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Author: Victor J. Katz Publisher: Princeton University Press ISBN: 0691149054 Category : Mathematics Languages : en Pages : 504
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: 0691149054 Category : Mathematics Languages : en Pages : 504
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: John Derbyshire Publisher: National Academies Press ISBN: 030909657X Category : Science Languages : en Pages : 391
Book Description
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: Jeffrey M. Binder Publisher: University of Chicago Press ISBN: 0226822540 Category : Technology & Engineering Languages : en Pages : 328
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: Anne Chittleborough Publisher: Wakefield Press ISBN: 9781862546035 Category : South Australia Languages : en Pages : 250
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: Shaul Kelner Publisher: NYU Press ISBN: 1479859109 Category : Social Science Languages : en Pages : 393
Book Description
Reveals the mass mobilization tactics that helped free Soviet Jews and reshaped the Jewish American experience from the Johnson era through the Reagan–Bush years What do these things have in common? Ingrid Bergman, Passover matzoh, Banana Republic®, the fitness craze, the Philadelphia Flyers, B-grade spy movies, and ten thousand Bar and Bat Mitzvah sermons? Nothing, except that social movement activists enlisted them all into the most effective human rights campaign of the Cold War. The plight of Jews in the USSR was marked by systemic antisemitism, a problem largely ignored by Western policymakers trying to improve relations with the Soviets. In the face of governmental apathy, activists in the United States hatched a bold plan: unite Jewish Americans to demand that Washington exert pressure on Moscow for change. A Cold War Exodus delves into the gripping narrative of how these men and women, through ingenuity and determination, devised mass mobilization tactics during a three-decade-long campaign to liberate Soviet Jews—an endeavor that would ultimately lead to one of the most significant mass emigrations in Jewish history. Drawing from a wealth of archival sources including the travelogues of thousands of American tourists who smuggled aid to Russian Jews, Shaul Kelner offers a compelling tale of activism and its profound impact, revealing how a seemingly disparate array of elements could be woven together to forge a movement and achieve the seemingly impossible. It is a testament to the power of unity, creativity, and the unwavering dedication of those who believe in the cause of human rights.
Author: Rick Carson Publisher: Harper Collins ISBN: 0061977861 Category : Self-Help Languages : en Pages : 194
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: Robert William Bennett Publisher: Stanford University Press ISBN: 9780804754101 Category : Political Science Languages : en Pages : 292
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: Ehud R. Toledano Publisher: Yale University Press ISBN: 0300126182 Category : Social Science Languages : en Pages : 288
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.
Author: Kenneth Morgan Publisher: Bloomsbury Publishing ISBN: 1350154784 Category : History Languages : en Pages : 352
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: Victor J. Katz
Author: Victor J. Katz
Author: John Derbyshire
Author: Jeffrey M. Binder
Author: Anne Chittleborough
Author: Shaul Kelner
Author: Rick Carson
Author: Robert William Bennett
Author: Ehud R. Toledano
Author: Mary Cowden Clarke
Author: Kenneth Morgan