Download or read book The Mathematics of Egypt Mesopotamia China India and Islam written by Victor J. Katz and published by Princeton University Press. This book was released on 2021-08-10 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Count Like an Egyptian written by David Reimer and published by Princeton University Press. This book was released on 2014-04-27 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lively collection of fun and challenging problems in ancient Egyptian math The mathematics of ancient Egypt was fundamentally different from our math today. Contrary to what people might think, it wasn't a primitive forerunner of modern mathematics. In fact, it can’t be understood using our current computational methods. Count Like an Egyptian provides a fun, hands-on introduction to the intuitive and often-surprising art of ancient Egyptian math. David Reimer guides you step-by-step through addition, subtraction, multiplication, and more. He even shows you how fractions and decimals may have been calculated—they technically didn’t exist in the land of the pharaohs. You’ll be counting like an Egyptian in no time, and along the way you’ll learn firsthand how mathematics is an expression of the culture that uses it, and why there’s more to math than rote memorization and bewildering abstraction. Reimer takes you on a lively and entertaining tour of the ancient Egyptian world, providing rich historical details and amusing anecdotes as he presents a host of mathematical problems drawn from different eras of the Egyptian past. Each of these problems is like a tantalizing puzzle, often with a beautiful and elegant solution. As you solve them, you’ll be immersed in many facets of Egyptian life, from hieroglyphs and pyramid building to agriculture, religion, and even bread baking and beer brewing. Fully illustrated in color throughout, Count Like an Egyptian also teaches you some Babylonian computation—the precursor to our modern system—and compares ancient Egyptian mathematics to today’s math, letting you decide for yourself which is better.
Download or read book An Illustrated Theory of Numbers written by Martin H. Weissman and published by American Mathematical Soc.. This book was released on 2020-09-15 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.
Download or read book Sourcebook in the Mathematics of Medieval Europe and North Africa written by Victor J. Katz and published by Princeton University Press. This book was released on 2016-11-01 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics in Ancient Iraq written by Eleanor Robson and published by Princeton University Press. This book was released on 2020-06-30 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monumental book traces the origins and development of mathematics in the ancient Middle East, from its earliest beginnings in the fourth millennium BCE to the end of indigenous intellectual culture in the second century BCE when cuneiform writing was gradually abandoned. Eleanor Robson offers a history like no other, examining ancient mathematics within its broader social, political, economic, and religious contexts, and showing that mathematics was not just an abstract discipline for elites but a key component in ordering society and understanding the world. The region of modern-day Iraq is uniquely rich in evidence for ancient mathematics because its prehistoric inhabitants wrote on clay tablets, many hundreds of thousands of which have been archaeologically excavated, deciphered, and translated. Drawing from these and a wealth of other textual and archaeological evidence, Robson gives an extraordinarily detailed picture of how mathematical ideas and practices were conceived, used, and taught during this period. She challenges the prevailing view that they were merely the simplistic precursors of classical Greek mathematics, and explains how the prevailing view came to be. Robson reveals the true sophistication and beauty of ancient Middle Eastern mathematics as it evolved over three thousand years, from the earliest beginnings of recorded accounting to complex mathematical astronomy. Every chapter provides detailed information on sources, and the book includes an appendix on all mathematical cuneiform tablets published before 2007.
Download or read book Mathematics in Ancient Egypt written by Annette Imhausen and published by Princeton University Press. This book was released on 2020-10-13 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of ancient Egyptian mathematics across three thousand years Mathematics in Ancient Egypt traces the development of Egyptian mathematics, from the end of the fourth millennium BC—and the earliest hints of writing and number notation—to the end of the pharaonic period in Greco-Roman times. Drawing from mathematical texts, architectural drawings, administrative documents, and other sources, Annette Imhausen surveys three thousand years of Egyptian history to present an integrated picture of theoretical mathematics in relation to the daily practices of Egyptian life and social structures. Imhausen shows that from the earliest beginnings, pharaonic civilization used numerical techniques to efficiently control and use their material resources and labor. Even during the Old Kingdom, a variety of metrological systems had already been devised. By the Middle Kingdom, procedures had been established to teach mathematical techniques to scribes in order to make them proficient administrators for their king. Imhausen looks at counterparts to the notation of zero, suggests an explanation for the evolution of unit fractions, and analyzes concepts of arithmetic techniques. She draws connections and comparisons to Mesopotamian mathematics, examines which individuals in Egyptian society held mathematical knowledge, and considers which scribes were trained in mathematical ideas and why. Of interest to historians of mathematics, mathematicians, Egyptologists, and all those curious about Egyptian culture, Mathematics in Ancient Egypt sheds new light on a civilization's unique mathematical evolution.
Download or read book A History of Mathematics written by Luke Hodgkin and published by OUP Oxford. This book was released on 2013-02-21 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Historical Modules for the Teaching and Learning of Mathematics written by Victor J. Katz and published by American Mathematical Soc.. This book was released on 2020-03-02 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A History of Mathematics written by Victor J. Katz and published by . This book was released on 2017-03-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is ideal for a junior or senior level course in the history of mathematics for mathematics majors intending to become teachers. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. A History of Mathematics, 3rd Edition, provides students with a solid background in the history of mathematics and focuses on the most important topics for today's elementary, high school, and college curricula. Students will gain a deeper understanding of mathematical concepts in their historical context, and future teachers will find this book a valuable resource in developing lesson plans based on the history of each topic.
Download or read book Naming Infinity written by Loren Graham and published by Harvard University Press. This book was released on 2009-03-31 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.
