Victor J. Katz - Böcker

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.

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.

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 H?d's extensive survey of mathematics, which included proofs of Heron's Theorem and Ceva's Theorem; and Muhy? al-D?n al-Maghrib?'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.

An invaluable reference book on the mathematics of Greek antiquityEuclid, Archimedes, and Apollonius are familiar names to many of us, and their contributions have shaped mathematical practice up to modern times. Yet the mathematical activity of Greek antiquity extended far beyond their achievements and was furthered by diverse individuals in different contexts. Sourcebook in the Mathematics of Ancient Greece and the Eastern Mediterranean brings together an extensive collection of primary source materials that document the extraordinary breadth of mathematical ideas developed in the Eastern Mediterranean from 500 BCE to 500 CE, a millennium in which Greek cultural influence spanned the ancient world.Weaving together ancient commentaries with the works themselves, Victor Katz and Clemency Montelle present a wealth of newly translated texts along with sources difficult to find elsewhere, from writings by the great mathematical thinkers of Greek antiquity to those by practitioners who used mathematics in everyday life. This comprehensive and wide-ranging sourcebook includes lesser-known authors who made critical contributions, sometimes in languages other than Greek, as well as accounts of technical instrumentation, papyri by anonymous authors designed for teaching purposes, and evidence of hand computations and numerical tables.An essential resource for anyone interested in the mathematical achievements of this remarkable intellectual culture, Sourcebook in the Mathematics of Ancient Greece and the Eastern Mediterranean encompasses disciplines that illustrate the important role of mathematics in ancient Greek society more broadly, from astronomy, music, and optics to philosophy, literature, and theater.