Download or read book Books IV to VII of Diophantus Arithmetica written by Jacques Sesiano and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition of Books IV to VII of Diophantus' Arithmetica, which are extant only in a recently discovered Arabic translation, is the outgrowth of a doctoral dissertation submitted to the Brown University Department of the History of Mathematics in May 1975. Early in 1973, my thesis adviser, Gerald Toomer, learned of the existence of this manuscript in A. Gulchln-i Macanl's just-published catalogue of the mathematical manuscripts in the Mashhad Shrine Library, and secured a photographic copy of it. In Sep tember 1973, he proposed that the study of it be the subject of my dissertation. Since limitations of time compelled us to decide on priorities, the first objective was to establish a critical text and to translate it. For this reason, the Arabic text and the English translation appear here virtually as they did in my thesis. Major changes, however, are found in the mathematical com mentary and, even more so, in the Arabic index. The discussion of Greek and Arabic interpolations is entirely new, as is the reconstruction of the history of the Arithmetica from Diophantine to Arabic times. It is with the deepest gratitude that I acknowledge my great debt to Gerald Toomer for his constant encouragement and invaluable assistance.
Download or read book Diophantus of Alexandria written by Thomas L. Heath and published by CUP Archive. This book was released on 1910 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Adventurer s Guide to Number Theory written by Richard Friedberg and published by Courier Corporation. This book was released on 2012-07-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.
Download or read book An Introduction to Diophantine Equations written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Number Theory and Geometry An Introduction to Arithmetic Geometry written by Álvaro Lozano-Robledo and published by American Mathematical Soc.. This book was released on 2019-03-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
Download or read book Recreations in mathematics and natural philosophy recomposed by m Montucla and tr by C Hutton written by Jacques Ozanam and published by . This book was released on 1840 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Greek Mathematical Thought and the Origin of Algebra written by Jacob Klein and published by Courier Corporation. This book was released on 2013-04-22 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Amazing Traces of a Babylonian Origin in Greek Mathematics written by Jran Friberg and published by World Scientific. This book was released on 2007 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sequel to Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific, 2005), this book is based on the author's intensive and ground breaking studies of the long history of Mesopotamian mathematics, from the late 4th to the late 1st millennium BC. It is argued in the book that several of the most famous Greek mathematicians appear to have been familiar with various aspects of Babylonian “metric algebra,” a convenient name for an elaborate combination of geometry, metrology, and quadratic equations that is known from both Babylonian and pre-Babylonian mathematical clay tablets. The book's use of “metric algebra diagrams” in the Babylonian style, where the side lengths and areas of geometric figures are explicitly indicated, instead of wholly abstract “lettered diagrams” in the Greek style, is essential for an improved understanding of many interesting propositions and constructions in Greek mathematical works. The author's comparisons with Babylonian mathematics also lead to new answers to some important open questions in the history of Greek mathematics.
Download or read book Critical Mathematics Education written by Paul Ernest and published by IAP. This book was released on 2016-01-01 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is traditionally seen as the most neutral of disciplines, the furthest removed from the arguments and controversy of politics and social life. However, critical mathematics challenges these assumptions and actively attacks the idea that mathematics is pure, objective, and value?neutral. It argues that history, society, and politics have shaped mathematics—not only through its applications and uses but also through molding its concepts, methods, and even mathematical truth and proof, the very means of establishing truth. Critical mathematics education also attacks the neutrality of the teaching and learning of mathematics, showing how these are value?laden activities indissolubly linked to social and political life. Instead, it argues that the values of openness, dialogicality, criticality towards received opinion, empowerment of the learner, and social/political engagement and citizenship are necessary dimensions of the teaching and learning of mathematics, if it is to contribute towards democracy and social justice. This book draws together critical theoretic contributions on mathematics and mathematics education from leading researchers in the field. Recurring themes include: The natures of mathematics and critical mathematics education, issues of epistemology and ethics; Ideology, the hegemony of mathematics, ethnomathematics, and real?life education; Capitalism, globalization, politics, social class, habitus, citizenship and equity. The book demonstrates the links between these themes and the discipline of mathematics, and its critical teaching and learning. The outcome is a groundbreaking collection unified by a shared concern with critical perspectives of mathematics and education, and of the ways they impact on practice.
