Advertisement
| diophantus of alexandria contributions to algebra: Great Moments in Mathematics (before 1650) Howard Whitley Eves, 1983 [V.2] This is a companion to Great moments in mathematics before 1650. It can be appreciated by anyone with a working knowledge of beginning deferential and integral calculus. Includes: the birth of mathematical probability, the invention of the differential calculus, the discovery of non-Euclidean geometry, the discovery of noncommutative algebra, and the resolution of the four-color problem. |
| diophantus of alexandria contributions to algebra: Diophantus of Alexandria Thomas L. Heath, 1910 |
| diophantus of alexandria contributions to algebra: Making up Numbers: A History of Invention in Mathematics Ekkehard Kopp, 2020-10-23 Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject. |
| diophantus of alexandria contributions to algebra: Science and Religion, 400 B.C. to A.D. 1550 Edward Grant, 2006-03-10 Grant illuminates how today's scientific culture originated with the religious thinkers of the Middle Ages. |
| diophantus of alexandria contributions to algebra: Ancient Mathematics Serafina Cuomo, 2005-08-19 The theorem of Pythagoras, Euclid's Elements, Archimedes' method to find the volume of a sphere: all parts of the invaluable legacy of ancient mathematics. But ancient mathematics was also about counting and measuring, surveying land and attributing mystical significance to the number six. This volume offers the first accessible survey of the discipline in all its variety and diversity of practices. The period covered ranges from the fifth century BC to the sixth century AD, with the focus on the Mediterranean region. Topics include: * mathematics and politics in classical Greece * the formation of mathematical traditions * the self-image of mathematicians in the Graeco-Roman period * mathematics and Christianity * and the use of the mathematical past in late antiquity. |
| diophantus of alexandria contributions to algebra: An Introduction to Diophantine Equations Titu Andreescu, Dorin Andrica, Ion Cucurezeanu, 2010-09-02 This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques. |
| diophantus of alexandria contributions to algebra: Greek Mathematical Thought and the Origin of Algebra Jacob Klein, 2013-04-22 Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th-16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. 1968 edition. Bibliography. |
| diophantus of alexandria contributions to algebra: Travelling Mathematics - The Fate of Diophantos' Arithmetic Ad Meskens, 2010-09-24 In this book the author presents a comprehensive study of Diophantos’ monumental work known as Arithmetika, a highly acclaimed and unique set of books within the known Greek mathematical corpus. Its author, Diophantos, is an enigmatic figure of whom we know virtually nothing. Starting with Egyptian, Babylonian and early Greek mathematics the author paints a picture of the sources the Arithmetika may have had. Life in Alexandria, where Diophantos lived, is described and, on the basis of the limited available evidence, his biography is outlined. Of Arithmetika’s 13 books only 6 survive in Greek. It was not until 1971 that these were complemented by the discovery of 4 other books in an Arab translation. This allows the author to describe the structure, the contents and the mathematics of the Arithmetika in detail. Furthermore it is shown that Diophantos had a remarkable skill to solve higher degree equations. In the second part, the author draws our attention to the survival of Diophantos’ work in both Arab and European mathematical cultures. Once Xylander’s critical 1575 edition reached its European public, the fame of the Arithmetika grew. It was studied, translated and modified by such authors as Bombelli, Stevin and Viète. It reached its pinnacle of fame in 1621 with the publication of Bachet’s translation into Latin. The marginal notes by Fermat in his copy of Diophantos, including his famous “Last Theorem”, were the starting point of a whole new research subject: the theory of numbers. |
| diophantus of alexandria contributions to algebra: A History of Greek Mathematics Sir Thomas Little Heath, Thomas Little Heath, 1981-01-01 Volume 1 of an authoritative two-volume set that covers the essentials of mathematics and includes every landmark innovation and every important figure. This volume features Euclid, Apollonius, others. |
| diophantus of alexandria contributions to algebra: A History of Algebra Bartel L. van der Waerden, 2013-06-29 |
| diophantus of alexandria contributions to algebra: Introduction to Analytic Number Theory Tom M. Apostol, 1998-05-28 This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages.-—MATHEMATICAL REVIEWS |
| diophantus of alexandria contributions to algebra: Brill's Companion to the Reception of Ancient Rhetoric Sophia Papaioannou, Andreas Serafim, Michael Edwards, 2022 This volume, examining the reception of ancient rhetoric, aims to demonstrate that the past is always part of the present: in the ways in which decisions about crucial political, social and economic matters have been made historically; or in organic interaction with literature, philosophy and culture at the core of the foundation principles of Western thought and values. Analysis is meant to cover the broadest possible spectrum of considerations that focus on the totality of rhetorical species (i.e. forensic, deliberative and epideictic) as they are applied to diversified topics (including, but not limited to, language, science, religion, literature, theatre and other cultural processes (e.g. athletics), politics and leadership, pedagogy and gender studies) and cross-cultural, geographical and temporal contexts-- |
