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The Rise And Development Of The Theory Of Series Up To The Early 1820s
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Book Synopsis The Rise and Development of the Theory of Series up to the Early 1820s by : Giovanni Ferraro
Download or read book The Rise and Development of the Theory of Series up to the Early 1820s written by Giovanni Ferraro and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The manuscript gives a coherent and detailed account of the theory of series in the eighteenth and early nineteenth centuries. It provides in one place an account of many results that are generally to be found - if at all - scattered throughout the historical and textbook literature. It presents the subject from the viewpoint of the mathematicians of the period, and is careful to distinguish earlier conceptions from ones that prevail today.
Book Synopsis Anachronisms in the History of Mathematics by : Niccol- Guicciardini
Download or read book Anachronisms in the History of Mathematics written by Niccol- Guicciardini and published by Cambridge University Press. This book was released on 2021-07-22 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover essays by leading scholars on the history of mathematics from ancient to modern times in European and non-European cultures.
Book Synopsis A Delicate Balance: Global Perspectives on Innovation and Tradition in the History of Mathematics by : David E. Rowe
Download or read book A Delicate Balance: Global Perspectives on Innovation and Tradition in the History of Mathematics written by David E. Rowe and published by Birkhäuser. This book was released on 2015-05-12 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Joseph W. Dauben, a leading authority on the history of mathematics in Europe, China, and North America, has played a pivotal role in promoting international scholarship over the last forty years. This Festschrift volume, showcasing recent historical research by leading experts on three continents, offers a global perspective on important themes in this field.
Book Synopsis Research in History and Philosophy of Mathematics by : Maria Zack
Download or read book Research in History and Philosophy of Mathematics written by Maria Zack and published by Springer. This book was released on 2018-09-14 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. A series of chapters all set in the eighteenth century consider topics such as John Marsh’s techniques for the computation of decimal fractions, Euler’s efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge’s use of descriptive geometry. After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov’s adaptation of the Boltzmann equation to ionized gases. The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng’s defenses of mathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue. Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.
Book Synopsis The History of Mathematics: A Source-Based Approach, Volume 2 by : June Barrow-Green
Download or read book The History of Mathematics: A Source-Based Approach, Volume 2 written by June Barrow-Green and published by American Mathematical Society. This book was released on 2022-12-23 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: The History of Mathematics: A Source-Based Approach is a comprehensive history of the development of mathematics. This, the second volume of a two-volume set, takes the reader from the invention of the calculus to the beginning of the twentieth century. The initial discoverers of calculus are given thorough investigation, and special attention is also paid to Newton's Principia. The eighteenth century is presented as primarily a period of the development of calculus, particularly in differential equations and applications of mathematics. Mathematics blossomed in the nineteenth century and the book explores progress in geometry, analysis, foundations, algebra, and applied mathematics, especially celestial mechanics. The approach throughout is markedly historiographic: How do we know what we know? How do we read the original documents? What are the institutions supporting mathematics? Who are the people of mathematics? The reader learns not only the history of mathematics, but also how to think like a historian. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.
Book Synopsis Teaching and Learning with Primary Source Projects by : Janet Heine Barnett
Download or read book Teaching and Learning with Primary Source Projects written by Janet Heine Barnett and published by American Mathematical Society. This book was released on 2023-09-27 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: “It appears to me that if one wants to make progress in mathematics one should study the masters and not the pupils.” —Niels Henrik Abel Recent pedagogical research has supported Abel's claim of the effectiveness of reading the masters. Students exposed to historically based pedagogy see mathematics not as a monolithic assemblage of facts but as a collection of mental processes and an evolving cultural construct built to solve actual problems. Exposure to the immediacy of the original investigations can inspire an inquiry mindset in students and lead to an appreciation of mathematics as a living intellectual activity. TRIUMPHS (TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources) is an NSF-funded initiative to design materials that effectively harness the power of reading primary historical documents in undergraduate mathematics instruction. Teaching and Learning with Primary Source Projects is a collection of 24 classroom modules (PSPs) produced by TRIUMPHS that incorporate the reading of primary source excerpts to teach core mathematical topics. The selected excerpts are intertwined with thoughtfully designed student tasks that prompt students to actively engage with and explore the source material. Rigorously classroom tested and scrupulously edited to comply with the standards developed by the TRIUMPHS project, each of the PSPs in this volume can be inserted directly into a course in real analysis, complex variables, or topology and used to replace a standard textbook treatment of core course content. The volume also contains a comprehensive historical overview of the sociocultural and mathematical contexts within which the three subjects developed, along with extensive implementation guidance. Students and faculty alike are afforded a deeper classroom experience as they heed Abel's advice by studying today's mathematics through the words of the masters who brought that mathematics to life. Primary sources provide motivation in the words of the original discoverers of new mathematics, draw attention to subtleties, encourage reflection on today's paradigms, and enhance students' ability to participate equally, regardless of their background. These beautifully written primary source projects that adopt an “inquiry” approach are rich in features lacking in modern textbooks. Prompted by the study of historical sources, students will grapple with uncertainties, ask questions, interpret, conjecture, and compare multiple perspectives, resulting in a unique and vivid guided learning experience. —David Pengelley, Oregon State University
Book Synopsis Hidden Harmony—Geometric Fantasies by : Umberto Bottazzini
Download or read book Hidden Harmony—Geometric Fantasies written by Umberto Bottazzini and published by Springer Science & Business Media. This book was released on 2013-06-21 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.
