Download or read book Symbols Impossible Numbers and Geometric Entanglements written by Helena M. Pycior and published by Cambridge University Press. This book was released on 1997-05-13 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symbols, Impossible Numbers, and Geometric Entanglements is the first history of the development and reception of algebra in early modern England and Scotland. Not primarily a technical history, this book analyzes the struggles of a dozen British thinkers to come to terms with early modern algebra, its symbolical style, and negative and imaginary numbers. Professor Pycior uncovers these thinkers as a "test-group" for the symbolic reasoning that would radically change not only mathematics but also logic, philosophy, and language studies. The book also shows how pedagogical and religious concerns shaped the British debate over the relative merits of algebra and geometry. The first book to position algebra firmly in the Scientific Revolution and pursue Newton the algebraist, it highlights Newton's role in completing the evolution of algebra from an esoteric subject into a major focus of British mathematics. Other thinkers covered include Oughtred, Harriot, Wallis, Hobbes, Barrow, Berkeley, and MacLaurin.
Download or read book Algebra in Context written by Amy Shell-Gellasch and published by JHU Press. This book was released on 2015-10-15 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engaging new approach to teaching algebra that takes students on a historical journey from its roots to modern times. This book’s unique approach to the teaching of mathematics lies in its use of history to provide a framework for understanding algebra and related fields. With Algebra in Context, students will soon discover why mathematics is such a crucial part not only of civilization but also of everyday life. Even those who have avoided mathematics for years will find the historical stories both inviting and gripping. The book’s lessons begin with the creation and spread of number systems, from the mathematical development of early civilizations in Babylonia, Greece, China, Rome, Egypt, and Central America to the advancement of mathematics over time and the roles of famous figures such as Descartes and Leonardo of Pisa (Fibonacci). Before long, it becomes clear that the simple origins of algebra evolved into modern problem solving. Along the way, the language of mathematics becomes familiar, and students are gradually introduced to more challenging problems. Paced perfectly, Amy Shell-Gellasch and J. B. Thoo’s chapters ease students from topic to topic until they reach the twenty-first century. By the end of Algebra in Context, students using this textbook will be comfortable with most algebra concepts, including • Different number bases • Algebraic notation • Methods of arithmetic calculation • Real numbers • Complex numbers • Divisors • Prime factorization • Variation • Factoring • Solving linear equations • False position • Solving quadratic equations • Solving cubic equations • nth roots • Set theory • One-to-one correspondence • Infinite sets • Figurate numbers • Logarithms • Exponential growth • Interest calculations
Download or read book Negative Math written by Alberto A. Martínez and published by Princeton University Press. This book was released on 2018-06-05 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A student in class asks the math teacher: "Shouldn't minus times minus make minus?" Teachers soon convince most students that it does not. Yet the innocent question brings with it a germ of mathematical creativity. What happens if we encourage that thought, odd and ungrounded though it may seem? Few books in the field of mathematics encourage such creative thinking. Fewer still are engagingly written and fun to read. This book succeeds on both counts. Alberto Martinez shows us how many of the mathematical concepts that we take for granted were once considered contrived, imaginary, absurd, or just plain wrong. Even today, he writes, not all parts of math correspond to things, relations, or operations that we can actually observe or carry out in everyday life. Negative Math ponders such issues by exploring controversies in the history of numbers, especially the so-called negative and "impossible" numbers. It uses history, puzzles, and lively debates to demonstrate how it is still possible to devise new artificial systems of mathematical rules. In fact, the book contends, departures from traditional rules can even be the basis for new applications. For example, by using an algebra in which minus times minus makes minus, mathematicians can describe curves or trajectories that are not represented by traditional coordinate geometry. Clear and accessible, Negative Math expects from its readers only a passing acquaintance with basic high school algebra. It will prove pleasurable reading not only for those who enjoy popular math, but also for historians, philosophers, and educators. Key Features? Uses history, puzzles, and lively debates to devise new mathematical systems Shows how departures from rules can underlie new practical applications Clear and accessible Requires a background only in basic high school algebra
Download or read book Tales of Impossibility written by David S. Richeson and published by Princeton University Press. This book was released on 2021-11-02 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive look at four of the most famous problems in mathematics Tales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems—squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle—have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs—which demonstrated the impossibility of solving them using only a compass and straightedge—depended on and resulted in the growth of mathematics. Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viète, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems. Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.