| diophantus of alexandria contributions to algebra: The Muslim Contribution to Mathematics Ali Abdullah Al-Daffa', 2020-09-10 This book, first published in 1977, discusses the Muslim contribution to mathematics during the golden age of Muslim learning from the seventh to the thirteenth century. It was during this period that Muslim culture exerted powerful economic, political and religious influence over a large part of the civilised world. The work of the Muslim scholars was by no means limited to religion, business and government. They researched and extended the theoretical and applied science of the Greeks and Romans of an earlier era in ways that preserved and strengthened man’s knowledge in these important fields. Although the main object of this book is to trace the history of the Muslim contribution to mathematics during the European Dark Ages, some effort is made to explain the progress of mathematical thought and its effects upon present day culture. Certain Muslim mathematicians are mentioned because of the important nature of their ideas in the evolution of mathematical thinking during this earlier era. Muslim mathematicians invented the present arithmetical decimal system and the fundamental operations connected with it – addition, subtraction, multiplication, division, raising to a power, and extracting the square root and the cubic root. They also introduced the ‘zero’ symbol to Western culture which simplified considerably the entire arithmetical system and its fundamental operations; it is no exaggeration if it is said that this specific invention marks the turning point in the development of mathematics into a science. |
| diophantus of alexandria contributions to algebra: Diophantus of Alexandri Thomas L. Heath, 2008-06 This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work. |
| diophantus of alexandria contributions to algebra: Notes on Geometry and Arithmetic Daniel Coray, 2020-07-06 This English translation of Daniel Coray’s original French textbook Notes de géométrie et d’arithmétique introduces students to Diophantine geometry. It engages the reader with concrete and interesting problems using the language of classical geometry, setting aside all but the most essential ideas from algebraic geometry and commutative algebra. Readers are invited to discover rational points on varieties through an appealing ‘hands on’ approach that offers a pathway toward active research in arithmetic geometry. Along the way, the reader encounters the state of the art on solving certain classes of polynomial equations with beautiful geometric realizations, and travels a unique ascent towards variations on the Hasse Principle. Highlighting the importance of Diophantus of Alexandria as a precursor to the study of arithmetic over the rational numbers, this textbook introduces basic notions with an emphasis on Hilbert’s Nullstellensatz over an arbitrary field. A digression on Euclidian rings is followed by a thorough study of the arithmetic theory of cubic surfaces. Subsequent chapters are devoted to p-adic fields, the Hasse principle, and the subtle notion of Diophantine dimension of fields. All chapters contain exercises, with hints or complete solutions. Notes on Geometry and Arithmetic will appeal to a wide readership, ranging from graduate students through to researchers. Assuming only a basic background in abstract algebra and number theory, the text uses Diophantine questions to motivate readers seeking an accessible pathway into arithmetic geometry. |
| diophantus of alexandria contributions to algebra: Introduction to Number Theory Anthony Vazzana, Martin Erickson, David Garth, 2007-10-30 One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi |
| diophantus of alexandria contributions to algebra: A History of Elementary Mathematics Florian Cajori, 1898 |
| diophantus of alexandria contributions to algebra: The Foundations of Geometry and the Non-Euclidean Plane G.E. Martin, 2012-12-06 This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref erence if necessary. |
| diophantus of alexandria contributions to algebra: The Saga of Mathematics Marty Lewinter, William Widulski, 2001 For undergraduate-level courses in the History of Mathematics, or Liberal Arts Mathematics. Perfect for the non-math major, this inexpensive paperback text uses lively language to put mathematics in an interesting, historical context and points out the many links to art, philosophy, music, computers, navigation, science, and technology. The arithmetic, algebra, and geometry are presented in a way that makes them relevant to daily life as well as larger issues. |
| diophantus of alexandria contributions to algebra: Hypatia Edward J. Watts, 2017-02-01 A philosopher, mathematician, and martyr, Hypatia is one of antiquity's best known female intellectuals. During the sixteen centuries following her murder, by a mob of Christians, Hypatia has been remembered in books, poems, plays, paintings, and films as a victim of religious intolerance whose death symbolized the end of the Classical world. But Hypatia was a person before she was a symbol. Her great skill in mathematics and philosophy redefined the intellectual life of her home city of Alexandria. Her talent as a teacher enabled her to assemble a circle of dedicated male students. Her devotion to public service made her a force for peace and good government in a city that struggled to maintain trust and cooperation between pagans and Christians. Despite these successes, Hypatia fought countless small battles to live the public and intellectual life that she wanted. This book rediscovers the life Hypatia led, the unique challenges she faced as a woman who succeeded spectacularly in a man's world, and the tragic story of the events that led to her tragic murder. |
