sourcebook in the mathematics of medieval europe and north africa

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Sourcebook In The Mathematics Of Medieval Europe And North Africa

Author : Victor J. Katz
ISBN : 9781400883202
Genre : Mathematics
File Size : 75. 46 MB
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Medieval Europe was a meeting place for the Christian, Jewish, and Islamic civilizations, and the fertile intellectual exchange of these cultures can be seen in the mathematical developments of the time. This sourcebook presents original Latin, Hebrew, and Arabic sources of medieval mathematics, and shows their cross-cultural influences. Most of the Hebrew and Arabic sources appear here in translation for the first time. Readers will discover key mathematical revelations, foundational texts, and sophisticated writings by Latin, Hebrew, and Arabic-speaking mathematicians, including Abner of Burgos's elegant arguments proving results on the conchoid—a curve previously unknown in medieval Europe; Levi ben Gershon’s use of mathematical induction in combinatorial proofs; Al-Mu’taman Ibn Hūd’s extensive survey of mathematics, which included proofs of Heron’s Theorem and Ceva’s Theorem; and Muhyī al-Dīn al-Maghribī’s interesting proof of Euclid’s parallel postulate. The book includes a general introduction, section introductions, footnotes, and references. The Sourcebook in the Mathematics of Medieval Europe and North Africa will be indispensable to anyone seeking out the important historical sources of premodern mathematics.

The Mathematics Of Egypt Mesopotamia China India And Islam

Author : Victor J. Katz
ISBN : 0691114854
Genre : Mathematics
File Size : 46. 92 MB
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In recent decades it has become obvious that mathematics has always been a worldwide activity. But this is the first book to provide a substantial collection of English translations of key mathematical texts from the five most important ancient and medieval non-Western mathematical cultures, and to put them into full historical and mathematical context. The Mathematics of Egypt, Mesopotamia, China, India, and Islam gives English readers a firsthand understanding and appreciation of these cultures' important contributions to world mathematics. The five section authors--Annette Imhausen (Egypt), Eleanor Robson (Mesopotamia), Joseph Dauben (China), Kim Plofker (India), and J. Lennart Berggren (Islam)--are experts in their fields. Each author has selected key texts and in many cases provided new translations. The authors have also written substantial section introductions that give an overview of each mathematical culture and explanatory notes that put each selection into context. This authoritative commentary allows readers to understand the sometimes unfamiliar mathematics of these civilizations and the purpose and significance of each text. Addressing a critical gap in the mathematics literature in English, this book is an essential resource for anyone with at least an undergraduate degree in mathematics who wants to learn about non-Western mathematical developments and how they helped shape and enrich world mathematics. The book is also an indispensable guide for mathematics teachers who want to use non-Western mathematical ideas in the classroom.

Making And Breaking Mathematical Sense

Author : Roi Wagner
ISBN : 9781400883783
Genre : Mathematics
File Size : 53. 21 MB
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In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.

Episodes In The Mathematics Of Medieval Islam

Author : J.L. Berggren
ISBN : 9781493937806
Genre : Mathematics
File Size : 26. 80 MB
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This book presents an account of selected topics from key mathematical works of medieval Islam, based on the Arabic texts themselves. Many of these works had a great influence on mathematics in Western Europe. Topics covered in the first edition include arithmetic, algebra, geometry, trigonometry, and numerical approximation; this second edition adds number theory and combinatorics. Additionally, the author has included selections from the western regions of medieval Islam—both North Africa and Spain. The author puts the works into their historical context and includes numerous examples of how mathematics interacted with Islamic society.

Handbook Of Discrete And Combinatorial Mathematics

Author : Kenneth H. Rosen
ISBN : 9781351644051
Genre : Mathematics
File Size : 47. 57 MB
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Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.

Plato S Forms Mathematics And Astronomy

Author : Theokritos Kouremenos
ISBN : 9783110601862
Genre : Literary Criticism
File Size : 41. 50 MB
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Plato's view that mathematics paves the way for his philosophy of forms is well known. This book attempts to flesh out the relationship between mathematics and philosophy as Plato conceived them by proposing that in his view, although it is philosophy that came up with the concept of beings, which he calls forms, and highlighted their importance, first to natural philosophy and then to ethics, the things that do qualify as beings are inchoately revealed by mathematics as the raw materials that must be further processed by philosophy (mathematicians, to use Plato's simile in the Euthedemus, do not invent the theorems they prove but discover beings and, like hunters who must hand over what they catch to chefs if it is going to turn into something useful, they must hand over their discoveries to philosophers). Even those forms that do not bear names of mathematical objects, such as the famous forms of beauty and goodness, are in fact forms of mathematical objects. The first chapter is an attempt to defend this thesis. The second argues that for Plato philosophy's crucial task of investigating the exfoliation of the forms into the sensible world, including the sphere of human private and public life, is already foreshadowed in one of its branches, astronomy.

