Diophantus And Arithmetica
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Author |
: Jacques Sesiano |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 507 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461381747 |
ISBN-13 |
: 1461381746 |
Rating |
: 4/5 (47 Downloads) |
Synopsis Books IV to VII of Diophantus’ Arithmetica by : Jacques Sesiano
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.
Author |
: Dr. Arun Kumar Mishra |
Publisher |
: Booksclinic Publishing |
Total Pages |
: 138 |
Release |
: 2022-12-13 |
ISBN-10 |
: 9789355352132 |
ISBN-13 |
: 9355352131 |
Rating |
: 4/5 (32 Downloads) |
Synopsis Diophantus And Arithmetica by : Dr. Arun Kumar Mishra
‘Arithmetica’ is an eminent book of mathematics, written by a Greek mathematician Diophantus. A systematic work on Diophantus was performed by Sir Thomas L. Heath, K.C.B. Sir Thomas L. Heath had written a very impressive book entitled, “Diophantus of Alexandria: A study in the History of Greek Algebra”. The first edition of the book in English on Diophantus appeared in 1885.
Author |
: Thomas L. Heath |
Publisher |
: CUP Archive |
Total Pages |
: 406 |
Release |
: 1910 |
ISBN-10 |
: |
ISBN-13 |
: |
Rating |
: 4/5 ( Downloads) |
Synopsis Diophantus of Alexandria by : Thomas L. Heath
Author |
: Jacques Ozanam |
Publisher |
: |
Total Pages |
: 850 |
Release |
: 1840 |
ISBN-10 |
: OXFORD:590747182 |
ISBN-13 |
: |
Rating |
: 4/5 (82 Downloads) |
Synopsis Recreations in mathematics and natural philosophy, recomposed by m. Montucla and tr. by C. Hutton by : Jacques Ozanam
Author |
: Titu Andreescu |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 350 |
Release |
: 2010-09-02 |
ISBN-10 |
: 9780817645496 |
ISBN-13 |
: 0817645497 |
Rating |
: 4/5 (96 Downloads) |
Synopsis An Introduction to Diophantine Equations by : Titu Andreescu
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.
Author |
: Richard Friedberg |
Publisher |
: Courier Corporation |
Total Pages |
: 241 |
Release |
: 2012-07-06 |
ISBN-10 |
: 9780486152691 |
ISBN-13 |
: 0486152693 |
Rating |
: 4/5 (91 Downloads) |
Synopsis An Adventurer's Guide to Number Theory by : Richard Friedberg
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.
Author |
: Álvaro Lozano-Robledo |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 506 |
Release |
: 2019-03-21 |
ISBN-10 |
: 9781470450168 |
ISBN-13 |
: 147045016X |
Rating |
: 4/5 (68 Downloads) |
Synopsis Number Theory and Geometry: An Introduction to Arithmetic Geometry by : Álvaro Lozano-Robledo
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.
Author |
: Isabella Grigoryevna Bashmakova |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 90 |
Release |
: 2019-01-29 |
ISBN-10 |
: 9781470450496 |
ISBN-13 |
: 1470450496 |
Rating |
: 4/5 (96 Downloads) |
Synopsis Diophantus and Diophantine Equations by : Isabella Grigoryevna Bashmakova
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.
Author |
: Jacob Klein |
Publisher |
: Courier Corporation |
Total Pages |
: 246 |
Release |
: 2013-04-22 |
ISBN-10 |
: 9780486319810 |
ISBN-13 |
: 0486319814 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Greek Mathematical Thought and the Origin of Algebra by : Jacob Klein
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.
Author |
: Jran Friberg |
Publisher |
: World Scientific |
Total Pages |
: 497 |
Release |
: 2007 |
ISBN-10 |
: 9789812704528 |
ISBN-13 |
: 9812704523 |
Rating |
: 4/5 (28 Downloads) |
Synopsis Amazing Traces of a Babylonian Origin in Greek Mathematics by : Jran Friberg
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.