Download or read book Isaac Newton on Mathematical Certainty and Method written by Niccolo Guicciardini and published by MIT Press. This book was released on 2011-08-19 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: An analysis of Newton's mathematical work, from early discoveries to mature reflections, and a discussion of Newton's views on the role and nature of mathematics. Historians of mathematics have devoted considerable attention to Isaac Newton's work on algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certainty and Method, Niccolò Guicciardini examines a critical aspect of Newton's work that has not been tightly connected to Newton's actual practice: his philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes's Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. Guicciardini shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity's legitimate heir, thereby distancing himself from the moderns. Guicciardini reconstructs Newton's own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton's works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton's understanding of method and his mathematical work then reveal themselves through Guicciardini's careful analysis of selected examples. Isaac Newton on Mathematical Certainty and Method uncovers what mathematics was for Newton, and what being a mathematician meant to him.
Download or read book From Newton to Hawking written by Kevin C. Knox and published by Cambridge University Press. This book was released on 2003-11-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cambridge University's Lucasian Professorship of Mathematics is one of the world's most celebrated academic positions. Since its foundation in 1663, the chair has been held by seventeen men who represent some of the most influential minds in science and technology. Principally a social history of mathematics and physics, the story of these great natural philosophers and mathematical physicists is told here by some of the finest historians of science. This informative work offers new perspectives on world famous scientists including Isaac Newton, Charles Babbage, Paul Dirac, and Stephen Hawking.
Download or read book Math through the Ages A Gentle History for Teachers and Others Expanded Second Edition written by William P. Berlinghoff and published by American Mathematical Soc.. This book was released on 2021-04-29 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind π π? … negative numbers? … the metric system? … quadratic equations? … sine and cosine? … logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that is accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch includes Questions and Projects to help you learn more about its topic and to see how the main ideas fit into the bigger picture of history. The 30 short stories are preceded by a 58-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. “What to Read Next” and reading suggestions after each sketch provide starting points for readers who want to learn more. This book is ideal for a broad spectrum of audiences, including students in history of mathematics courses at the late high school or early college level, pre-service and in-service teachers, and anyone who just wants to know a little more about the origins of mathematics.
Download or read book Science Philosophy and Religion in the Age of the Enlightenment written by John Gascoigne and published by Taylor & Francis. This book was released on 2024-10-28 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking as its focus the wide-ranging character of the Enlightenment, both in geographical and intellectual terms, this second collection of articles by John Gascoigne explores this movement's filiation and influence in a range of contexts. In contrast to some recently influential views it emphasises the evolutionary rather than the revolutionary character of the Enlightenment and its ability to change society by adaptation rather than demolition. This it does by reference, firstly, to developments in Britain tracing the changing views of history in relation to the Biblical account, the ideological uses of science (and particularly the work of Newton) and their connections to developments in moral philosophy and the teaching of science and philosophy in response to Enlightenment modes of thought. The collection then turns to the wider global setting of the Enlightenment and the way in which that movement served to provide a justification for European exploration and expansion, developments which found one of their most potent embodiments in the diverse uses of mapping. The collection concludes with an exploration of the interplay between the experience of Pacific contact and the currents of thought which characterised the Enlightenment in Germany.
Download or read book Perspectives on Mathematical Practices written by Bart van Kerkhove and published by Springer Science & Business Media. This book was released on 2007-06-01 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.
Download or read book Algebraic Art written by Andrea K. Henderson and published by Oxford University Press. This book was released on 2018 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. Drawing on literature, art, and photography, it explores how the Victorian mathematical conception of form still resonates today.
Download or read book Beyond the Learned Academy written by Philip Beeley and published by Oxford University Press. This book was released on 2024-01-05 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprising fifteen essays by leading authorities in the history of mathematics, this volume aims to exemplify the richness, diversity, and breadth of mathematical practice from the seventeenth century through to the middle of the nineteenth century.