A Brief History Of Numbers

Author : Leo Corry
ISBN : 9780191007064
Genre : Mathematics
File Size : 63. 34 MB
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The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century. Focusing on both foundational debates and practical use numbers, and showing how the story of numbers is intimately linked to that of the idea of equation, this book provides a valuable insight to numbers for undergraduate students, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics.

The Oxford Handbook Of Women And Gender In Medieval Europe

Author : Judith M. Bennett
ISBN : 9780191667299
Genre : History
File Size : 30. 22 MB
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The Oxford Handbook of Women and Gender in Medieval Europe provides a comprehensive overview of the gender rules encountered in Europe in the period between approximately 500 and 1500 C.E. The essays collected in this volume speak to interpretative challenges common to all fields of women's and gender history - that is, how best to uncover the experiences of ordinary people from archives formed mainly by and about elite males, and how to combine social histories of lived experiences with cultural histories of gendered discourses and identities. The collection focuses on Western Europe in the Middle Ages but offers some consideration of medieval Islam and Byzantium. The Handbook is structured into seven sections: Christian, Jewish, and Muslim thought; law in theory and practice; domestic life and material culture; labour, land, and economy; bodies and sexualities; gender and holiness; and the interplay of continuity and change throughout the medieval period. It contains material from some of the foremost scholars in this field, and it not only serves as the major reference text in medieval and gender studies, but also provides an agenda for future new research.

Women S Lives In Medieval Europe

Author : Emilie Amt
ISBN : 9781134720606
Genre : History
File Size : 39. 23 MB
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Praise for the first edition: 'It is difficult to imagine another book in which one could find all this diverse material, and no doubt Amt's collection, in its richness, and in its genuine clarity and simplicity will takes prominent place in our expanded, diversified medieval curriculum, a curriculum that takes class, gender, and ethnicity as central to an understanding of world cultural history.' - The Medieval Review Long considered to be a definitive and truly groundbreaking collection of sources, Women’s Lives in Medieval Europe uniquely presents the everyday lives and experiences of women in the Middle Ages. This indispensible text has now been thoroughly updated and expanded to reflect new research, and includes previously unavailable source material. This new edition includes expanded sections on marriage and sexuality, and on peasant women and townswomen, as well as a new section on women and the law. There are brief introductions both to the period and to the individual documents, study questions to accompany each reading, a glossary of terms and a fully updated bibliography. Working within a multi-cultural framework, the book focuses not just on the Christian majority, but also present material about women in minority groups in Europe, such as Jews, Muslims, and those considered to be heretics. Incorporating both the laws, regulations and religious texts that shaped the way women lived their lives, and personal narratives by and about medieval women, the book is unique in examining women’s lives through the lens of daily activities, and in doing so as far as possible through the voices of women themselves.

Islam And The European Empires

Author : David Motadel
ISBN : 9780191645297
Genre : History
File Size : 86. 94 MB
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At the height of the imperial age, European powers ruled over most parts of the Islamic world. The British, French, Russian, and Dutch empires each governed more Muslims than any independent Muslim state. European officials believed Islam to be of great political significance, and were quite cautious when it came to matters of the religious life of their Muslim subjects. In the colonies, they regularly employed Islamic religious leaders and institutions to bolster imperial rule. At the same time, the European presence in Muslim lands was confronted by religious resistance movements and Islamic insurgency. Across the globe, from the West African savanna to the shores of Southeast Asia, Muslim rebels called for holy war against non-Muslim intruders. Islam and the European Empires presents the first comparative account of the engagement of all major European empires with Islam. Bringing together fifteen of the world's leading scholars in the field, the volume explores a wide array of themes, ranging from the accommodation of Islam under imperial rule to Islamic anti-colonial resistance. A truly global history of empire, the volume makes a major contribution not only to our knowledge of the intersection of Islam and imperialism, but also more generally to our understanding of religion and power in the modern world.

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