| diophantus of alexandria contributions to algebra: Recreations in Mathematics and Natural Philosophy, Recomposed by M. Montucla and Tr. by C. Hutton Jacques Ozanam, 2022-10-27 This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. |
| diophantus of alexandria contributions to algebra: Episodes in the History of Modern Algebra (1800-1950) Jeremy J. Gray, Karen Hunger Parshall, 2011-08-31 Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call modern algebra is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a ``rising sea'' in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics. |
| diophantus of alexandria contributions to algebra: The Development of Mathematics Throughout the Centuries Brian Evans, 2014-02-24 Throughout the book, readers take a journey throughout time and observe how people around the world have understood these patterns of quantity, structure, and dimension around them. The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Contex provides a brief overview of the history of mathematics in a very straightforward and understandable manner and also addresses major findings that influenced the development of mathematics as a coherent discipline. This book: Highlights the contributions made by various world cultures including African, Egyptian, Babylonian, Chinese, Indian, Islamic, and pre-Columbian American mathematics Features an approach that is not too rigorous and is ideal for a one-semester course of the history of mathematics. Includes a Resources and Recommended Reading section for further exploration and has been extensively classroom-tested |
| diophantus of alexandria contributions to algebra: Euclid's Elements A. C. McKay, R. A. Thompson, 2016-08-26 This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. |
| diophantus of alexandria contributions to algebra: Score Stars Pasquale De Marco, 2025-05-23 In a world where math is often seen as a daunting and inaccessible subject, this book is a beacon of hope for students who want to conquer their fear of numbers and unlock their full potential. Written in a clear and engaging style, this book takes readers on a journey through the world of mathematics, revealing its beauty and power. With comprehensive coverage of all the essential math topics that students need to know for success in high school and beyond, this book is the perfect resource for students who want to build a strong foundation in the subject. From basic algebra to calculus, the book covers everything in a way that is easy to understand and apply. But this book is more than just a math textbook. It's also a guide to help students develop the mindset and skills they need to succeed in math class and beyond. With chapters on study skills, test-taking strategies, and math anxiety, this book provides students with the tools they need to overcome challenges and achieve their goals. Whether you're a student who is struggling with math or a parent who wants to help your child succeed, this book is for you. With its clear explanations, engaging examples, and helpful tips, this book will help you conquer your fear of math and achieve your full potential. This book is more than just a math textbook. It's a guide to help students understand and appreciate the beauty of mathematics. It's a book that will inspire students to pursue their dreams and achieve their full potential. In this book, you'll discover: * Clear and concise explanations of all the essential math topics * Engaging examples and practice problems to help you learn * Tips and strategies for overcoming math anxiety * Study skills and test-taking strategies to help you succeed in math class * A deeper understanding of the beauty and power of mathematics If you like this book, write a review on google books! |
| diophantus of alexandria contributions to algebra: Mathematical Thought From Ancient to Modern Times Morris Kline, 1990-03 Traces the development of mathematics from its beginnings in Babylonia and ancient Egypt to the work of Riemann and Godel in modern times. |
| diophantus of alexandria contributions to algebra: The Facts on File Algebra Handbook Deborah Todd, 2014-05-14 Contains a history of the subject of algebra with over 350 entries providing definitions and explanations of related topics, plus brief biographies of over 100 mathematicians. |
| diophantus of alexandria contributions to algebra: Math Insights Tb S1a S/e , 2007 |
| diophantus of alexandria contributions to algebra: A Glimpse into the Golden Age Pasquale De Marco, 2025-05-10 **A Glimpse into the Golden Age takes you on a journey through the Golden Age of ancient Greece, a time of unparalleled cultural, scientific, and technological advancement.** In this book, you will learn about the great philosophers, artists, and writers of the Golden Age, including Socrates, Plato, Aristotle, Sophocles, and Euripides. You will also learn about the important scientific and technological discoveries of the Greeks, such as the development of mathematics, astronomy, and medicine. **A Glimpse into the Golden Age is a comprehensive guide to the Golden Age, written in a clear and concise style.** It is perfect for students, teachers, and anyone who is interested in learning more about this fascinating period of history. **Here is a brief overview of what you will find in A Glimpse into the Golden Age:** * A detailed overview of the political, social, and cultural history of the Golden Age * Biographies of the major figures of the Golden Age * An examination of the major philosophical, scientific, and technological achievements of the Golden Age * A discussion of the legacy of the Golden Age **A Glimpse into the Golden Age is the perfect way to learn about the Golden Age of ancient Greece.** Order your copy today! If you like this book, write a review on google books! |
