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| number theory and its history by oystein ore: Number Theory and Its History Oystein Ore, 1988-01-01 Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography. |
| number theory and its history by oystein ore: An Adventurer's Guide to Number Theory Richard Friedberg, 1968 Presents an historical approach to number theory, treating the properties of numbers as abstract concepts, and encouraging the young student to use his imagination. |
| number theory and its history by oystein ore: Invitation to Number Theory Øystein Ore, 1967 |
| number theory and its history by oystein ore: Excursions in Number Theory Charles Stanley Ogilvy, John Timothy Anderson, 1988-01-01 Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers. — Martin Gardner. |
| number theory and its history by oystein ore: Elementary Number Theory in Nine Chapters James J. Tattersall, 1999-10-14 This book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject. |
| number theory and its history by oystein ore: Modern Algebra and the Rise of Mathematical Structures Leo Corry, 2003-11-27 This book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-1800s to 1930, and then considers attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea. |
| number theory and its history by oystein ore: Number Theory André Weil, 2013-06-29 This book presents a historical overview of number theory. It examines texts that span some thirty-six centuries of arithmetical work, from an Old Babylonian tablet to Legendre’s Essai sur la Théorie des Nombres, written in 1798. Coverage employs a historical approach in the analysis of problems and evolving methods of number theory and their significance within mathematics. The book also takes the reader into the workshops of four major authors of modern number theory: Fermat, Euler, Lagrange and Legendre and presents a detailed and critical examination of their work. |
| number theory and its history by oystein ore: The History of Arithmetic Louis Charles Karpinski, 1925 |
| number theory and its history by oystein ore: Number Theory and Its History Øystein Ore, 1955 |
| number theory and its history by oystein ore: Discrete Mathematics and Its Applications Kenneth Rosen, 2006-07-26 Discrete Mathematics and its Applications, Sixth Edition, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide a wide variety of real-world applications...from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields. |
| number theory and its history by oystein ore: The Shaping of Arithmetic after C.F. Gauss's Disquisitiones Arithmeticae Catherine Goldstein, Norbert Schappacher, Joachim Schwermer, 2007-02-03 Since its publication, C.F. Gauss's Disquisitiones Arithmeticae (1801) has acquired an almost mythical reputation, standing as an ideal of exposition in notation, problems and methods; as a model of organisation and theory building; and as a source of mathematical inspiration. Eighteen authors - mathematicians, historians, philosophers - have collaborated in this volume to assess the impact of the Disquisitiones, in the two centuries since its publication. |
| number theory and its history by oystein ore: Number Theory and Its History Oystein Ore, 1948 |
| number theory and its history by oystein ore: Fibonacci’s Liber Abaci Laurence Sigler, 2003-11-11 First published in 1202, Fibonacci’s Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe. This is the first translation into a modern European language, of interest not only to historians of science but also to all mathematicians and mathematics teachers interested in the origins of their methods. |
| number theory and its history by oystein ore: Taming the Unknown Victor J. Katz, Karen Hunger Parshall, 2014-07-21 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. |
| number theory and its history by oystein ore: Lattices and Ordered Sets Steven Roman, 2008-12-15 This book is intended to be a thorough introduction to the subject of order and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. This is a book on pure mathematics: I do not discuss the applications of lattice theory to physics, computer science or other disciplines. Lattice theory began in the early 1890s, when Richard Dedekind wanted to know the answer to the following question: Given three subgroups EF , and G of an abelian group K, what is the largest number of distinct subgroups that can be formed using these subgroups and the operations of intersection and sum (join), as in E?FßÐE?FÑ?GßE?ÐF?GÑ and so on? In lattice-theoretic terms, this is the number of elements in the relatively free modular lattice on three generators. Dedekind [15] answered this question (the answer is #)) and wrote two papers on the subject of lattice theory, but then the subject lay relatively dormant until Garrett Birkhoff, Oystein Ore and others picked it up in the 1930s. Since then, many noted mathematicians have contributed to the subject, including Garrett Birkhoff, Richard Dedekind, Israel Gelfand, George Grätzer, Aleksandr Kurosh, Anatoly Malcev, Oystein Ore, Gian-Carlo Rota, Alfred Tarski and Johnny von Neumann. |
| number theory and its history by oystein ore: Foundations of Combinatorics with Applications Edward A. Bender, S. Gill Williamson, 2013-01-18 This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises. |
| number theory and its history by oystein ore: Elementary Number Theory: Primes, Congruences, and Secrets William Stein, 2008-10-28 This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predeterminedsecret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem. |
