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Author: Giovanni Ferraro
Publisher: Springer Science & Business Media
ISBN: 0387734686
Category : Mathematics
Languages : en
Pages : 392
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Book Description
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.
Author: Giovanni Ferraro
Publisher: Springer Science & Business Media
ISBN: 0387734686
Category : Mathematics
Languages : en
Pages : 392
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Book Description
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.
Author: Ethan D. Bloch
Publisher: Springer Science & Business Media
ISBN: 0387721770
Category : Mathematics
Languages : en
Pages : 577
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Book Description
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.
Author: Aaron Garrett
Publisher: Routledge
ISBN: 1317807928
Category : History
Languages : en
Pages : 874
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Book Description
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.
Author: David S. Richeson
Publisher: Princeton University Press
ISBN: 0691218722
Category : Mathematics
Languages : en
Pages : 450
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Book Description
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.
Author: June Barrow-Green
Publisher: American Mathematical Society
ISBN: 1470443821
Category : Mathematics
Languages : en
Pages : 703
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Book Description
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.
Author: Niccol- Guicciardini
Publisher: Cambridge University Press
ISBN: 1108834965
Category : History
Languages : en
Pages : 393
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Book Description
Discover essays by leading scholars on the history of mathematics from ancient to modern times in European and non-European cultures.
Author: Glen Van Brummelen
Publisher: Princeton University Press
ISBN: 0691219877
Category : Mathematics
Languages : en
Pages : 392
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Book Description
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.
Author: Aloysius Martinich
Publisher: Oxford University Press
ISBN: 0199791945
Category : Philosophy
Languages : en
Pages : 665
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Book Description
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.
Author: Craig Smorynski
Publisher: Springer
ISBN: 3319529560
Category : Mathematics
Languages : en
Pages : 504
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Book Description
This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mathematics majors as well as graduate students. Unlike other books, the present monograph treats the mathematical and historical aspects in equal measure, providing detailed and rigorous proofs of the mathematical results and even including original source material presenting the flavour of the history.
Author: Raffaele Pisano
Publisher: Springer Nature
ISBN: 3031261747
Category :
Languages : en
Pages : 820
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Book Description
