in an undergraduate curriculum or in elementary schools or high schools. At least one year of calculus is a prerequisite for this course. This book contains enough material for a 2 semester course but it is flexible enough to be used in the more common 1 semester course.

For The Learning Of Mathematics

Author :
ISBN : UOM:39015035147688
Genre : Mathematics
File Size : 50. 17 MB
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History Mathematics

Author : Jack A. Goldstone
ISBN : 9785705746705
Genre :
File Size : 49. 97 MB
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Among different important issues, which are discussed in Political Demography the issue of global ageing becomes more and more pressing every year. It is sufficient to take into account the point that within two forthcoming decades a rapid global increase in the number of retirement-age persons will lead to its doubling within this fairly small historical period. The concerns about population ageing apply to both developed and many developing countries and it has turned into a global issue. In forthcoming decades the population ageing is likely to become one of the most important processes determining the future society characteristics and the direction of technological development. The present volume of the Yearbook (which is the fifth in the series) is subtitled ‘Political Demography & Global Ageing’. It brings together a number of interesting articles by scholars from Europe, Asia, and America. They examine global ageing from a variety of perspectives. This issue of the Yearbook consists of two main sections: (I) Aspects of Political Demography; (II) Facing Population Ageing. We hope that this issue will be interesting and useful both for historians and mathematicians, as well as for all those dealing with various social and natural sciences.

Prime Obsession

Author : John Derbyshire
ISBN : 9780309141253
Genre : Science
File Size : 60. 99 MB
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In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark â€" a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false? Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic â€" defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark â€" the Riemann Hypothesis â€" that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows â€" subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age. It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many â€" the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof â€" and those who have been consumed by it.

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