| number theory and its history by oystein ore: Number Theory Robin Wilson, 2020-05-28 Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the 'building blocks' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no-one has ever been able to resolve them. But number theory has also recently become of great practical importance - in the area of cryptography, where the security of your credit card, and indeed of the nation's defence, depends on a result concerning prime numbers that dates back to the 18th century. Recent years have witnessed other spectacular developments, such as Andrew Wiles's proof of 'Fermat's last theorem' (unproved for over 250 years) and some exciting work on prime numbers. In this Very Short Introduction Robin Wilson introduces the main areas of classical number theory, both ancient and modern. Drawing on the work of many of the greatest mathematicians of the past, such as Euclid, Fermat, Euler, and Gauss, he situates some of the most interesting and creative problems in the area in their historical context. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. |
| number theory and its history by oystein ore: Cardano Øystein Ore, 2017-03-14 Cardano, next to Vesalius the greatest physician of his day, was also a devoted and skilled gambler who played for personal pleasure and profit. His mathematical genius enabled him to devise simple rules of probability for his own benefit and for his gambling contemporaries. These he collected in his Book on Games of Chance and embellished them with essays on the tricks of cheats and kibitzers, as well as on psychological rules of play. In this biography of a stormy Renaissance personality, Cardano's gambling studies are deciphered for the first time, and a translation of the Book on Games of Chance is appended. Originally published in 1953. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. |
| number theory and its history by oystein ore: Topics In Number Theory Minking Eie, 2008-12-22 This is a first-ever textbook written in English about the theory of modular forms and Jacobi forms of several variables. It contains the classical theory as well as a new theory on Jacobi forms over Cayley numbers developed by the author from 1990 to 2000. Applications to the classical Euler sums are of special interest to those who are eager to evaluate double Euler sums or more general multiple zeta values. The celebrated sum formula proved by Granville in 1997 is given in a more general form here. |
| number theory and its history by oystein ore: Graph Theory with Applications to Engineering and Computer Science DEO, NARSINGH, 2004-10-01 Because of its inherent simplicity, graph theory has a wide range of applications in engineering, and in physical sciences. It has of course uses in social sciences, in linguistics and in numerous other areas. In fact, a graph can be used to represent almost any physical situation involving discrete objects and the relationship among them. Now with the solutions to engineering and other problems becoming so complex leading to larger graphs, it is virtually difficult to analyze without the use of computers. This book is recommended in IIT Kharagpur, West Bengal for B.Tech Computer Science, NIT Arunachal Pradesh, NIT Nagaland, NIT Agartala, NIT Silchar, Gauhati University, Dibrugarh University, North Eastern Regional Institute of Management, Assam Engineering College, West Bengal Univerity of Technology (WBUT) for B.Tech, M.Tech Computer Science, University of Burdwan, West Bengal for B.Tech. Computer Science, Jadavpur University, West Bengal for M.Sc. Computer Science, Kalyani College of Engineering, West Bengal for B.Tech. Computer Science. Key Features: This book provides a rigorous yet informal treatment of graph theory with an emphasis on computational aspects of graph theory and graph-theoretic algorithms. Numerous applications to actual engineering problems are incorpo-rated with software design and optimization topics. |
| number theory and its history by oystein ore: Number Theory George E. Andrews, 2012-04-30 Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more. |
| number theory and its history by oystein ore: Mathematical Mysteries Calvin C. Clawson, 2013-11-09 A meditation on the beauty and meaning of numbers, exploring mathematical equations, describing some of the mathematical discoveries of the past millennia, and pondering philosophical questions about the relation of numbers to the universe. |
| number theory and its history by oystein ore: The History of the Calculus and Its Conceptual Development Carl B. Boyer, 1959-01-01 Traces the development of the integral and the differential calculus and related theories since ancient times |
| number theory and its history by oystein ore: Mathematics in the Time of the Pharaohs Richard J. Gillings, 1982-01-01 In this carefully researched study, the author examines Egyptian mathematics, demonstrating that although operations were limited in number, they were remarkably adaptable to a great many applications: solution of problems in direct and inverse proportion, linear equations of the first degree, and arithmetical and geometrical progressions. |
| number theory and its history by oystein ore: Mathematicians of the World, Unite! Guillermo Curbera, 2009-02-23 This vividly illustrated history of the International Congress of Mathematicians- a meeting of mathematicians from around the world held roughly every four years- acts as a visual history of the 25 congresses held between 1897 and 2006, as well as a story of changes in the culture of mathematics over the past century. Because the congress is an int |
| number theory and its history by oystein ore: Time Alexander Waugh, 2001 Examines the mysteries of time and chronicles the human struggle to measure, utilize, understand, and explain it, from the era of homo erectus to modern theorists like Stephen Hawkings. Reprint. |
| number theory and its history by oystein ore: Niels Henrik Abel Øystein Ore, 1957 Niels Henrik Abel was first published in 1957. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. Few men are more famous in the world of modern mathematics than Niels Henrik Abel, whose concepts and results are familiar to all present-day mathematicians. This volume, the first biography of Abel published in English, presents the story of the brilliant young Norwegian whose scientific achievements were not fully recognized until after his untimely death. It is also a case history of our perennial problem of how to detect genius and ease its path. Abel was born in 1802 in Finnoy, a little island on the coast of Norway. His father was a minister and politician of national importance, but his family descended from prominence to moral dissolution. Abel's studies were financed by his professors, aware of his extraordinary abilities. He was granted a fellowship to travel and study on the continent, and the year and a half which he then spent in Germany, Italy, and France was a most happy period in his life. When Abel returned to Norway, he could only obtain a temporary position, and in his last years he was harassed by grave difficulties. He managed, however, to write inspired mathematical articles which made a reputation for him among the mathematicians of Europe. Just as the security he longed for seemed within his grasp, he died of tuberculosis at the age of twenty-six. Abel's life has been the subject of several books, published in the Scandinavian countries, France, and Germany, but, in preparing this biography, Mr. Ore made use of much new material obtained from private letters, official documents, and newspaper files in various European sources. |
| number theory and its history by oystein ore: A Guide to Feynman Diagrams in the Many-Body Problem Richard D. Mattuck, 2012-08-21 Superb introduction for nonspecialists covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and more. A great delight. — Physics Today. 1974 edition. |
| number theory and its history by oystein ore: Introduction to Statistical Inference E. S. Keeping, 1995-01-01 This excellent text emphasizes the inferential and decision-making aspects of statistics. The first chapter is mainly concerned with the elements of the calculus of probability. Additional chapters cover the general properties of distributions, testing hypotheses, and more. |
| number theory and its history by oystein ore: Space, Time, Matter Hermann Weyl, 2013-04-26 Excellent introduction probes deeply into Euclidean space, Riemann's space, Einstein's general relativity, gravitational waves and energy, and laws of conservation. A classic of physics. — British Journal for Philosophy and Science. |
| number theory and its history by oystein ore: Time's Arrow Michael C. Mackey, 2011-11-30 Exploration of Second Law of Thermodynamics details fundamental dynamic properties behind the construction of statistical mechanics. Geared toward physicists and applied mathematicians; suitable for advanced undergraduate, graduate courses. 1992 edition. |
| number theory and its history by oystein ore: Fundamentals of Scientific Mathematics George E. Owen, 2012-12-03 Offering undergraduates a solid mathematical background (and functioning equally well for independent study), this rewarding, beautifully illustrated text covers geometry and matrices, vector algebra, analytic geometry, functions, and differential and integral calculus. 1961 edition. |
| number theory and its history by oystein ore: Pythagorean Triangles Waclaw Sierpinski, 2013-04-10 This classic text, written by a distinguished mathematician and teacher, focuses on a fundamental theory of geometry. Topics include all types of Pythagorean triangles. |
| number theory and its history by oystein ore: Light Scattering by Small Particles H. C. van de Hulst, 2012-06-08 Comprehensive treatment of light-scattering properties of small, independent particles, including a full range of useful approximation methods for researchers in chemistry, meteorology, and astronomy. 46 tables. 59 graphs. 44 illustrations. |
| number theory and its history by oystein ore: Introduction to Matrix Methods in Optics Anthony Gerrard, James M. Burch, 1994-01-01 Clear, accessible guide requires little prior knowledge and considers just two topics: paraxial imaging and polarization. Lucid discussions of paraxial imaging properties of a centered optical system, optical resonators and laser beam propagation, matrices in polarization optics and propagation of light through crystals, much more. 60 illustrations. Appendixes. Bibliography. |
| number theory and its history by oystein ore: Lectures on Linear Algebra I. M. Gelfand, 1989-01-01 Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector. |
| number theory and its history by oystein ore: The Chemical Philosophy Allen G. Debus, 2002-01-01 This rich record of the major interests of Paracelsus and other 16th-century chemical philosophers covers chemistry and nature in the Renaissance, Paracelsian debates, theories of Fludd, Helmontian restatement of chemical philosophy, and other fascinating aspects of the era. Well researched, compellingly related study. 36 black-and-white illustrations. |
| number theory and its history by oystein ore: Lie Groups for Pedestrians Harry J. Lipkin, 2012-06-08 This book shows how well-known methods of angular momentum algebra can be extended to treat other Lie groups. Chapters cover isospin, the three-dimensional harmonic oscillator, Young diagrams, more. 1966 edition. |
| number theory and its history by oystein ore: A Course in Advanced Calculus Robert S. Borden, 1998-01-01 An excellent undergraduate text examines sets and structures, limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, more. Problems with tips and solutions for some. |
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＜阪神タイガース90周年記念＞ 猛虎猛打列伝。 - Number1118 …
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