| diophantus of alexandria contributions to algebra: Ptolemy's Almagest Ptolemy, 1998-11-08 Ptolemy's Almagest is one of the most influential scientific works in history. A masterpiece of technical exposition, it was the basic textbook of astronomy for more than a thousand years, and still is the main source for our knowledge of ancient astronomy. This translation, based on the standard Greek text of Heiberg, makes the work accessible to English readers in an intelligible and reliable form. It contains numerous corrections derived from medieval Arabic translations and extensive footnotes that take account of the great progress in understanding the work made in this century, due to the discovery of Babylonian records and other researches. It is designed to stand by itself as an interpretation of the original, but it will also be useful as an aid to reading the Greek text. |
| diophantus of alexandria contributions to algebra: Logic and Discrete Mathematics Willem Conradie, Valentin Goranko, 2015-04-28 A concise yet rigorous introduction to logic and discrete mathematics. This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical logic as well as practical applications through the easy to understand and use deductive systems of Semantic Tableaux and Resolution. The chapters on set theory, number theory, combinatorics and graph theory combine the necessary minimum of theory with numerous examples and selected applications. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in the accompanying solutions manual. Key Features: Suitable for a variety of courses for students in both Mathematics and Computer Science. Extensive, in-depth coverage of classical logic, combined with a solid exposition of a selection of the most important fields of discrete mathematics Concise, clear and uncluttered presentation with numerous examples. Covers some applications including cryptographic systems, discrete probability and network algorithms. Logic and Discrete Mathematics: A Concise Introduction is aimed mainly at undergraduate courses for students in mathematics and computer science, but the book will also be a valuable resource for graduate modules and for self-study. |
| diophantus of alexandria contributions to algebra: Diophantus of Alexandria -A Study in the History of Greek Algebra Sir Thomas L. Heath, 2008-11 This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 Excerpt: ...earth. r' = radius of moon, or other body. P = moon's horizontal parallax = earth's angular semidiameter as seen from the moon. f = moon's angular semidiameter. Now = P (in circular measure), r'-r = r (in circular measure);.'. r: r':: P: P', or (radius of earth): (radios of moon):: (moon's parallax): (moon's semidiameter). Examples. 1. Taking the moon's horizontal parallax as 57', and its angular diameter as 32', find its radius in miles, assuming the earth's radius to be 4000 miles. Here moon's semidiameter = 16';.-. 4000::: 57': 16';.-. r = 400 16 = 1123 miles. 2. The sun's horizontal parallax being 88, and his angular diameter 32V find his diameter in miles. ' Am. 872,727 miles. 3. The synodic period of Venus being 584 days, find the angle gained in each minute of time on the earth round the sun as centre. Am. l-54 per minute. 4. Find the angular velocity with which Venus crosses the sun's disc, assuming the distances of Venus and the earth from the sun are as 7 to 10, as given by Bode's Law. Since (fig. 50) S V: VA:: 7: 3. But Srhas a relative angular velocity round the sun of l-54 per minute (see Example 3); therefore, the relative angular velocity of A V round A is greater than this in the ratio of 7: 3, which gives an approximate result of 3-6 per minute, the true rate being about 4 per minute. Annual ParaUax. 95. We have already seen that no displacement of the observer due to a change of position on the earth's surface could apparently affect the direction of a fixed star. However, as the earth in its annual motion describes an orbit of about 92 million miles radius round the sun, the different positions in space from which an observer views the fixed stars from time to time throughout the year must be separated ... |
| diophantus of alexandria contributions to algebra: Mathematics: A Concise History and Philosophy W.S. Anglin, 2012-12-06 This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathemat ics majors, philosophy students, history of science students, and (future) secondary school mathematics teachers. The only prerequisite is a solid command of precalculus mathematics. On the one hand, this book is designed to help mathematics majors ac quire a philosophical and cultural understanding of their subject by means of doing actual mathematical problems from different eras. On the other hand, it is designed to help philosophy, history, and education students come to a deeper understanding of the mathematical side of culture by means of writing short essays. The way I myself teach the material, stu dents are given a choice between mathematical assignments, and more his torical or philosophical assignments. (Some sample assignments and tests are found in an appendix to this book. ) This book differs from standard textbooks in several ways. First, it is shorter, and thus more accessible to students who have trouble coping with vast amounts of reading. Second, there are many detailed explanations of the important mathematical procedures actually used by famous mathe maticians, giving more mathematically talented students a greater oppor tunity to learn the history and philosophy by way of problem solving. |
