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Taming The Unknown

Author: Victor J. Katz
Publisher: Princeton University Press
ISBN: 1400850525
Size: 56.58 MB
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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.

Unknown Quantity

Author: John Derbyshire
Publisher: National Academies Press
ISBN: 030909657X
Size: 42.41 MB
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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.

An Introduction To The History Of Algebra

Author: Jacques Sesiano
Publisher: American Mathematical Soc.
ISBN: 0821844733
Size: 42.25 MB
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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.

A History Of Mathematics

Author: Luke Hodgkin
Publisher: OUP Oxford
ISBN: 0191664367
Size: 55.90 MB
Format: PDF, Kindle
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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.

The European Mathematical Awakening

Author: Frank J. Swetz
Publisher: Courier Corporation
ISBN: 0486498050
Size: 48.33 MB
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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"--

A Primer On Statistical Distributions

Author: N. Balakrishnan
Publisher: John Wiley & Sons
ISBN: 9780471722212
Size: 53.81 MB
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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.

Bridging Traditions

Author: Karen Hunger Parshall
Publisher:
ISBN: 9781612481340
Size: 78.76 MB
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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.

Essential Mathematics For Economics And Business

Author: Teresa Bradley
Publisher: John Wiley & Sons
ISBN: 1118358295
Size: 79.45 MB
Format: PDF, Docs
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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.