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Mathematical History and Development Books
African Mathematics: From Bones to Computers by This is the first comprehensive text on African Mathematics that can be used to address some of the problematic issues in this area. What unifies the chapters in this book can appear rather banal, but many mathematical insights are so obvious and so fundamental that they are difficult to absorb, appreciate, and express with fresh clarity. Some of the more basic insights are isolated by accounts of investigators who have earned their contemporaries' respect.
Publication Date: 2011-01-01
Descartes's Secret Notebook by RenÈ Descartes (1596Â€"1650) is one of the towering and central figures in Western philosophy and mathematics. His apothegm "Cogito, ergo sum" marked the birth of the mind-body problem, while his creation of so-called Cartesian coordinates has made our intellectual conquest of physical space possible. But Descartes had a mysterious and mystical side, as well. Almost certainly a member of the occult brotherhood of the Rosicrucians, he kept a secret notebook, now lost, most of which was written in code. After Descartes's death, Gottfried Leibniz, inventor of calculus and one of the greatest mathematicians of all time, moved to Paris in search of this notebook–and eventually found it in the possession of Claude Clerselier, a friend of Descartes's. Liebniz called on Clerselier and was allowed to copy only a couple of pages–which, though written in code, he amazingly deciphered there on the spot. Liebniz's hastily scribbled notes are all we have today of Descartes's notebook. Why did Descartes keep a secret notebook, and what were its contents? The answers to these questions will lead the reader on an exciting, swashbuckling journey, and offer a fascinating look at one of the great figures of Western culture.
Publication Date: 2005-10-11
Essays in the Philosophy and History of Logic and Mathematics by Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered.
Publication Date: 2010-10-01
From Eudoxus to Einstein: A History of Mathematical Astronomy by Since man first looked towards the heavens, a great deal of effort has been put into trying to predict and explain the motions of the sun, moon and planets. Developments in man's understanding have been closely linked to progress in the mathematical sciences. Whole new areas of mathematics, such as trigonometry, were developed to aid astronomical calculations, and on numerous occasions throughout history, breakthroughs in astronomy have only been possible because of progress in mathematics. This book describes the theories of planetary motion that have been developed through the ages, beginning with the homocentric spheres of Eudoxus and ending with Einstein's general theory of relativity. It emphasizes the interaction between progress in astronomy and in mathematics, showing how the two have been inextricably linked since Babylonian times.
Publication Date: 2004-08-12
From Kant to Hilbert, Volume 1 : A Source Book in the Foundations of Mathematics by Immanuel Kant's Critique of Pure Reason is widely taken to be the starting point of the modern period of mathematics while David Hilbert was the last great mainstream mathematician to pursue important nineteenth century ideas. This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics - algebra, geometry, number theory, analysis, logic, and set theory - with narratives to show how they are linked. Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are reproduced in reliable translations and many selections from writers such as Gauss, Cantor, Kronecker, and Zermelo are here translated for the first time. The collection is an invaluable source for anyone wishing to gain an understanding of the foundation of modern mathematics.
Publication Date: 2007-10-12
Galileo's Muse: Renaissance Mathematics and the Arts by Galileo's Muse argues that painters, poets, musicians, and architects brought about a scientific revolution that eluded the philosopher-scientists of the day, steeped as they were in a medieval cosmos and its underlying philosophy. According to Peterson, the recovery of classical science owes much to the Renaissance artists who first turned to Greek sources for inspiration and instruction. Chapters devoted to their insights into mathematics, ranging from perspective in painting to tuning in music, are interspersed with chapters about Galileo's own life and work. Himself an artist turned scientist and an avid student of Hellenistic culture, Galileo pulled together the many threads of his artistic and classical education in designing unprecedented experiments to unlock the secrets of nature. An intellectual adventure, Galileo’s Muse offers surprising ideas that will capture the imagination of anyone-scientist, mathematician, history buff, lover of literature, or artist-who cares about the humanistic roots of modern science.
Publication Date: 2011-10-17
Geometry: The Language of Space and Form by Geometry is a look not only at how this branch of mathematics arose and flourished in different cultures at different times but also at its useful applications in science and in society. Author John Tabak pinpoints the beginnings of geometry to ancient Egypt and Mesopotamia and traces its extraordinary progress in Greece. Greek ideas about geometry, straight-edge and compass constructions, and the nature of mathematical proof dominated mathematical thought for about 2,000 years. Geometry continued its evolution with projective geometry, an area born through the work of Renaissance artists, such as da Vinci and Durer, and their exploration of methods for representing three-dimensional objects on two-dimensional surfaces. Over centuries, mathematicians refined these concepts to the extent that projective geometry found application in the area of computer graphics.