Book Synopsis Abraham De Moivre by : David R. Bellhouse
Download or read book Abraham De Moivre written by David R. Bellhouse and published by CRC Press. This book was released on 2011-10-19 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extensively researched, this book traces the life and work of Abraham De Moivre as well as the state of probability and statistics in eighteenth-century Britain. It is the first extensive biography of De Moivre and is based on recently discovered material and translations, including some of De Moivre’s letters. The book begins with discussions on De Moivre’s early life in France and his initial work in pure mathematics with some excursions into celestial mechanics. It then describes his fundamental contributions to probability theory and applications, including those in finance and actuarial science. The author explores how De Moivre’s wide network of personal and professional connections often motivated his research. The book also covers De Moivre’s contemporaries and his impact on the field. Written in a clear, approachable style, this biography will appeal to historians and practitioners of the art of probability and statistics in a wide range of applications, including finance and actuarial science.
Book Synopsis Logic in Question by : Jean-Yves Béziau
Download or read book Logic in Question written by Jean-Yves Béziau and published by Springer Nature. This book was released on 2023-01-11 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume collects papers related to the Logic in Question workshop, which has taken place annually at Sorbonne University in Paris since 2011. Each year, the workshop brings together historians, philosophers, mathematicians, linguists, and computer scientists to explore questions related to the nature of logic and how it has developed over the years. As a result, chapter authors provide a thorough, interdisciplinary exploration of topics that have been studied in the workshop. Organized into three sections, the first part of the book focuses on historical questions related to logic, the second explores philosophical questions, and the third section is dedicated to mathematical discussions. Specific topics include: • logic and analogy• Chinese logic• nineteenth century British logic (in particular Boole and Lewis Carroll)• logical diagrams • the place and value of logic in Louis Couturat’s philosophical thinking• contributions of logical analysis for mathematics education• the exceptionality of logic• the logical expressive power of natural languages• the unification of mathematics via topos theory Logic in Question will appeal to pure logicians, historians of logic, philosophers, linguists, and other researchers interested in the history of logic, making this volume a unique and valuable contribution to the field.
Book Synopsis Leonhard Euler by : Ronald S. Calinger
Download or read book Leonhard Euler written by Ronald S. Calinger and published by Princeton University Press. This book was released on 2019-12-03 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is the first full-scale biography of Leonhard Euler (1707-83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler's massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler's work in its multilayered context--personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler's fundamental contributions to almost every area of pure and applied mathematics--especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics--to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory. The narrative takes the reader from Euler's childhood and education in Basel through his first period in St. Petersburg, 1727-41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton's dynamics, and published the best-selling Letters to a German Princess--all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment."--Publisher's description.
Book Synopsis The Oxford Handbook of Hobbes by : A.P. Martinich
Download or read book The Oxford Handbook of Hobbes written by A.P. Martinich and published by Oxford University Press. This book was released on 2016-03-07 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Oxford Handbook of Hobbes collects twenty-six newly commissioned, original chapters on the philosophy of the English thinker Thomas Hobbes (1588-1679). Best known today for his important influence on political philosophy, Hobbes was in fact a wide and deep thinker on a diverse range of issues. The chapters included in this Oxford Handbook cover the full range of Hobbes's thought--his philosophy of logic and language; his view of physics and scientific method; his ethics, political philosophy, and philosophy of law; and his views of religion, history, and literature. Several of the chapters overlap in fruitful ways, so that the reader can see the richness and depth of Hobbes's thought from a variety of perspectives. The contributors are experts on Hobbes from many countries, whose home disciplines include philosophy, political science, history, and literature. A substantial introduction places Hobbes's work, and contemporary scholarship on Hobbes, in a broad context.
