Contributions to the History of Number Theory in the 20th Century PDF Download
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Author: Peter Roquette
Publisher: Amer Mathematical Society
ISBN: 9783037191132
Category : Mathematics
Languages : en
Pages : 278
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Book Description
The 20th century was a time of great upheaval and great progress in mathematics. In order to get the overall picture of trends, developments, and results, it is illuminating to examine their manifestations locally, in the personal lives and work of mathematicians who were active during this time. The university archives of Gottingen harbor a wealth of papers, letters, and manuscripts from several generations of mathematicians--documents which tell the story of the historic developments from a local point of view. This book offers a number of essays based on documents from Gottingen and elsewhere--essays which have not yet been included in the author's collected works. These essays, independent from each other, are meant as contributions to the imposing mosaic of the history of number theory. They are written for mathematicians, but there are no special background requirements. The essays discuss the works of Abraham Adrian Albert, Cahit Arf, Emil Artin, Richard Brauer, Otto Grun, Helmut Hasse, Klaus Hoechsmann, Robert Langlands, Heinrich-Wolfgang Leopoldt, Emmy Noether, Abraham Robinson, Ernst Steinitz, Hermann Weyl, and others.
Author: Peter Roquette
Publisher: Amer Mathematical Society
ISBN: 9783037191132
Category : Mathematics
Languages : en
Pages : 278
Get Book Here
Book Description
The 20th century was a time of great upheaval and great progress in mathematics. In order to get the overall picture of trends, developments, and results, it is illuminating to examine their manifestations locally, in the personal lives and work of mathematicians who were active during this time. The university archives of Gottingen harbor a wealth of papers, letters, and manuscripts from several generations of mathematicians--documents which tell the story of the historic developments from a local point of view. This book offers a number of essays based on documents from Gottingen and elsewhere--essays which have not yet been included in the author's collected works. These essays, independent from each other, are meant as contributions to the imposing mosaic of the history of number theory. They are written for mathematicians, but there are no special background requirements. The essays discuss the works of Abraham Adrian Albert, Cahit Arf, Emil Artin, Richard Brauer, Otto Grun, Helmut Hasse, Klaus Hoechsmann, Robert Langlands, Heinrich-Wolfgang Leopoldt, Emmy Noether, Abraham Robinson, Ernst Steinitz, Hermann Weyl, and others.
Author: Carl Friedrich Gauss
Publisher: Springer
ISBN: 1493975609
Category : Mathematics
Languages : en
Pages : 491
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Book Description
Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .
Author: Władysław Narkiewicz
Publisher: Springer
ISBN: 3030037541
Category : Mathematics
Languages : en
Pages : 448
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Book Description
The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results obtained before 1950. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.
Author: Leonard Eugene Dickson
Publisher: Legare Street Press
ISBN: 9781022895782
Category :
Languages : en
Pages : 0
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Book Description
A landmark work in the field of mathematics, History of the Theory of Numbers - I traces the development of number theory from ancient civilizations to the early 20th century. Written by mathematician Leonard Eugene Dickson, this book is a comprehensive and accessible introduction to the history of one of the most fundamental branches of mathematics. 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.
Author: Peter Gustav Lejeune Dirichlet
Publisher: American Mathematical Soc.
ISBN: 0821820176
Category : Mathematics
Languages : en
Pages : 297
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Book Description
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.
Author: Boris Nikolaevich Delone
Publisher: American Mathematical Soc.
ISBN: 0821834576
Category : Education
Languages : en
Pages : 297
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Book Description
"The book acquaints the reader with the most important works of these six eminent members of the St. Petersburg school. A short biography is given for each of them, followed by an exposition of some of his most significant contributions. Each contribution is presented as a summary of the author's original work and is followed by commentary. Certain works receive relatively complete expositions, while others are dealt with more briefly." "With a Foreword written for the English edition, this volume will appeal to a broad mathematical audience, including mathematical historians and mathematicians working in number theory."--Jacket.
Author: Purabi Mukherji
Publisher: Springer Nature
ISBN: 9811596204
Category : Mathematics
Languages : en
Pages : 187
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Book Description
This book is an attempt to describe the gradual development of the major schools of research on number theory in South India, Punjab, Mumbai, Bengal, and Bihar—including the establishment of Tata Institute of Fundamental Research (TIFR), Mumbai, a landmark event in the history of research of number theory in India. Research on number theory in India during modern times started with the advent of the iconic genius Srinivasa Ramanujan, inspiring mathematicians around the world. This book discusses the national and international impact of the research made by Indian number theorists. It also includes a carefully compiled, comprehensive bibliography of major 20th century Indian number theorists making this book important from the standpoint of historic documentation and a valuable resource for researchers of the field for their literature survey. This book also briefly discusses the importance of number theory in the modern world of mathematics, including applications of the results developed by indigenous number theorists in practical fields. Since the book is written from the viewpoint of the history of science, technical jargon and mathematical expressions have been avoided as much as possible.
Author: Jean Dieudonné
Publisher: Springer Science & Business Media
ISBN: 0817649077
Category : Mathematics
Languages : en
Pages : 666
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Book Description
This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet
Author: John J. Watkins
Publisher: Princeton University Press
ISBN: 0691159408
Category : Mathematics
Languages : en
Pages : 592
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Book Description
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)
Author: Peter Roquette
Publisher: Springer Nature
ISBN: 303112880X
Category : Mathematics
Languages : en
Pages : 328
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Book Description
Providing the first comprehensive account of the widely unknown cooperation and friendship between Emmy Noether and Helmut Hasse, this book contains English translations of all available letters which were exchanged between them in the years 1925-1935. It features a special chapter on class field theory, a subject which was completely renewed in those years, Noether and Hasse being among its main proponents. These historical items give evidence that Emmy Noether's impact on the development of mathematics is not confined to abstract algebra but also extends to important ideas in modern class field theory as part of algebraic number theory. In her letters, details of proofs appear alongside conjectures and speculations, offering a rich source for those who are interested in the rise and development of mathematical notions and ideas. The letters are supplemented by extensive comments, helping the reader to understand their content within the mathematical environment of the 1920s and 1930s.