Publication Date: 2004-05-01
History and Philosophy of Modern Mathematics by The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics.
Publication Date: 1988-01-01
History of Mathematical Sciences : Portugal and East Asia III: The Jesuits, The Padroado and East Asian Science (1552-1773) by At the end of the 15th century, Portugal was given the oversight (Padroado) of all Catholic missions in Asia. The Society of Jesus played a major role in this enterprise of evangelization, which in Jesuit hands led to the transmission of major elements of European mathematical sciences to East Asia. The essays in this volume present important new data and analysis on the extent to and ways in which Jesuit scientific culture and Portuguese policies regarding education, trade and mission shaped the reception of "Western learning" in China, Japan, Korea and Vietnam in the early modern period.
Publication Date: 2008-02-01
Italian Mathematics Between the Two World Wars by This book describes Italian mathematics in the period between the two World Wars. It analyzes the development by focusing on both the interior and the external influences. Italian mathematics in that period was shaped by a colorful array of strong personalities who concentrated their efforts on a select number of fields and won international recognition and respect in an incredibly short time. Consequently, Italy was considered a third mathematical power after France and Germany.
Publication Date: 2005-11-17
Kepler's Conjecture by The fascinating story of a problem that perplexed mathematicians for nearly 400 years In 1611, Johannes Kepler proposed that the best way to pack spheres as densely as possible was to pile them up in the same way that grocers stack oranges or tomatoes. This proposition, known as Kepler's Conjecture, seemed obvious to everyone except mathematicians, who seldom take anyone's word for anything. In the tradition of Fermat's Enigma, George Szpiro shows how the problem engaged and stymied many men of genius over the centuries--Sir Walter Raleigh, astronomer Tycho Brahe, Sir Isaac Newton, mathematicians C. F. Gauss and David Hilbert, and R. Buckminster Fuller, to name a few--until Thomas Hales of the University of Michigan submitted what seems to be a definitive proof in 1998. George G. Szpiro (Jerusalem, Israel) is a mathematician turned journalist. He is currently the Israel correspondent for the Swiss daily Neue Zurcher Zeitung.
Publication Date: 2003-02-14
Mathematical Thought from Ancient to Modern Times by Now available in a new three-volume paperback edition, Morris Kline's monumental work presents the major creations in mathematics from its beginnings in Babylonia and Egypt through the first few decades of the twentieth century.
Publication Date: 1990-03-01
Mathematics and the Laws of Nature: Developing the Language of Science by The History of Mathematics is a fascinating survey of the development of math through discovery, innovation, collaboration, and experimentation. The set presents a compelling overview of myriad aspects of mathematics using understandable language and appealing line illustrations and photographs. Mathematics and the Laws of Nature is an insightful examination of the pioneering ideas, works, and applications that have made mathematics the language of science. Author John Tabak looks at the many ways in which so-called pure math has been used in the applied sciences. For example, he explores how mathematical theories contributed to the development of Kepler's laws of planetary motion as well as to combustion modeling and hydrodynamics. The book gives students insight into the ways that math is used to explain the world around them, offering many examples that show how nature can be descibed mathematically and how the physical sciences and math connect. Mathematics and the Laws of Nature includes an index, a chronology of notable events, a glossary of terms, a helpful list of Internet resources, and an array of historical and current print sources for further research. Keyed to current principles and standards in teaching math, The History of Mathematics set is essential for young readers who require information on relevant topics in mathematics. Book jacket.
Publication Date: 2004-05-01
Mathematics Emerging by Aimed at graduates and researchers in Mathematics, History of Mathematics and Science, this book examines the development of mathematics from the late 16th Century to the end of the 19th Century. Mathematics has an amazingly long and rich history, it has been practised in every society and culture, with written records reaching back in some cases as far as four thousand years. This book will focus on just a small part of the story, in a sense the most recent chapter of it: the mathematicsof western Europe from the sixteenth to the nineteenth centuries. Each chapter will focus on a particular topic and outline its history with the provision of facsimiles of primary source material along with explanatory notes and modern interpretations. Almost every source is given in its original form, not just in the language in which it was first written, but as far as practicable in the layout and typeface in which it was read by contemporaries.This book is designed to provide mathematics undergraduates with some historical background to the material that is now taught universally to students in their final years at school and the first years at college or university: the core subjects of calculus, analysis, and abstract algebra, along with others such as mechanics, probability, and number theory. All of these evolved into their present form in a relatively limited area of western Europe from the mid sixteenth century onwards, and it is there that we find the major writings that relate in a recognizable way to contemporary mathematics.
