Author: Victor J. Katz, Karen Hunger Parshall

Publisher: Princeton University Press

ISBN: 1400850525

Pages: 504

Year: 2014-07-21

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What is algebra? For some, it is an abstract language of x's and y’s. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century. Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians. With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era. Taming the Unknown follows algebra’s remarkable growth through different epochs around the globe.

Author: John Derbyshire

Publisher: National Academies Press

ISBN: 030909657X

Pages: 390

Year: 2006-05-02

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Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages -- and it promises to be just what his die-hard fans have been waiting for. "Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel's proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics -- it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.

Author: Bartel L. van der Waerden

Publisher: Springer Science & Business Media

ISBN: 3642515991

Pages: 274

Year: 2013-06-29

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Author: Jacques Sesiano

Publisher: American Mathematical Soc.

ISBN: 0821844733

Pages: 174

Year: 2009

View: 361

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This text should not be viewed as a comprehensive history of algebra before 1600, but as a basic introduction to the types of problems that illustrate the earliest forms of algebra. It would be particularly useful for an instructor who is looking for examples to help enliven a course on elementary algebra with problems drawn from actual historical texts. --Warren Van Egmond about the French edition for MathSciNet This book does not aim to give an exhaustive survey of the history of algebra up to early modern times but merely to present some significant steps in solving equations and, wherever applicable, to link these developments to the extension of the number system. Various examples of problems, with their typical solution methods, are analyzed, and sometimes translated completely. Indeed, it is another aim of this book to ease the reader's access to modern editions of old mathematical texts, or even to the original texts; to this end, some of the problems discussed in the text have been reproduced in the appendices in their original language (Greek, Latin, Arabic, Hebrew, French, German, Provencal, and Italian) with explicative notes.

Author: Luke Hodgkin

Publisher: OUP Oxford

ISBN: 0191664367

Pages: 296

Year: 2013-02-21

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A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwarizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.

Author: Frank J. Swetz

Publisher: Courier Corporation

ISBN: 0486498050

Pages: 250

Year: 2013

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" A global survey of the history of mathematics, this newly corrected and updated collection of 32 highly readable essays features contributions by such distinguished educators as Carl Boyer and Morris Kline. Fascinating articles explore studies by Fibonacci, Descartes, Cardano, Kepler, Galileo, Pascal, Newton, Euler, and others. Suitable for readers with no background in math"--

Author: N. Balakrishnan, V. B. Nevzorov

Publisher: John Wiley & Sons

ISBN: 0471722219

Pages: 305

Year: 2004-12-04

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Designed as an introduction to statistical distribution theory. * Includes a first chapter on basic notations and definitions that are essential to working with distributions. * Remaining chapters are divided into three parts: Discrete Distributions, Continuous Distributions, and Multivariate Distributions. * Exercises are incorporated throughout the text in order to enhance understanding of materials just taught.

Author:

Publisher: McGraw-Hill Higher Education

ISBN: 0077419219

Pages:

Year: 2011

View: 308

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Author: Karen Hunger Parshall, Michael Thomson Walton, Bruce T. Moran

Publisher:

ISBN: 1612481345

Pages: 330

Year: 2015-05-01

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This book explores the connections between apparently different zones of comprehension and experience -- magic and experiment, alchemy and mechanics, practical mathematics and geometrical mysticism, things earthy and heavenly, and especially science and medicine -- by focusing on points of intersection among alchemy, chemistry, and Paracelsian medical philosophy. In exploring the varieties of natural knowledge in the early modern era, the authors pay tribute to the work of Allen Debus, whose own endeavours cleared the way for scholars to examine subjects that were once snubbed as suitable only to the refuse heap of the history of science.

Author: Teresa Bradley

Publisher: John Wiley & Sons

ISBN: 1118358295

Pages: 688

Year: 2013-05-06

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Containing numerous worked examples and exercises, this text aims to help students improve their understanding of key concepts and to develop stronger mathematical skills.

Author: Ian Hacking

Publisher: Cambridge University Press

ISBN: 1107729823

Pages: 212

Year: 2014-01-30

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This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.

Author: Timothy Goodman, Jessica Walsh

Publisher: ABRAMS

ISBN: 1613127154

Pages: 304

Year: 2015-01-20

View: 331

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“What would happen if Harry met Sally in the age of Tinder and Snapchat? . . . A field guide to Millennial dating in New York City” (New York Daily News). When New York–based graphic designers and long-time friends Timothy Goodman and Jessica Walsh found themselves single at the same time, they decided to try an experiment. The old adage says that it takes 40 days to change a habit—could the same be said for love? So they agreed to date each other for 40 days, record their experiences in questionnaires, photographs, videos, texts, and artworks, and post the material on a website they would create for this purpose. What began as a small experiment between two friends became an Internet sensation, drawing 5 million unique (and obsessed) visitors from around the globe to their site and their story. 40 Days of Dating: An Experiment is a beautifully designed, expanded look at the experiment and the results, including a great deal of material that never made it onto the site, such as who they were as friends and individuals before the 40 days and who they have become since.

Author: Ian Hacking

Publisher: Cambridge University Press

ISBN: 0521388848

Pages: 264

Year: 1990-08-31

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This book combines detailed scientific historical research with characteristic philosophic breadth and verve.

Author: John R. Durbin

Publisher: Wiley Global Education

ISBN: 1118117611

Pages: 352

Year: 2015-01-22

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Engineers and computer scientists who need a basic understanding of algebra will benefit from this accessible book. The sixth edition includes many carefully worked examples and proofs to guide them through abstract algebra successfully. It introduces the most important kinds of algebraic structures, and helps them improve their ability to understand and work with abstract ideas. New and revised exercise sets are integrated throughout the first four chapters. A more in-depth discussion is also included on Galois Theory. The first six chapters provide engineers and computer scientists with the core of the subject and then the book explores the concepts in more detail.

Author: Roger L. Cooke

Publisher: John Wiley & Sons

ISBN: 0470277971

Pages: 192

Year: 2008-05-16

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This insightful book combines the history, pedagogy, and popularization of algebra to present a unified discussion of the subject. Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors. This book successfully ties together the disconnect between classical and modern algebraand provides readers with answers to many fascinating questions that typically go unexamined, including: What is algebra about? How did it arise? What uses does it have? How did it develop? What problems and issues have occurred in its history? How were these problems and issues resolved? The author answers these questions and more, shedding light on a rich history of the subject—from ancient and medieval times to the present. Structured as eleven "lessons" that are intended to give the reader further insight on classical algebra, each chapter contains thought-provoking problems and stimulating questions, for which complete answers are provided in an appendix. Complemented with a mixture of historical remarks and analyses of polynomial equations throughout, Classical Algebra: Its Nature, Origins, and Uses is an excellent book for mathematics courses at the undergraduate level. It also serves as a valuable resource to anyone with a general interest in mathematics.