| diophantus of alexandria contributions to algebra: The Crest of the Peacock George Gheverghese Joseph, 1992 |
| diophantus of alexandria contributions to algebra: The Britannica Guide to Algebra and Trigonometry William L. Hosch Associate Editor, Science and Technology, 2010-08-15 Presents the concepts and applications of algebra and trigonometry, including information on the people behind the math and explanations to enhance understanding. |
| diophantus of alexandria contributions to algebra: Elements of Algebra Leonhard Euler, 1810 |
| diophantus of alexandria contributions to algebra: Līlāvatī of Bhāskarācārya Bhāskarācārya, 2001 In 1150 AD, Bhaskaracarya (b. 1114 AD), renowned mathematician and astronomer of Vedic tradition composed Lilavati as the first part of his larger work called Siddhanta Siromani, a comprehensive exposition of arithmetic, algebra, geometry, mensuration, number theory and related topics. Lilavati has been used as a standard textbook for about 800 years. This lucid, scholarly and literary presentation has been translated into several languages of the world. Bhaskaracarya himself never gave any derivations of his formulae. N.H. Phadke (1902-1973) worked hard to construct proofs of several mathematical methods and formulae given in original Lilavati. The present work is an enlargement of his Marathi work and attempts a thorough mathematical explanation of definitions, formulae, short cuts and methodology as intended by Bhaskara. Stitches are followed by literal translations so that the reader can enjoy and appreciate the beauty of accurate and musical presentation in Lilavati. The book is useful to school going children, sophomores, teachers, scholars, historians and those working for cause of mathematics. |
| diophantus of alexandria contributions to algebra: Numbers, Groups and Codes J. F. Humphreys, M. Y. Prest, 2004-05-13 This textbook is an introduction to algebra via examples. The book moves from properties of integers, through other examples, to the beginnings of group theory. Applications to public key codes and to error correcting codes are emphasised. These applications, together with sections on logic and finite state machines, make the text suitable for students of computer science as well as mathematics students. Attention is paid to historical development of the mathematical ideas. This second edition contains new material on mathematical reasoning skills and a new chapter on polynomials has been added. The book was developed from first-level courses taught in the UK and USA. These courses proved successful in developing not only a theoretical understanding but also algorithmic skills. This book can be used at a wide range of levels: it is suitable for first- or second-level university students, and could be used as enrichment material for upper-level school students. |
| diophantus of alexandria contributions to algebra: Sherlock Holmes in Babylon and Other Tales of Mathematical History Marlow Anderson, Victor Katz, Robin Wilson, 2022-04-26 Covering a span of almost 4000 years, from the ancient Babylonians to the eighteenth century, this collection chronicles the enormous changes in mathematical thinking over this time as viewed by distinguished historians of mathematics from the past and the present. Each of the four sections of the book (Ancient Mathematics, Medieval and Renaissance Mathematics, The Seventeenth Century, The Eighteenth Century) is preceded by a Foreword, in which the articles are put into historical context, and followed by an Afterword, in which they are reviewed in the light of current historical scholarship. In more than one case, two articles on the same topic are included to show how knowledge and views about the topic changed over the years. This book will be enjoyed by anyone interested in mathematics and its history - and, in particular, by mathematics teachers at secondary, college, and university levels. |
| diophantus of alexandria contributions to algebra: The Little Book of Almost Everything carl scutt, 2023-02-15 Your guide to social mobility on every occasion. Never be stuck for something to say in the company of strangers and new friends with The little book of almost everything. Knowing everything is impossible but knowing a little about a lot gives you the upper hand in any situation. With The little book of almost everything you will be in the procession of basic knowledge and understanding of a wide range of subjects, making you the person with the broadest range and appeal. This book is a comprehensive exploration of multiple subjects, including Art, Humanities, Technology, Science, Health, Philosophy, Civilisations, and Humans. By examining the intersections between these areas, I hope to offer a broad understanding of the world we inhabit and our place in it. Whether you are an academic, a curious reader, or someone who simply seeks to expand your horizons, this book provides a wealth of knowledge and insights to enhance your understanding of the multifaceted world around us. So, come on this journey of discovery and explore the many fascinating facets of human experience. |
Diophantus' Lifespan - Mathematics Stack Exchange
Today I saw Diophantus' Epitaph. For those of you who don't know it and don't feel like googling: 'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone tells how old: 'God...
reference request - Is there an English translation of Diophantus's ...