Publication Date: 2008-11-15
Mathematics in India, 500BCE -1800CE by Based on extensive research in Sanskrit sources,Mathematics in Indiachronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic scientific traditions. Plofker shows that Indian mathematics appears not as a disconnected set of discoveries, but as a lively, diverse, yet strongly unified discipline, intimately linked to other Indian forms of learning. Far more than in other areas of the history of mathematics, the literature on Indian mathematics reveals huge discrepancies between what researchers generally agree on and what general readers pick up from popular ideas. This book explains with candor the chief controversies causing these discrepancies--both the flaws in many popular claims, and the uncertainties underlying many scholarly conclusions. Supplementing the main narrative are biographical resources for dozens of Indian mathematicians; a guide to key features of Sanskrit for the non-Indologist; and illustrations of manuscripts, inscriptions, and artifacts.Mathematics in Indiaprovides a rich and complex understanding of the Indian mathematical tradition. **Author's note: The concept of "computational positivism" in Indian mathematical science, mentioned on p. 120, is due to Prof. Roddam Narasimha and is explored in more detail in some of his works, including "The Indian half of Needham's question: some thoughts on axioms, models, algorithms, and computational positivism" (Interdisciplinary Science Reviews28, 2003, 1-13).
Publication Date: 2008-12-29
New Perspectives on Mathematical Practices : Essays in Philosophy and History of Mathematics by This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally established experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly naturalistic tradition in the philosophy of mathematics. In this alternative philosophical current, which has been dramatically growing in importance in the last few decades, unlike in the traditional schools, proper attention is paid to scientific practices as informing for philosophical accounts.
Publication Date: 2009
Numbers: Computers, Philosophers, and the Search for Meaning by The History of Mathematics is a fascinating survey of the development of math through discovery, innovation, collaboration, and experimentation. The set presents a compelling overview of myriad aspects of mathematics using understandable language and appealing line illustrations and photographs. Numbers is an insightful look at the properties and uses of numerical quantities, from fractions to algebraic numbers, transcendental numbers, and complex numbers. We rely on numbers to carry out countless daily activities -- from mapping the universe to running word-processing programs to buying lunch. Author John Tabak points out that numbers are a human invention, as seen through the compelling histories of Babylonian, Roman, and Arab thinkers and their influential systems for representing numbers. The book examines in detail the number pi, the evolution of the idea of infinity, the representation of numbers in computers, the metric and American systems of measurement, and the application of some historical concepts of numbers in such modern forms as cryptography and hand calculators. Numbers includes an index, a chronology of notable events, a glossary of terms, a helpful list of Internet resources, and an array of historical and current print sources for further research. Keyed to current principles and standards in teaching math, The History of Mathematics set is essential for young readers who require information on relevant topics in mathematics. Book jacket.
Publication Date: 2004-05-01
Plato's Ghost by Plato's Ghostis 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. Plato's Ghostevokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method--debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghostis essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
Publication Date: 2008-09-02
Probability and Statistics by Probability deals with measuring the likelihood of a particular outcome or event. Statistics is the collection
Publication Date: 2004-05-01
The Architecture of Modern Mathematics by This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research and how a number of historical accounts can be deepened by embracing philosophical questions.
Publication Date: 2006-06-29
The Good Life in the Scientific Revolution by Amid the unrest, dislocation, and uncertainty of seventeenth-century Europe, readers seeking consolation and assurance turned to philosophical and scientific books that offered ways of conquering fears and training the mindOCoguidance for living a good life. a "The Good Life in the Scientific Revolution" presents a triptych showing how three key early modern scientists, Ren(r) Descartes, Blaise Pascal, and Gottfried Leibniz, envisioned their new work as useful for cultivating virtue and for pursuing a good life. Their scientific and philosophical innovations stemmed in part from their understanding of mathematics and science as cognitive and spiritual exercises that could create a truer mental and spiritual nobility.a In portraying the rich contexts surrounding DescartesOCO geometry, PascalOCOs arithmetical triangle, and LeibnizOCOs calculus, Matthew L. Jones argues that this drive for moral therapeutics guided important developments of early modern philosophy and the Scientific Revolution. "
Publication Date: 2006
The History of Mathematics by A History of Mathematicscovers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwasizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.
