Greek Mathematical Thought and the Origin of Algebra

Author: Jacob Klein

Publisher: Courier Corporation

ISBN: 0486319814

Category: Mathematics

Page: 384

View: 8911

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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.

Greek Mathematical Thought and the Origin of Algebra

Author: Jacob Klein

Publisher: Courier Corporation

ISBN: 9780486272894

Category: Mathematics

Page: 360

View: 4004

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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.

The Origin of the Logic of Symbolic Mathematics

Edmund Husserl and Jacob Klein

Author: Burt C. Hopkins

Publisher: Indiana University Press

ISBN: 0253005272

Category: Philosophy

Page: 592

View: 2714

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Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.

A Brief History of Mathematical Thought

Author: Luke Heaton

Publisher: Oxford University Press

ISBN: 0190621761

Category: Math anxiety

Page: 336

View: 7390

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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. --

Geometry and Algebra in Ancient Civilizations

Author: Bartel L. van der Waerden

Publisher: Springer Science & Business Media

ISBN: 3642617794

Category: Mathematics

Page: 226

View: 2615

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Originally, my intention was to write a "History of Algebra", in two or three volumes. In preparing the first volume I saw that in ancient civiliza tions geometry and algebra cannot well be separated: more and more sec tions on ancient geometry were added. Hence the new title of the book: "Geometry and Algebra in Ancient Civilizations". A subsequent volume on the history of modem algebra is in preparation. It will deal mainly with field theory, Galois theory and theory of groups. I want to express my deeply felt gratitude to all those who helped me in shaping this volume. In particular, I want to thank Donald Blackmore Wagner (Berkeley) who put at my disposal his English translation of the most interesting parts of the Chinese "Nine Chapters of the Art of Arith metic" and of Liu Hui's commentary to this classic, and also Jacques Se siano (Geneva), who kindly allowed me to use his translation of the re cently discovered Arabic text of four books of Diophantos not extant in Greek. Warm thanks are also due to Wyllis Bandler (Colchester, England) who read my English text very carefully and suggested several improve ments, and to Annemarie Fellmann (Frankfurt) and Erwin Neuenschwan der (Zurich) who helped me in correcting the proof sheets. Miss Fellmann also typed the manuscript and drew the figures. I also want to thank the editorial staff and production department of Springer-Verlag for their nice cooperation.

A Source Book in Mathematics

Author: David Eugene Smith

Publisher: Courier Corporation

ISBN: 0486158292

Category: Mathematics

Page: 736

View: 8177

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The writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises dating from the Renaissance to the late 19th century — most unavailable elsewhere.

Introduction to the Foundations of Mathematics

Second Edition

Author: Raymond L. Wilder

Publisher: Courier Corporation

ISBN: 0486276201

Category: Mathematics

Page: 352

View: 8412

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Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.

Robert Grosseteste and the Origins of Experimental Science, 1100-1700

Author: Alistair Cameron Crombie

Publisher: N.A

ISBN: 9780198241898

Category: Science

Page: 373

View: 7629

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Crombie shows how the particular intellectual and practical interests of Western thinkers, especially from the 12th century, led them to ask particular kinds of questions about the natural world. In the 13th century the Oxford School, with Robert Grosseteste as its founder, assumed a paramount importance and the work of this school marked the beginning of the modern tradition of experimental science. The first half of the book is devoted to Grosseteste and the Oxford school; the second half deals with their influences on the spread of the experimental method in Western Christendom and with its history down to Newton. The study of optics and of the rainbow had a special place in the interests of the Oxford school and the history of these subjects is used to provide examples of the experimental method in operation. `...this is one of the most stimulating and carefully prepared studies in medieval science ... nowhere else do we have so much material assembled for the study of medieval scientific methodology.' Marshall Clagett in Isis .

Mathematical Thought From Ancient to Modern Times

Author: Morris Kline

Publisher: Oxford University Press

ISBN: 0199770468

Category: Mathematics

Page: 432

View: 5200

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The major creations and developments in mathematics from the beginnings in Babylonia and Egypt through the first few decades of the twentieth century are presented with clarity and precision in this comprehensive historical study.

The History of Mathematics

A Brief Course

Author: Roger L. Cooke

Publisher: John Wiley & Sons

ISBN: 1118460294

Category: Mathematics

Page: 648

View: 9027

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Praise for the Second Edition "An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential." —CHOICE This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include: Material arranged in a chronological and cultural context Specific parts of the history of mathematics presented as individual lessons New and revised exercises ranging between technical, factual, and integrative Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book) An emphasis on geography, culture, and mathematics In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.