Aug 24, 2011 · Is Heath's book really a translation? It seems more like a book ABOUT Diophantus's "Arithmetica", not the translation of the actual book. There's just an "abstract" …
How to solve the problem that determines the age of Diophantus?
Let D D be the number of years Diophantus lived, and S S the number of years his son lived. First we make an obvious relation, that his son lived for half his own lifetime.
Are problems in "Arithmetica" of Diophantus all solved now?
Jan 31, 2019 · It's well-known that Diophantus had written ”Diophantus“ which contains many problems about solving arithmetic equations. I wonder whether all of them has been solved …
Fermat's Notes on Diophantus - Mathematics Stack Exchange
Aug 17, 2016 · I am looking for a free online copy of Diophantus' Arithmetica as well as Fermat's Notes on it. After some google searching, I couldn't find any. Thanks for your help! Edit: …
How to find solutions of linear Diophantine ax + by = c?
The diophantine equation ax + by = c has solutions if and only if gcd(a, b) c. If so, it has infinitely many solutions, and any one solution can be used to generate all the other ones. To see this, …
abstract algebra - Diophantus math - Mathematics Stack Exchange
Diophantus math Ask Question Asked 11 years, 7 months ago Modified 11 years, 7 months ago
Nonlinear system Diophantus. - Mathematics Stack Exchange
Aug 18, 2015 · In the extant books of Diophantus, are considered in the system of equations. Of interest is the non-linear system of Diophantine equations. Some simple systems from his …
Question on proving Primitive Pythagorean triples using …
Jan 25, 2020 · Question on proving Primitive Pythagorean triples using Diophantus method? [duplicate] Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago
abstract algebra - Diophantus mathematics - Mathematics Stack …
Find a number whose subtraction from two given numbers (say, $9$ and $21$) allows both differences to be squares. Call the required number $9 - x^2$ so that the condition holds …
Diophantus' Lifespan - Mathematics Stack Exchange
Today I saw Diophantus' Epitaph. For those of you who don't know it and don't feel like googling: 'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone tells how old: 'God...
reference request - Is there an English translation of Diophantus's ...
Aug 24, 2011 · Is Heath's book really a translation? It seems more like a book ABOUT Diophantus's "Arithmetica", not the translation of the actual book. There's just an "abstract" …
How to solve the problem that determines the age of Diophantus?
Let D D be the number of years Diophantus lived, and S S the number of years his son lived. First we make an obvious relation, that his son lived for half his own lifetime.
Are problems in "Arithmetica" of Diophantus all solved now?
Jan 31, 2019 · It's well-known that Diophantus had written ”Diophantus“ which contains many problems about solving arithmetic equations. I wonder whether all of them has been solved …
Fermat's Notes on Diophantus - Mathematics Stack Exchange
Aug 17, 2016 · I am looking for a free online copy of Diophantus' Arithmetica as well as Fermat's Notes on it. After some google searching, I couldn't find any. Thanks for your help! Edit: …
How to find solutions of linear Diophantine ax + by = c?
The diophantine equation ax + by = c has solutions if and only if gcd(a, b) c. If so, it has infinitely many solutions, and any one solution can be used to generate all the other ones. To see this, …
abstract algebra - Diophantus math - Mathematics Stack Exchange
Diophantus math Ask Question Asked 11 years, 7 months ago Modified 11 years, 7 months ago
Nonlinear system Diophantus. - Mathematics Stack Exchange
Aug 18, 2015 · In the extant books of Diophantus, are considered in the system of equations. Of interest is the non-linear system of Diophantine equations. Some simple systems from his book …
Question on proving Primitive Pythagorean triples using …
Jan 25, 2020 · Question on proving Primitive Pythagorean triples using Diophantus method? [duplicate] Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago
abstract algebra - Diophantus mathematics - Mathematics Stack …
Find a number whose subtraction from two given numbers (say, $9$ and $21$) allows both differences to be squares. Call the required number $9 - x^2$ so that the condition holds …