Download or read book Ancient Mesopotamia written by A. Leo Oppenheim and published by University of Chicago Press. This book was released on 2013-01-31 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This splendid work of scholarship . . . sums up with economy and power all that the written record so far deciphered has to tell about the ancient and complementary civilizations of Babylon and Assyria."—Edward B. Garside, New York Times Book Review Ancient Mesopotamia—the area now called Iraq—has received less attention than ancient Egypt and other long-extinct and more spectacular civilizations. But numerous small clay tablets buried in the desert soil for thousands of years make it possible for us to know more about the people of ancient Mesopotamia than any other land in the early Near East. Professor Oppenheim, who studied these tablets for more than thirty years, used his intimate knowledge of long-dead languages to put together a distinctively personal picture of the Mesopotamians of some three thousand years ago. Following Oppenheim's death, Erica Reiner used the author's outline to complete the revisions he had begun. "To any serious student of Mesopotamian civilization, this is one of the most valuable books ever written."—Leonard Cottrell, Book Week "Leo Oppenheim has made a bold, brave, pioneering attempt to present a synthesis of the vast mass of philological and archaeological data that have accumulated over the past hundred years in the field of Assyriological research."—Samuel Noah Kramer, Archaeology A. Leo Oppenheim, one of the most distinguished Assyriologists of our time, was editor in charge of the Assyrian Dictionary of the Oriental Institute and John A. Wilson Professor of Oriental Studies at the University of Chicago.
Download or read book Geminos s Introduction to the Phenomena written by James Evans and published by Princeton University Press. This book was released on 2018-06-05 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first complete English translation of Geminos's Introduction to the Phenomena--one of the most important and interesting astronomical works of its type to have survived from Greek antiquity. Gracefully and charmingly written, Geminos's first-century BC textbook for beginning students of astronomy can now be read straight through with understanding and enjoyment by a wider audience than ever before. James Evans and Lennart Berggren's accurate and readable translation is accompanied by a thorough introduction and commentary that set Geminos's work in its historical, scientific, and philosophical context. This book is generously illustrated with diagrams from medieval manuscripts of Geminos's text, as well as drawings and photographs of ancient astronomical instruments. It will be of great interest to students of the history of science, to classicists, and to professional and amateur astronomers who seek to learn more about the origins of their science. Geminos provides a clear view of Greek astronomy in the period between Hipparchos and Ptolemy, treating such subjects as the zodiac, the constellations, the theory of the celestial sphere, lunar cycles, and eclipses. Most significantly, Geminos gives us the earliest detailed discussion of Babylonian astronomy by a Greek writer, thus offering valuable insight into the cross-cultural transmission of astronomical knowledge in antiquity.
Download or read book How to Read Historical Mathematics written by Benjamin Wardhaugh and published by Princeton University Press. This book was released on 2010-03-01 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: Techniques for deciphering texts by early mathematicians Writings by early mathematicians feature language and notations that are quite different from what we're familiar with today. Sourcebooks on the history of mathematics provide some guidance, but what has been lacking is a guide tailored to the needs of readers approaching these writings for the first time. How to Read Historical Mathematics fills this gap by introducing readers to the analytical questions historians ask when deciphering historical texts. Sampling actual writings from the history of mathematics, Benjamin Wardhaugh reveals the questions that will unlock the meaning and significance of a given text—Who wrote it, why, and for whom? What was its author's intended meaning? How did it reach its present form? Is it original or a translation? Why is it important today? Wardhaugh teaches readers to think about what the original text might have looked like, to consider where and when it was written, and to formulate questions of their own. Readers pick up new skills with each chapter, and gain the confidence and analytical sophistication needed to tackle virtually any text in the history of mathematics. Introduces readers to the methods of textual analysis used by historians Uses actual source material as examples Features boxed summaries, discussion questions, and suggestions for further reading Supplements all major sourcebooks in mathematics history Designed for easy reference Ideal for students and teachers
Download or read book Heavenly Mathematics written by Glen Van Brummelen and published by Princeton University Press. This book was released on 2017-04-04 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth."--Jacket.
Download or read book Taming the Unknown written by Victor J. Katz and published by Princeton University Press. This book was released on 2014-07-21 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics in India written by Kim Plofker and published by Princeton University Press. This book was released on 2009-01-18 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic scientific traditions. Plofker shows that Indian mathematics appears not as a disconnected set of discoveries, but as a lively, diverse, yet strongly unified discipline, intimately linked to other Indian forms of learning. Far more than in other areas of the history of mathematics, the literature on Indian mathematics reveals huge discrepancies between what researchers generally agree on and what general readers pick up from popular ideas. This book explains with candor the chief controversies causing these discrepancies--both the flaws in many popular claims, and the uncertainties underlying many scholarly conclusions. Supplementing the main narrative are biographical resources for dozens of Indian mathematicians; a guide to key features of Sanskrit for the non-Indologist; and illustrations of manuscripts, inscriptions, and artifacts. Mathematics in India provides a rich and complex understanding of the Indian mathematical tradition. **Author's note: The concept of "computational positivism" in Indian mathematical science, mentioned on p. 120, is due to Prof. Roddam Narasimha and is explored in more detail in some of his works, including "The Indian half of Needham's question: some thoughts on axioms, models, algorithms, and computational positivism" (Interdisciplinary Science Reviews 28, 2003, 1-13).
Download or read book The Crest of the Peacock written by George Gheverghese Joseph and published by Penguin Group. This book was released on 1992 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