From Discrete to Continuous

The Broadening of Number Concepts in Early Modern England

Author: K. Neal

Publisher: Springer Science & Business Media

ISBN: 940170077X

Category: Mathematics

Page: 175

View: 9997

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In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways. This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.

Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences

Author: Ivor Grattan-Guinness

Publisher: Routledge

ISBN: 1134957491

Category: Reference

Page: 1840

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* Examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century * 176 articles contributed by authors of 18 nationalities * Chronological table of main events in the development of mathematics * Fully integrated index of people, events and topics * Annotated bibliographies of both classic and contemporary sources * Unique coverage of Ancient and non-Western traditions of mathematics

A History of Greek Mathematics, Volume I

From Thales to Euclid

Author: Sir Thomas Heath

Publisher: Courier Corporation

ISBN: 0486162699

Category: Mathematics

Page: 464

View: 562

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Volume 1 of an authoritative two-volume set that covers the essentials of mathematics and features every landmark innovation and every important figure, including Euclid, Apollonius, Archimedes, and others.

Enlightening Symbols

A Short History of Mathematical Notation and Its Hidden Powers

Author: Joseph Mazur

Publisher: Princeton University Press

ISBN: 1400850118

Category: Mathematics

Page: 312

View: 5702

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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.

Amazing Traces of a Babylonian Origin in Greek Mathematics

Author: J”ran Friberg

Publisher: World Scientific

ISBN: 9812704523

Category: Science

Page: 476

View: 747

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The sequel to Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific, 2005), this book is based on the author's intensive and ground breaking studies of the long history of Mesopotamian mathematics, from the late 4th to the late 1st millennium BC. It is argued in the book that several of the most famous Greek mathematicians appear to have been familiar with various aspects of Babylonian “metric algebra,” a convenient name for an elaborate combination of geometry, metrology, and quadratic equations that is known from both Babylonian and pre-Babylonian mathematical clay tablets. The book's use of “metric algebra diagrams” in the Babylonian style, where the side lengths and areas of geometric figures are explicitly indicated, instead of wholly abstract “lettered diagrams” in the Greek style, is essential for an improved understanding of many interesting propositions and constructions in Greek mathematical works. The author's comparisons with Babylonian mathematics also lead to new answers to some important open questions in the history of Greek mathematics.

An Episodic History of Mathematics

Mathematical Culture Through Problem Solving

Author: Steven G. Krantz

Publisher: MAA

ISBN: 0883857669

Category: Mathematics

Page: 381

View: 3182

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An Episodic History of Mathematics will acquaint students and readers with mathematical language, thought, and mathematical life by means of historically important mathematical vignettes. It will also serve to help prospective teachers become more familiar with important ideas of in the history of mathematicsboth classical and modern.Contained within are wonderful and engaging stories and anecdotes about Pythagoras and Galois and Cantor and Poincar, which let readers indulge themselves in whimsy, gossip, and learning. The mathematicians treated here were complex individuals who led colorful and fascinating lives, and did fascinating mathematics. They remain interesting to us as people and as scientists.This history of mathematics is also an opportunity to have some fun because the focus in this text is also on the practicalgetting involved with the mathematics and solving problems. This book is unabashedly mathematical. In the course of reading this book, the neophyte will become involved with mathematics by working on the same problems that, for instance, Zeno and Pythagoras and Descartes and Fermat and Riemann worked on.This is a book to be read, therefore, with pencil and paper in hand, and a calculator or computer close by. All will want to experiment; to try things; and become a part of the mathematical process.

A Commentary on Plato's Meno

Author: Jacob Klein

Publisher: University of Chicago Press

ISBN: 9780226439594

Category: Philosophy

Page: 256

View: 4182

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The Meno, one of the most widely read of the Platonic dialogues, is seen afresh in this original interpretation that explores the dialogue as a theatrical presentation. Just as Socrates's listeners would have questioned and examined their own thinking in response to the presentation, so, Klein shows, should modern readers become involved in the drama of the dialogue. Klein offers a line-by-line commentary on the text of the Meno itself that animates the characters and conversation and carefully probes each significant turn of the argument. "A major addition to the literature on the Meno and necessary reading for every student of the dialogue."—Alexander Seasonske, Philosophical Review "There exists no other commentary on Meno which is so thorough, sound, and enlightening."—Choice Jacob Klein (1899-1978) was a student of Martin Heidegger and a tutor at St. John's College from 1937 until his death. His other works include Plato's Trilogy: Theaetetus, the Sophist, and the Statesman, also published by the University of Chicago Press.