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Author: Victor J. Katz
Publisher: Princeton University Press
ISBN: 0691204071
Category : Mathematics
Languages : en
Pages : 502
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Book Description
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: Victor J. Katz
Publisher: Princeton University Press
ISBN: 0691204071
Category : Mathematics
Languages : en
Pages : 502
Get Book
Book Description
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: Jacques Sesiano
Publisher: American Mathematical Soc.
ISBN: 0821844733
Category : Algebra
Languages : en
Pages : 187
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Book Description
Offers a basic introduction to the types of problems that illustrate the earliest forms of algebra. This book presents some significant steps in solving equations and, wherever applicable, to link these developments to the extension of the number system. It analyzes various examples of problems, with their typical solution methods.
Author: Hans Christian Von Baeyer
Publisher: Courier Corporation
ISBN: 9780486414478
Category : Science
Languages : en
Pages : 276
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Book Description
Fascinating, accessible study recounts the process of discovery, from atomism of the Greeks to quantum revolutions of the 1920s and the theories and conjectures of today. Topics include components of the atom, quantum mechanics, atomic landscape, atoms in isolation, more. "Lucid and entertaining." — The New York Times Book Review.
Author: Robert William Bennett
Publisher: Stanford University Press
ISBN: 9780804754101
Category : Political Science
Languages : en
Pages : 292
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Book Description
This book examines the history and weaknesses of the electoral college and proposes reforms that could be made to our electoral process without a constitutional amendment.
Author: Jeffrey M. Binder
Publisher: University of Chicago Press
ISBN: 0226822540
Category : Computers
Languages : en
Pages : 328
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Book Description
A wide-ranging history of the algorithm. Bringing together the histories of mathematics, computer science, and linguistic thought, Language and the Rise of the Algorithm reveals how recent developments in artificial intelligence are reopening an issue that troubled mathematicians well before the computer age: How do you draw the line between computational rules and the complexities of making systems comprehensible to people? By attending to this question, we come to see that the modern idea of the algorithm is implicated in a long history of attempts to maintain a disciplinary boundary separating technical knowledge from the languages people speak day to day. Here Jeffrey M. Binder offers a compelling tour of four visions of universal computation that addressed this issue in very different ways: G. W. Leibniz’s calculus ratiocinator; a universal algebra scheme Nicolas de Condorcet designed during the French Revolution; George Boole’s nineteenth-century logic system; and the early programming language ALGOL, short for algorithmic language. These episodes show that symbolic computation has repeatedly become entangled in debates about the nature of communication. Machine learning, in its increasing dependence on words, erodes the line between technical and everyday language, revealing the urgent stakes underlying this boundary. The idea of the algorithm is a levee holding back the social complexity of language, and it is about to break. This book is about the flood that inspired its construction.
Author: Rick Carson
Publisher: Harper Collins
ISBN: 0061977861
Category : Self-Help
Languages : en
Pages : 194
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Book Description
The completely updated edition of this classic includes powerful methods for freeing oneself from self-defeating behaviors and beliefs Your gremlin interprets your every experience. He has nothing good to say about you or anything you do. Just when you feel you’ve out-argued him, he changes his strategy. Grapple with him and you become more enmeshed. What he hates is simply being noticed. That’s the first step to his taming. This and many other powerful techniques await you. This is a low-key but tremendously effective approach to banishing the tenacious nemesis within. Readers will learn: How simply noticing their gremlin is the first step in gremlin taming. How to experiment playfully with new actions and attitudes. Simple exercises for tuning in to their true self and tuning out their gremlin…and much more.
Author: Anne Chittleborough
Publisher: Wakefield Press
ISBN: 9781862546035
Category : South Australia
Languages : en
Pages : 250
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Book Description
In 1802 a Frenchman and an Englishman famously encountered each other off the shores of South Australia. The voyages of discovery of Nicolas Baudin and Matthew Flinders opened the way for the increasingly rapid colonisation of 'Terra Australis'.
Author: Susan Anderson
Publisher: New World Library
ISBN: 1608683141
Category : Self-Help
Languages : en
Pages : 298
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Book Description
Take Control of Your Life Chances are, you’ve already had run-ins with your Outer Child — the self-sabotaging, bungling, and impulsive part of your personality. This misguided, hidden nemesis blows your diet, overspends, and ruins your love life. Your Outer Child acts out and fulfills your legitimate childlike needs and wants in the wrong place, at the wrong time, and in counterproductive ways: It goes for immediate gratification and the quick fix in spite of your best-laid plans. Now, in a revolutionary rethinking of the link between emotion and behavior, veteran psychotherapist Susan Anderson offers a three-step program to tame your Outer Child’s destructive behavior. This dynamic, transformational set of strategies — action steps that act like physical therapy for the brain — calms your Inner Child, strengthens your Adult Self, releases you from the self-blame and shame at the root of Outer Child issues, and paves new neural pathways that can lead to more productive behavior. The result is happiness, fulfillment, self-mastery, and self-love.
Author: Kenneth Morgan
Publisher: Bloomsbury Publishing
ISBN: 1350154784
Category : History
Languages : en
Pages : 352
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Book Description
In this comprehensive study, Kenneth Morgan provides an authoritative account of European exploration and discovery in Australia. The book presents a detailed chronological overview of European interests in the Australian continent, from initial speculations about the 'Great Southern Land' to the major hydrographic expeditions of the 19th century. In particular, he analyses the early crossings of the Dutch in the 17th century, the exploits of English 'buccaneer adventurer' William Dampier, the famous voyages of James Cook and Matthew Flinders, and the little-known French annexation of Australia in 1772. Introducing new findings and drawing on the latest in historiographical research, this book situates developments in navigation, nautical astronomy and cartography within the broader contexts of imperial, colonial, and maritime history.
Author: Ehud R. Toledano
Publisher: Yale University Press
ISBN: 0300126182
Category : Social Science
Languages : en
Pages : 288
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Book Description
This groundbreaking book reconceptualizes slavery through the voices of enslaved persons themselves, voices that have remained silent in the narratives of conventional history. Focusing in particular on the Islamic Middle East from the late eighteenth to the early twentieth century, Ehud R. Toledano examines how bonded persons experienced enslavement in Ottoman societies. He draws on court records and a variety of other unexamined primary sources to uncover important new information about the Africans and Circassians who were forcibly removed from their own societies and transplanted to Middle East cultures that were alien to them. Toledano also considers the experiences of these enslaved people within the context of the global history of slavery. The book looks at the bonds of slavery from an original perspective, moving away from the traditional master/slave domination paradigm toward the point of view of the enslaved and their responses to their plight. With keen and original insights, Toledano suggests new ways of thinking about enslavement.