Download or read book A Material History of Medieval and Early Modern Ciphers written by Katherine Ellison and published by Routledge. This book was released on 2017-09-14 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first cultural history of early modern cryptography, this collection brings together scholars in history, literature, music, the arts, mathematics, and computer science who study ciphering and deciphering from new materialist, media studies, cognitive studies, disability studies, and other theoretical perspectives. Essays analyze the material forms of ciphering as windows into the cultures of orality, manuscript, print, and publishing, revealing that early modern ciphering, and the complex history that preceded it in the medieval period, not only influenced political and military history but also played a central role in the emergence of the capitalist media state in the West, in religious reformation, and in the scientific revolution. Ciphered communication, whether in etched stone and bone, in musical notae, runic symbols, polyalphabetic substitution, algebraic equations, graphic typographies, or literary metaphors, took place in contested social spaces and offered a means of expression during times of political, economic, and personal upheaval. Ciphering shaped the early history of linguistics as a discipline, and it bridged theological and scientific rhetoric before and during the Reformation. Ciphering was an occult art, a mathematic language, and an aesthetic that influenced music, sculpture, painting, drama, poetry, and the early novel. This collection addresses gaps in cryptographic history, but more significantly, through cultural analyses of the rhetorical situations of ciphering and actual solved and unsolved medieval and early modern ciphers, it traces the influences of cryptographic writing and reading on literacy broadly defined as well as the cultures that generate, resist, and require that literacy. This volume offers a significant contribution to the history of the book, highlighting the broader cultural significance of textual materialities.
Download or read book By Good and Necessary Consequence written by Carlos R. Bovell and published by Wipf and Stock Publishers. This book was released on 2009-06-05 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: By Good and Necessary Consequence presents a critical examination of the reasoning behind the good and necessary consequence clause in the Westminster Confession of Faith and makes five observations regarding its suitability for contemporary Reformed and evangelical adherents. 1) In the seventeenth century, religious leaders in every quarter were expected to respond to a thoroughgoing, cultural skepticism. 2) In response to the onslaught of cultural and epistemological skepticism, many looked to mimic as far as possible the deductive methods of mathematicians. 3) The use to which biblicist foundationalism was put by the Westminster divines is at variance with the classical invention, subsequent appropriation, and contemporary estimation of axiomatic and deductive methodology. 4) Although such methodological developments in theology might have seemed natural during the seventeenth century, their epistemological advantage is not evident today. 5) When a believer's faith is epistemologically ordered in a biblicist foundationalist way, once the foundation--the axiomatic use of a veracious scripture--is called into question, the entire faith is in serious danger of crashing down. In a nutshell, Bovell argues that it is not wise to structure the Christian faith in this biblicist foundationalist way, and that it is high time alternate approaches be sought.
Download or read book Historical Modules for the Teaching and Learning of Mathematics written by Victor J. Katz and published by American Mathematical Soc.. This book was released on 2020-03-02 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Literature After Euclid written by Matthew Wickman and published by University of Pennsylvania Press. This book was released on 2016-02-16 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Literature After Euclid tells the story of the creative adaptation of geometry in Scotland during and after the long eighteenth century. Analyzing the work of Scottish literati, Matthew Wickman challenges how we perceive the Scottish Enlightenment and the modernist ethos that relegated "classical" Enlightenment to the dustbin of history.
Download or read book The Application of Mathematics to the Sciences of Nature written by P. CERRAI (Ed) and published by Springer Science & Business Media. This book was released on 2002-03-31 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Application of Mathematics to the Natural Sciences brings together scientists and historians of science to discuss how, in an increasingly interdisciplinary manner, mathematics and mathematical models are used in the natural sciences.
Download or read book Global Romanticism written by Evan Gottlieb and published by Bucknell University Press. This book was released on 2014-12-18 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: For several decades, interest in the British Romantics’ theorizations and representations of the world beyond their national borders has been guided by postcolonial and, more recently, transatlantic paradigms. GlobalRomanticism: Origins, Orientations, andEngagements, 1760–1820 charts a new intellectual course by exploring the literature and culture of the Romantic era through the lens of long-durational globalization. In a series of wide-ranging but complementary chapters, this provocative collection of essays by established scholars makes the case that many British Romantics were committed to conceptualizing their world as an increasingly interconnected whole. In doing so, moreover, they were both responding to and shaping early modern versions of the transnational economic, political, sociocultural, and ecological forces known today as globalization.