Publication Date: 2005-08-11
The Honors Class by This eminently readable book focuses on the people of mathematics and draws the reader into their fascinating world. In a monumental address, given to the International Congress of Mathematicians in Paris in 1900, David Hilbert, perhaps the most respected mathematician of his time, developed a blueprint for mathematical research in the new century. Jokingly called a natural introduction to thesis writing with examples, this collection of problems has indeed become a guiding inspiration to many mathematicians, and those who succeeded in solving or advancing their solutions form an Honors Class among research mathematicians of this century. In a remarkable labor of love and with the support of many of the major players in the field, Ben Yandell has written a fascinating account of the achievements of this Honors Class, covering mathematical substance and biographical aspects.
Publication Date: 2001-12-12
The Legacy of Leonhard Euler by This book primarily serves as a historical research monograph on the biographical sketch and career of Leonhard Euler and his major contributions to numerous areas in the mathematical and physical sciences. It contains fourteen chapters describing Eulers works on number theory, algebra, geometry, trigonometry, differential and integral calculus, analysis, infinite series and infinite products, ordinary and elliptic integrals and special functions, ordinary and partial differential equations, calculus of variations, graph theory and topology, mechanics and ballistic research, elasticity and fluid mechanics, physics and astronomy, probability and statistics. The book is written to provide a definitive impression of Eulers personal and professional life as well as of the range, power, and depth of his unique contributions. This tricentennial tribute commemorates Euler the great man and Euler the universal mathematician of all time. Based on the author's historically motivated method of teaching, special attention is given to demonstrate that Eulers work had served as the basis of research and developments of mathematical and physical sciences for the last 300 years. An attempt is also made to examine his research and its relation to current mathematics and science. Based on a series of Eulers extraordinary contributions, the historical development of many different subjects of mathematical sciences is traced with a linking commentary so that it puts the reader at the forefront of current research.
Publication Date: 2009-10-01
Ancient Mathematics by The theorem of Pythagoras, Euclid's "Elements", Archimedes' method to find the volume of a sphere: all parts of the invaluable legacy of ancient mathematics. But ancient mathematics was also about counting and measuring, surveying land and attributing mystical significance to the number six. This volume offers the first accessible survey of the discipline in all its variety and diversity of practices. The period covered ranges from the fifth century BC to the sixth century AD, with the focus on the Mediterranean region. Topics include: * mathematics and politics in classical Greece * the formation of mathematical traditions * the self-image of mathematicians in the Graeco-Roman period * mathematics and Christianity * and the use of the mathematical past in late antiquity.
Publication Date: 2001-09-07
Calculus and Its Origins by Calculus answers questions that had been explored for centuries before calculus was born. Calculus and Its Origins begins with these ancient questions and details the remarkable story of how subsequent scholars wove these inquiries into a unified theory. This book does not presuppose knowledge of calculus, it requires only a basic knowledge of geometry and algebra (similar triangles, polynomials, factoring). Inside you will find the accounts of how Archimedes discovered the area of a parabolic segment, ibn Al-Haytham calculated the volume of a revolved area, Jyesthadeva explained the infinite series for sine and cosine, Wallis deduced the link between hyperbolas and logarithms, Newton generalized the binomial theorem, Leibniz discovered integration by parts, and much more. Each chapter ends with further results, in the form of exercises, by such luminaries as Pascal, Maclaurin, Barrow, Cauchy and Euler.
Publication Date: 2012-03-22
A Historian Looks Back: The Calculus as Algebra and Selected Writings by Judith Grabiner has written extensively on the history of mathematics, principally for mathematicians rather than historians. This collection of her work highlights the benefits of studying the development of mathematical ideas and the relationship between culture and mathematics. She also considers the struggles and successes of famous mathematicians with the aim of inspiring students and teachers alike. A large part of this book is the author's The Calculus as Algebra: J.-L. Lagrange, 1736-1813 which focuses on Lagrange's pioneering attempt to reduce the calculus to algebra. The nine other articles are on a broad range of other topics such as some widely held myths about the history of mathematics and the work of heavyweight mathematicians such as Descartes, Newton, Maclaurin and Lagrange. Six of these articles have won awards from the MAA for expository excellence. This collection is an inspiring resource for history of mathematics courses.
Publication Date: 2010-09-23
History of Mathematics Websites
A Brief History of Mathematics | BBC