A Modern Introduction To Classical Number Theory

Author : K. Ireland,M. Rosen
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 47,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475717792

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A Classical Introduction to Modern Number Theory by K. Ireland,M. Rosen Pdf

This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time.

Author : Tianxin Cai
Publisher : World Scientific
Page : 430 pages
File Size : 53,8 Mb
Release : 2021-07-21
Category : Mathematics
ISBN : 9789811218316

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A Modern Introduction To Classical Number Theory by Tianxin Cai Pdf

Natural numbers are the oldest human invention. This book describes their nature, laws, history and current status. It has seven chapters. The first five chapters contain not only the basics of elementary number theory for the convenience of teaching and continuity of reading, but also many latest research results. The first time in history, the traditional name of the Chinese Remainder Theorem is replaced with the Qin Jiushao Theorem in the book to give him a full credit for his establishment of this famous theorem in number theory. Chapter 6 is about the fascinating congruence modulo an integer power, and Chapter 7 introduces a new problem extracted by the author from the classical problems of number theory, which is out of the combination of additive number theory and multiplicative number theory.One feature of the book is the supplementary material after each section, there by broadening the reader's knowledge and imagination. These contents either discuss the rudiments of some aspects or introduce new problems or conjectures and their extensions, such as perfect number problem, Egyptian fraction problem, Goldbach's conjecture, the twin prime conjecture, the 3x + 1 problem, Hilbert Waring problem, Euler's conjecture, Fermat's Last Theorem, Laudau's problem and etc.This book is written for anyone who loves natural numbers, and it can also be read by mathematics majors, graduate students, and researchers. The book contains many illustrations and tables. Readers can appreciate the author's sensitivity of history, broad range of knowledge, and elegant writing style, while benefiting from the classical works and great achievements of masters in number theory.

Author : Kenneth Ireland,Michael Rosen
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 50,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475721034

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A Classical Introduction to Modern Number Theory by Kenneth Ireland,Michael Rosen Pdf

This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.

Author : Franz Halter-Koch
Publisher : CRC Press
Page : 431 pages
File Size : 42,6 Mb
Release : 2013-06-17
Category : Mathematics
ISBN : 9781466591844

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Quadratic Irrationals by Franz Halter-Koch Pdf

Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups.T

Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 44,5 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233

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A Brief Guide to Algebraic Number Theory by H. P. F. Swinnerton-Dyer Pdf

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Author : Oystein Ore
Publisher : Courier Corporation
Page : 400 pages
File Size : 41,8 Mb
Release : 2012-07-06
Category : Mathematics
ISBN : 9780486136431

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Number Theory and Its History by Oystein Ore Pdf

Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.

Author : Song Y. Yan
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 41,5 Mb
Release : 2013-11-11
Category : Computers
ISBN : 9783662047736

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Number Theory for Computing by Song Y. Yan Pdf

This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.

Author : Álvaro Lozano-Robledo
Publisher : American Mathematical Soc.
Page : 488 pages
File Size : 45,7 Mb
Release : 2019-03-21
Category : Arithmetical algebraic geometry
ISBN : 9781470450168

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Number Theory and Geometry: An Introduction to Arithmetic Geometry by Álvaro Lozano-Robledo Pdf

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 : Emmanuel Kowalski
Publisher : Cambridge University Press
Page : 271 pages
File Size : 51,9 Mb
Release : 2021-05-06
Category : Mathematics
ISBN : 9781108840965

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An Introduction to Probabilistic Number Theory by Emmanuel Kowalski Pdf

This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.

Author : Victor Shoup
Publisher : Cambridge University Press
Page : 544 pages
File Size : 46,9 Mb
Release : 2005-04-28
Category : Computers
ISBN : 0521851548

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A Computational Introduction to Number Theory and Algebra by Victor Shoup Pdf

This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes.

Author : Peter Gustav Lejeune Dirichlet,Peter Dirichlet,Richard Dedekind
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 55,7 Mb
Release : 1999
Category : Number theory
ISBN : 9780821820179

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Lectures on Number Theory by Peter Gustav Lejeune Dirichlet,Peter Dirichlet,Richard Dedekind Pdf

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 : Paul Pollack
Publisher : American Mathematical Soc.
Page : 312 pages
File Size : 52,9 Mb
Release : 2017-08-01
Category : Algebraic number theory
ISBN : 9781470436537

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A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond Z by Paul Pollack Pdf

Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.

Author : K. Ireland,M. Rosen
Publisher : Unknown
Page : 362 pages
File Size : 44,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475717806

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A Classical Introduction to Modern Number Theory by K. Ireland,M. Rosen Pdf

Author : Kenneth F. Ireland,Michael Ira Rosen
Publisher : Unknown
Page : 341 pages
File Size : 46,5 Mb
Release : 1982
Category : Number theory
ISBN : 7506201143

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A Classical Introduction to Modern Number Theory by Kenneth F. Ireland,Michael Ira Rosen Pdf

Author : T. Estermann
Publisher : Cambridge University Press
Page : 94 pages
File Size : 48,6 Mb
Release : 2011-08-11
Category : Mathematics
ISBN : 0521168287

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Introduction to Modern Prime Number Theory by T. Estermann Pdf

This 1952 book attempts to prove the Vinogradov-Goldbach theorem: that every sufficiently large odd number is the sum of three primes.