Book Synopsis The Routledge Companion to Eighteenth Century Philosophy by : Aaron Garrett
Download or read book The Routledge Companion to Eighteenth Century Philosophy written by Aaron Garrett and published by Routledge. This book was released on 2014-03-21 with total page 1390 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Eighteenth century is one of the most important periods in the history of Western philosophy, witnessing philosophical, scientific, and social and political change on a vast scale. In spite of this, there are few single volume overviews of the philosophy of the period as a whole. The Routledge Companion to Eighteenth Century Philosophy is an authoritative survey and assessment of this momentous period, covering major thinkers, topics and movements in Eighteenth century philosophy. Beginning with a substantial introduction by Aaron Garrett, the thirty-five specially commissioned chapters by an outstanding team of international contributors are organised into seven clear parts: Context and Movements Metaphysics and Understanding Mind, Soul, and Perception Morals and Aesthetics Politics and Society Philosophy in relation to the Arts and Sciences Major Figures. Major topics and themes are explored and discussed, ranging from materialism, free will and personal identity; to the emotions, the social contract, aesthetics, and the sciences, including mathematics and biology. The final section examines in more detail three figures central to the period: Hume, Rousseau and Kant. As such The Routledge Companion to Eighteenth Century Philosophy is essential reading for all students of the period, both in philosophy and related disciplines such as politics, literature, history and religious studies.
Book Synopsis The Doctrine of Triangles by : Glen Van Brummelen
Download or read book The Doctrine of Triangles written by Glen Van Brummelen and published by Princeton University Press. This book was released on 2021-06-08 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry’s participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms. A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry’s rich historical past full circle into the modern era.
Book Synopsis Economics [4 volumes] by : David A. Dieterle
Download or read book Economics [4 volumes] written by David A. Dieterle and published by Bloomsbury Publishing USA. This book was released on 2017-03-27 with total page 2345 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive four-volume resource that explains more than 800 topics within the foundations of economics, macroeconomics, microeconomics, and global economics, all presented in an easy-to-read format. As the global economy becomes increasingly complex, interconnected, and therefore relevant to each individual, in every country, it becomes more important to be economically literate—to gain an understanding of how things work beyond the microcosm of the economic needs of a single individual or family unit. This expansive reference set serves to establish basic economic literacy of students and researchers, providing more than 800 objective and factually driven entries on all the major themes and topics in economics. Written by leading scholars and practitioners, the set provides readers with a framework for understanding economics as mentioned and debated in the public forum and media. Each of the volumes includes coverage of important events throughout economic history, biographies of the major economists who have shaped the world of economics, and highlights of the legislative acts that have shaped the U.S. economy throughout history. The extensive explanations of major economic concepts combined with selected key historical primary source documents and a glossary will endow readers with a fuller comprehension of our economic world.
Book Synopsis The Real Numbers and Real Analysis by : Ethan D. Bloch
Download or read book The Real Numbers and Real Analysis written by Ethan D. Bloch and published by Springer Science & Business Media. This book was released on 2011-05-14 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.
Book Synopsis An Invitation to Analytic Combinatorics by : Stephen Melczer
Download or read book An Invitation to Analytic Combinatorics written by Stephen Melczer and published by Springer Nature. This book was released on 2020-12-22 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.
Book Synopsis The Impossibility of Squaring the Circle in the 17th Century by : Davide Crippa
Download or read book The Impossibility of Squaring the Circle in the 17th Century written by Davide Crippa and published by Springer. This book was released on 2019-03-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about James Gregory’s attempt to prove that the quadrature of the circle, the ellipse and the hyperbola cannot be found algebraically. Additonally, the subsequent debates that ensued between Gregory, Christiaan Huygens and G.W. Leibniz are presented and analyzed. These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle. The author shows how the controversy around the possibility of solving the quadrature of the circle by certain means (algebraic curves) pointed to metamathematical issues, particularly to the completeness of algebra with respect to geometry. In other words, the question underlying the debate on the solvability of the circle-squaring problem may be thus phrased: can finite polynomial equations describe any geometrical quantity? As the study reveals, this question was central in the early days of calculus, when transcendental quantities and operations entered the stage. Undergraduate and graduate students in the history of science, in philosophy and in mathematics will find this book appealing as well as mathematicians and historians with broad interests in the history of mathematics.
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