Turning Points in the History of Mathematics

Author: Hardy Grant,Israel Kleiner
Publisher: Birkhäuser
ISBN: 1493932640
Category: Mathematics
Page: 109
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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

Turning Points in the Conception of Mathematics
Author: Detlef Laugwitz
Publisher: Springer Science & Business Media
ISBN: 0817647775
Category: Mathematics
Page: 357
View: 8726

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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

A Brief Course
Author: Roger L. Cooke
Publisher: John Wiley & Sons
ISBN: 1118460294
Category: Mathematics
Page: 648
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Praise for the Second Edition "An amazing assemblage of worldwide contributions in mathematicsand, in addition to use as a course book, a valuable resource . . .essential." —CHOICE This Third Edition of The History of Mathematicsexamines the elementary arithmetic, geometry, and algebra ofnumerous cultures, tracing their usage from Mesopotamia, Egypt,Greece, India, China, and Japan all the way to Europe during theMedieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the historyof mathematics for science, engineering, and secondary education,the book focuses on three main ideas: the facts of who, what, when,and where major advances in mathematics took place; the type ofmathematics involved at the time; and the integration of thisinformation into a coherent picture of the development ofmathematics. In addition, the book features carefully designedproblems that guide readers to a fuller understanding of therelevant mathematics and its social and historical context.Chapter-end exercises, numerous photographs, and a listing ofrelated websites are also included for readers who wish to pursue aspecialized topic in more depth. Additional features of TheHistory of Mathematics, Third Edition include: Material arranged in a chronological and cultural context Specific parts of the history of mathematics presented asindividual lessons New and revised exercises ranging between technical, factual,and integrative Individual PowerPoint presentations for each chapter and a bankof homework and test questions (in addition to the exercises in thebook) An emphasis on geography, culture, and mathematics In addition to being an ideal coursebook for undergraduatestudents, the book also serves as a fascinating reference formathematically inclined individuals who are interested in learningabout the history of mathematics.

Featured Reviews in Mathematical Reviews 1997-1999

With Selected Reviews of Classic Books and Papers from 1940-1969
Author: Donald G. Babbitt,Jane E. Kister
Publisher: American Mathematical Soc.
ISBN: 9780821896709
Category: Mathematics
Page: 541
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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.

Classics in the History of Greek Mathematics

Author: Jean Christianidis
Publisher: Springer Science & Business Media
ISBN: 9781402000812
Category: Mathematics
Page: 474
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The twentieth century is the period during which the history of Greek mathematics reached its greatest acme. Indeed, it is by no means exaggerated to say that Greek mathematics represents the unique field from the wider domain of the general history of science which was included in the research agenda of so many and so distinguished scholars, from so varied scientific communities (historians of science, historians of philosophy, mathematicians, philologists, philosophers of science, archeologists etc. ), while new scholarship of the highest quality continues to be produced. This volume includes 19 classic papers on the history of Greek mathematics that were published during the entire 20th century and affected significantly the state of the art of this field. It is divided into six self-contained sections, each one with its own editor, who had the responsibility for the selection of the papers that are republished in the section, and who wrote the introduction of the section. It constitutes a kind of a Reader book which is today, one century after the first publications of Tannery, Zeuthen, Heath and the other outstanding figures of the end of the 19th and the beg- ning of 20th century, rather timely in many respects.

Encyclopedia of Mathematics Education

Author: Louise Grinstein,Sally I. Lipsey
Publisher: Routledge
ISBN: 1136787224
Category: Education
Page: 912
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First published in 2001. Routledge is an imprint of Taylor & Francis, an informa company.

Infinitesimal Analysis

Author: E.I. Gordon,A.G. Kusraev,Semën Samsonovich Kutateladze
Publisher: Springer Science & Business Media
ISBN: 9781402007385
Category: Mathematics
Page: 422
View: 6071

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Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics. The book sets forth the basics of the theory, as well as the most recent applications in, for example, functional analysis, optimization, and harmonic analysis. The concentric style of exposition enables this work to serve as an elementary introduction to one of the most promising mathematical technologies, while revealing up-to-date methods of monadology and hyperapproximation. This is a companion volume to the earlier works on nonstandard methods of analysis by A.G. Kusraev and S.S. Kutateladze (1999), ISBN 0-7923-5921-6 and Nonstandard Analysis and Vector Lattices edited by S.S. Kutateladze (2000), ISBN 0-7923-6619-0

History of Topology

Author: I.M. James
Publisher: Elsevier
ISBN: 9780080534077
Category: Mathematics
Page: 1056
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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.

Engineering Optics

Author: Keigo Iizuka
Publisher: Springer Science & Business Media
ISBN: 0387757236
Category: Science
Page: 532
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Engineering Optics is a book for students who want to apply their knowledge of optics to engineering problems, as well as for engineering students who want to acquire the basic principles of optics. It covers such important topics as optical signal processing, holography, tomography, holographic radars, fiber optical communication, electro- and acousto-optic devices, and integrated optics (including optical bistability). Practical examples, such as the video disk, the Fresnel zone plate, and many more, appear throughout the text, together with numerous solved exercises. There is an entirely new section in this updated edition on 3-D imaging.

Prime Obsession

Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
Author: John Derbyshire
Publisher: Joseph Henry Press
ISBN: 0309141257
Category: Science
Page: 446
View: 2551

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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.