Download or read book The Arithmetica of Diophantus written by Jean Christianidis and published by Taylor & Francis. This book was released on 2022-11-01 with total page 891 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers an English translation of all ten extant books of Diophantus of Alexandria’s Arithmetica, along with a comprehensive conceptual, historical, and mathematical commentary. Before his work became the inspiration for the emerging field of number theory in the seventeenth century, Diophantus (ca. 3rd c. CE) was known primarily as an algebraist. This volume explains how his method of solving arithmetical problems agrees both conceptually and procedurally with the premodern algebra later practiced in Arabic, Latin, and European vernaculars, and how this algebra differs radically from the modern algebra initiated by François Viète and René Descartes. It also discusses other surviving traces of ancient Greek algebra and follows the influence of the Arithmetica in medieval Islam, Byzantium, and the European Renaissance down to the 1621 publication of Claude-Gaspard Bachet’s edition. After the English translation the book provides a problem-by-problem commentary explaining the solutions in a manner compatible with Diophantus’s mode of thought. The Arithmetica of Diophantus provides an invaluable resource for historians of mathematics, science, and technology, as well as those studying ancient Greek, medieval Islamic and Byzantine, and Renaissance history. In addition, the volume is also suitable for mathematicians and mathematics educators.
Download or read book Diophantus and Diophantine Equations written by Isabella Grigoryevna Bashmakova and published by American Mathematical Soc.. This book was released on 2019-01-29 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. This new treatment of the methods of Diophantus--a person whose very existence has long been doubted by most historians of mathematics--will be accessible to readers who have taken some university mathematics. It includes the elementary facts of algebraic geometry indispensable for its understanding. The heart of the book is a fascinating account of the development of Diophantine methods during the.
Download or read book Making up Numbers A History of Invention in Mathematics written by Ekkehard Kopp and published by Open Book Publishers. This book was released on 2020-10-23 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Elements of Algebra written by Leonhard Euler and published by . This book was released on 1810 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Arithmetic of Infinitesimals written by John Wallis and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Wallis (1616-1703) was the most influential English mathematician prior to Newton. He published his most famous work, Arithmetica Infinitorum, in Latin in 1656. This book studied the quadrature of curves and systematised the analysis of Descartes and Cavelieri. Upon publication, this text immediately became the standard book on the subject and was frequently referred to by subsequent writers. This will be the first English translation of this text ever to be published.
Download or read book The Fermat Diary written by Charles J. Mozzochi and published by American Mathematical Soc.. This book was released on 2000 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on the final chapter of the story of perhaps the most famous mathematics problem of our time: Fermat's Last Theorem. The full story begins in 1637, with Pierre de Fermat's enigmatic marginal note in his copy of Diophantus's Arithmetica. It ends with the spectacular solution by Andrew Wiles some 350 years later. The Fermat Diary provides a record in pictures and words of the dramatic time from June 1993 to August 1995, including the period when Wiles completed the last stages of the proof and concluding with the mathematical world's celebration of Wiles' result at Boston University. This diary takes us through the process of discovery as reported by those who worked on the great puzzle: Gerhard Frey who conjectured that Shimura-Taniyama implies Fermat; Ken Ribet who followed a difficult and speculative plan of attack suggested by Jean-Pierre Serre and established the statement by Frey; and Andrew Wiles who announced a proof of enough of the Shimura-Taniyama conjecture to settle Fermat's Last Theorem, only to announce months later that there was a gap in the proof. Finally, we are brought to the historic event on September 19, 1994, when Wiles, with the collaboration of Richard Taylor, dramatically closed the gap. The book follows the much-in-demand Wiles through his travels and lectures, finishing with the Instructional Conference on Number Theory and Arithmetic Geometry at Boston University. There are many important names in the recent history of Fermat's Last Theorem. This book puts faces and personalities to those names. Mozzochi also uncovers the details of certain key pieces of the story. For instance, we learn in Frey's own words the story of his conjecture, about his informal discussion and later lecture at Oberwolfach and his letter containing the actual statement. We learn from Faltings about his crucial role in the weeks before Wiles made his final announcement. An appendix contains the Introduction of Wiles' Annals paper in which he describes the evolution of his solution and gives a broad overview of his methods. Shimura explains his position concerning the evolution of the Shimura-Taniyama conjecture. Mozzochi also conveys the atmosphere of the mathematical community--and the Princeton Mathematics Department in particular--during this important period in mathematics. This eyewitness account and wonderful collection of photographs capture the marvel and unfolding drama of this great mathematical and human story.
Download or read book Geometric Theorems Diophantine Equations and Arithmetic Functions written by J. Sándor and published by Infinite Study. This book was released on 2002 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Disquisitiones Arithmeticae written by Carl Friedrich Gauss and published by Springer. This book was released on 2018-02-07 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .
