a brief history of mathematical thought

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A Brief History Of Mathematical Thought

Author : Luke Heaton
ISBN : 9780190621766
Genre : Math anxiety
File Size : 73. 99 MB
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Emblazoned on many advertisements for the wildly popular game of Sudoku are the reassuring words, "no mathematical knowledge required." Anxiety about math plagues many of us, and school memories can still summon intense loathing. In A Brief History of Mathematical Thought, Luke Heaton shows that much of what many think-and fear-about mathematics is misplaced, and to overcome our insecurities we need to understand its history. To help, he offers a lively guide into and through the world of mathematics and mathematicians, one in which patterns and arguments are traced through logic in a language grounded in concrete experience. Heaton reveals how Greek and Roman mathematicians like Pythagoras, Euclid, and Archimedes helped shaped the early logic of mathematics; how the Fibonacci sequence, the rise of algebra, and the invention of calculus are connected; how clocks, coordinates, and logical padlocks work mathematically; and how, in the twentieth century, Alan Turing's revolutionary work on the concept of computation laid the groundwork for the modern world. A Brief History of Mathematical Thought situates mathematics as part of, and essential to, lived experience. Understanding it requires not abstract thought or numbing memorization but an historical imagination and a view to its origins. --

Mathematical Thought From Ancient To Modern Times

Author : Morris Kline
ISBN : 0195061365
Genre : Mathematics
File Size : 56. 42 MB
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Traces the development of mathematics from its beginnings in Babylonia and ancient Egypt to the work of Riemann and Godel in modern times

Descartes S Mathematical Thought

Author : C. Sasaki
ISBN : 9789401712255
Genre : Mathematics
File Size : 32. 21 MB
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Covering both the history of mathematics and of philosophy, Descartes's Mathematical Thought reconstructs the intellectual career of Descartes most comprehensively and originally in a global perspective including the history of early modern China and Japan. Especially, it shows what the concept of "mathesis universalis" meant before and during the period of Descartes and how it influenced the young Descartes. In fact, it was the most fundamental mathematical discipline during the seventeenth century, and for Descartes a key notion which may have led to his novel mathematics of algebraic analysis.

Greek Mathematical Thought And The Origin Of Algebra

Author : Jacob Klein
ISBN : 0486272893
Genre : Mathematics
File Size : 20. 66 MB
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Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

Alan Turing Enigma

Author : Andrew Hodges
ISBN : 3211826270
Genre : Biography & Autobiography
File Size : 66. 5 MB
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Alan Turing, Enigma ist die Biographie des legendAren britischen Mathematikers, Logikers, Kryptoanalytikers und Computerkonstrukteurs Alan Mathison Turing (1912-1954). Turing war einer der bedeutendsten Mathematiker dieses Jahrhunderts und eine hAchst exzentrische PersAnlichkeit. Er gilt seit seiner 1937 erschienenen Arbeit "On Computable Numbers," in der er das Prinzip des abstrakten Universalrechners entwickelte, als der Erfinder des Computers. Er legte auch die Grundlagen fA1/4r das heute "KA1/4nstliche Intelligenz" genannte Forschungsgebiet. Turings zentrale Frage "Kann eine Maschine denken?" war das Motiv seiner Arbeit und wird die SchlA1/4sselfrage des Umgangs mit dem Computer werden. Die bis 1975 geheimgehaltene TAtigkeit Turings fA1/4r den britischen Geheimdienst, die zur EntschlA1/4sselung des deutschen Funkverkehrs fA1/4hrte, trug entscheidend zum Verlauf und Ausgang des Zweiten Weltkriegs bei.

Enlightening Symbols

Author : Joseph Mazur
ISBN : 9781400850112
Genre : Mathematics
File Size : 32. 29 MB
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While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

Mathematical Thought From Ancient To Modern Times Volume 3

Author : Morris Kline
ISBN : 0195061373
Genre : Mathematics
File Size : 29. 69 MB
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Traces the development of mathematics from its beginnings in Babylonia and ancient Egypt to the work of Riemann and Godel in modern times

Mathematical Thought And Its Objects

Author : Charles Parsons
ISBN : 1139467271
Genre : Science
File Size : 37. 75 MB
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Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.

God Created The Integers

Author : Stephen Hawking
ISBN : 9780762432721
Genre : Science
File Size : 42. 54 MB
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Bestselling author and physicist Stephen Hawking explores the "masterpieces" of mathematics, 25 landmarks spanning 2,500 years and representing the work of 15 mathematicians, including Augustin Cauchy, Bernard Riemann, and Alan Turing. This extensive anthology allows readers to peer into the mind of genius by providing them with excerpts from the original mathematical proofs and results. It also helps them understand the progression of mathematical thought, and the very foundations of our present-day technologies. Each chapter begins with a biography of the featured mathematician, clearly explaining the significance of the result, followed by the full proof of the work, reproduced from the original publication.

The Oxford Handbook Of The History Of Mathematics

Author : Eleanor Robson
ISBN : 9780191607448
Genre : Mathematics
File Size : 51. 87 MB
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This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood. The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. A vital reference for graduates and researchers in mathematics, historians of science, and general historians.

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