Reminiscences of a Statistician

The Company I Kept
Author: Erich L. Lehmann
Publisher: Springer Science & Business Media
ISBN: 9780387715971
Category: Mathematics
Page: 316
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This relatively nontechnical book is the first account of the history of statistics from the Fisher revolution to the computer revolution. It sketches the careers, and highlights some of the work, of 65 people, most of them statisticians. What gives the book its special character is its emphasis on the author's interaction with these people and the inclusion of many personal anecdotes. Combined, these portraits provide an amazing fly-on-the-wall view of statistics during the period in question. The stress is on ideas and technical material is held to a minimum. Thus the book is accessible to anyone with at least an elementary background in statistics.

MOSFET Modeling for Circuit Analysis and Design

Author: Carlos Galup-Montoro,M rcio Cherem Schneider
Publisher: World Scientific
ISBN: 9812568107
Category: Technology & Engineering
Page: 418
View: 9984

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This is the first book dedicated to the next generation of MOSFET models. Addressed to circuit designers with an in-depth treatment that appeals to device specialists, the book presents a fresh view of compact modeling, having completely abandoned the regional modeling approach.Both an overview of the basic physics theory required to build compact MOSFET models and a unified treatment of inversion-charge and surface-potential models are provided. The needs of digital, analog and RF designers as regards the availability of simple equations for circuit designs are taken into account. Compact expressions for hand analysis or for automatic synthesis, valid in all operating regions, are presented throughout the book. All the main expressions for computer simulation used in the new generation compact models are derived.Since designers in advanced technologies are increasingly concerned with fluctuations, the modeling of fluctuations is strongly emphasized. A unified approach for both space (matching) and time (noise) fluctuations is introduced.


The Experimental Life
Author: Christa Jungnickel,Russell McCormmach
Publisher: Bucknell University Press
ISBN: 9780838754450
Category: Biography & Autobiography
Page: 814
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History of Lord Charles Cavendish and his son Henry, who made their mark in eighteenth-century Britain in the fields of politics and science respectively.

Constructing Mathematical Knowledge

Epistemology and Mathematics Education
Author: Paul Ernest
Publisher: Routledge
ISBN: 1135716188
Category: Education
Page: 300
View: 2669

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This book provides a panorama of complimentary and forward looking perspectives on the learning of mathematics and epistemology from some of the leading contributors to the field. It explores constructivist and social theories of learning, and discusses the role of the computer in the light of these theories. It brings analyses from psychoanalysis, Hermeneutics and other perspectives to bear on the issues of mathematics and learning. It enquires into the nature of enquiry itself, and an important emergent theme is the role of language. Finally it relates the history of mathematics to its teaching and learning. The book both surveys current research and indicates orientations for fruitful work in the future.

Opus Mago-cabbalisticum Et Theosophicum

In Which The Origin, Nature, Characteristics, And Use Of Salt , Sulfur and Mercury are Described in Three Parts Together with Much Wonderful Mathematical...
Author: Georg Von Welling
Publisher: Weiser Books
ISBN: 9781578633272
Category: Body, Mind & Spirit
Page: 576
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After nearly 300 years, one of the most important alchemical and magical texts of all time has finally been translated into English! DuQuette In Goethe's immortal play, Faust, the brooding hero reflects upon the vainness of earthly knowledge and education. He opens a book of magic and is transfixed by an illustration of the magical universe. He resolves there and then to become a magician. The book that fired Goethe's imagination for that dramatic scene was a real book - the book of forbidden knowledge that evoked every mystical cliché - Opus Mago-Cabbalisticum et Theosophicum. This first ever English edition of Opus Mago-Cabbalisticum et Theosophicum will appeal to anyone interested in the history or practical aspects of alchemy, astrology, magick, Rosicrucianism, esoteric Freemasonry, and the Golden Dawn. A perfect addition to any library of classic esoteric literature, this edition reproduces famous illustrations.

Terrible Beauty: A Cultural History of the Twentieth Century

The People and Ideas that Shaped the Modern Mind: A History
Author: Peter Watson
Publisher: Hachette UK
ISBN: 178022673X
Category: Philosophy
Page: 848
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A history of the twentieth century which covers all the ideas, people, great events, literary and artistic movements, scientific discoveries which have shaped the twentieth century. Terrible Beauty presents a unique narrative of the twentieth century. Unlike more conventional histories, where the focus is on political events and personalities, on wars, treaties and elections, this book concentrates on the ideas that made the century so rich, rewarding and provocative. Beginning with four seminal ideas which were introduced in 1900 - the unconscious, the gene, the quantum and Picasso's first paintings in Paris - the book brings together the main areas of thought and juxtaposes the most original and influential ideas of our time in an immensely readable narrative. From the creation of plastic to Norman Mailer, from the discovery of the 'Big Bang' to the Counterculture, from Relativity to Susan Sontag, from Proust to Salman Rushdie, and Henri Bergson to Saul Bellow, the book's range is encyclopedic. We meet in these pages the other twentieth century, the writers, the artists, the scientists and philosophers who were not cowed by the political and military disasters raging around them, and produced some of the most amazing and rewarding ideas by which we live. Terrible Beauty, endlessly stimulating and provocative, affirms that there was much more to the twentieth century than war and genocide.

Number Theory and Its History

Author: Oystein Ore
Publisher: Courier Corporation
ISBN: 0486136434
Category: Mathematics
Page: 400
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Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.

The Princeton Companion to Mathematics

Author: Timothy Gowers,June Barrow-Green,Imre Leader
Publisher: Princeton University Press
ISBN: 9781400830398
Category: Mathematics
Page: 1056
View: 8210

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This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors incude: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger