Number Theory And Its History
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Number Theory And Its History
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Author : Oystein Ore
language : en
Publisher: Courier Corporation
Release Date : 1988-01-01
Number Theory And Its History written by Oystein Ore and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
History Of The Theory Of Numbers Volume Ii
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Author : Leonard Eugene Dickson
language : en
Publisher: Courier Corporation
Release Date : 2005-06-07
History Of The Theory Of Numbers Volume Ii written by Leonard Eugene Dickson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-07 with Mathematics categories.
The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms. Featured topics include polygonal, pyramidal, and figurate numbers; linear diophantine equations and congruences; partitions; rational right triangles; triangles, quadrilaterals, and tetrahedra; the sums of two, three, four, and n squares; the number of solutions of quadratic congruences in n unknowns; Liouville's series of eighteen articles; the Pell equation; squares in arithmetical or geometrical progression; equations of degrees three, four, and n; sets of integers with equal sums of like powers; Waring's problem and related results; Fermat's last theorem; and many other related subjects. Indexes of authors cited and subjects appear at the end of the book.
Number Theory
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Author : André Weil
language : en
Publisher: Birkhäuser
Release Date : 2013-06-29
Number Theory written by André Weil and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Labyrinth Of Thought
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Author : Jose Ferreiros
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-01
Labyrinth Of Thought written by Jose Ferreiros and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-01 with Mathematics categories.
"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
Number Theory
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Author : John J. Watkins
language : en
Publisher: Princeton University Press
Release Date : 2013-12-29
Number Theory written by John J. Watkins and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-29 with Mathematics categories.
An introductory textbook with a unique historical approach to teaching number theory The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the most fascinating subjects in mathematics. Written in an informal style by an award-winning teacher, Number Theory covers prime numbers, Fibonacci numbers, and a host of other essential topics in number theory, while also telling the stories of the great mathematicians behind these developments, including Euclid, Carl Friedrich Gauss, and Sophie Germain. This one-of-a-kind introductory textbook features an extensive set of problems that enable students to actively reinforce and extend their understanding of the material, as well as fully worked solutions for many of these problems. It also includes helpful hints for when students are unsure of how to get started on a given problem. Uses a unique historical approach to teaching number theory Features numerous problems, helpful hints, and fully worked solutions Discusses fun topics like Pythagorean tuning in music, Sudoku puzzles, and arithmetic progressions of primes Includes an introduction to Sage, an easy-to-learn yet powerful open-source mathematics software package Ideal for undergraduate mathematics majors as well as non-math majors Digital solutions manual (available only to professors)
Lectures On Number Theory
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Author : Peter Gustav Lejeune Dirichlet
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Lectures On Number Theory written by Peter Gustav Lejeune Dirichlet and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions.
Rational Number Theory In The 20th Century
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Author : Władysław Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-02
Rational Number Theory In The 20th Century written by Władysław Narkiewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-02 with Mathematics categories.
The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
The Development Of Prime Number Theory
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Author : Wladyslaw Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Development Of Prime Number Theory written by Wladyslaw Narkiewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical details of the people who have played a role in this development and we do not discuss the questions concerning why each particular person became in terested in primes, because, usually, exact answers to them are impossible to obtain. Our idea is to present the development of the theory of the distribu tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century. We shall also present some later developments, mostly in short comments, although the reader will find certain exceptions to that rule. The period of the last 80 years was full of new ideas (we mention only the applications of trigonometrical sums or the advent of various sieve methods) and certainly demands a separate book.
A Classical Introduction To Modern Number Theory
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Author : Kenneth Ireland
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A Classical Introduction To Modern Number Theory written by Kenneth Ireland and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.
Number Theory And Its History
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Author : Oystein Ore
language : en
Publisher: Courier Corporation
Release Date : 2012-07-06
Number Theory And Its History written by Oystein Ore and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-06 with Mathematics categories.
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.