A New Theory Of Numbers

Author : Adrian de Groot
Publisher : Unknown
Page : 402 pages
File Size : 46,6 Mb
Release : 2020-07-20
Category : Electronic
ISBN : 1716714877

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A New Theory of Numbers by Adrian de Groot Pdf

This book represents a breakthrough in number theory, by showing the inner, hidden structure of numbers, such as two types of dual characteristics; the surprising inner structure of prime number reciprocals; hidden multiplication and division tables; the many different ways to "construct" a prime number reciprocal; palindromes; perfect balances of evens and odds; plus and minus differences; a predictable and perfect 12/24-based prime number structure; inner secrets hiding in the Fibonacci series and the Pascal Triangle; ratios related to the square roots of numbers; the special roles of the numbers 1, 2 and 3, as well as 3, 6 and 9; the amazing number 7; the fundamental roles of 81 and 19; the mediating roles of 2 and 5, etc. A bonus chapter has been added about the numbers operating in our solar system. One question will baffle any reader: how is it possible that so many phenomena are happening all at the same time? One question cannot be escaped; Is there an inherent intelligent logic hiding in the world of numbers?

Author : Martin H. Weissman
Publisher : American Mathematical Soc.
Page : 341 pages
File Size : 46,5 Mb
Release : 2020-09-15
Category : Education
ISBN : 9781470463717

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An Illustrated Theory of Numbers by Martin H. Weissman Pdf

News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.

Author : Andrew Adler,John E. Coury
Publisher : Jones & Bartlett Publishers
Page : 424 pages
File Size : 47,5 Mb
Release : 1995
Category : Mathematics
ISBN : UOM:39015048558236

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The Theory of Numbers by Andrew Adler,John E. Coury Pdf

Author : Emil Grosswald
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 40,9 Mb
Release : 2010-02-23
Category : Mathematics
ISBN : 9780817648381

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Topics from the Theory of Numbers by Emil Grosswald Pdf

Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate.

Author : Anonim
Publisher : Unknown
Page : 435 pages
File Size : 50,8 Mb
Release : 2007
Category : Number theory
ISBN : 7115156115

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数论导引 by Anonim Pdf

本书内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分化等。

Author : I. M. Vinogradov
Publisher : Courier Corporation
Page : 194 pages
File Size : 44,8 Mb
Release : 2013-10-30
Category : Mathematics
ISBN : 9780486154527

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The Method of Trigonometrical Sums in the Theory of Numbers by I. M. Vinogradov Pdf

This text investigates Waring's problem, approximation by fractional parts of the values of a polynomial, estimates for Weyl sums, distribution of fractional parts of polynomial values, Goldbach's problem, more. 1954 edition.

Author : Leonard E. Dickson
Publisher : Legare Street Press
Page : 0 pages
File Size : 50,6 Mb
Release : 2022-10-27
Category : Mathematics
ISBN : 1017465576

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History of the Theory of Numbers; Volume 2 by Leonard E. Dickson Pdf

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 : Janos Suranyi,Paul Erdös
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 50,9 Mb
Release : 2003-01-14
Category : Mathematics
ISBN : 0387953205

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Topics in the Theory of Numbers by Janos Suranyi,Paul Erdös Pdf

Number theory, the branch of mathematics that studies the properties of the integers, is a repository of interesting and quite varied problems, sometimes impossibly difficult ones. In this book, the authors have gathered together a collection of problems from various topics in number theory that they find beautiful, intriguing, and from a certain point of view instructive.

Author : Alan Baker
Publisher : Cambridge University Press
Page : 116 pages
File Size : 55,8 Mb
Release : 1984-11-29
Category : Mathematics
ISBN : 0521286549

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A Concise Introduction to the Theory of Numbers by Alan Baker Pdf

In this book, Professor Baker describes the rudiments of number theory in a concise, simple and direct manner.

Author : G. H. Hardy,E. M. Wright,Joseph Silverman
Publisher : Oxford University Press
Page : 645 pages
File Size : 46,6 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780199219865

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An Introduction to the Theory of Numbers by G. H. Hardy,E. M. Wright,Joseph Silverman Pdf

The sixth edition of the classic undergraduate text in elementary number theory includes a new chapter on elliptic curves and their role in the proof of Fermat's Last Theorem, a foreword by Andrew Wiles and extensively revised and updated end-of-chapter notes.

Author : Joseph B. Dence,Thomas P. Dence
Publisher : Academic Press
Page : 542 pages
File Size : 46,8 Mb
Release : 1999-01-20
Category : Mathematics
ISBN : 0122091302

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Elements of the Theory of Numbers by Joseph B. Dence,Thomas P. Dence Pdf

Elements of the Theory of Numbers teaches students how to develop, implement, and test numerical methods for standard mathematical problems. The authors have created a two-pronged pedagogical approach that integrates analysis and algebra with classical number theory. Making greater use of the language and concepts in algebra and analysis than is traditionally encountered in introductory courses, this pedagogical approach helps to instill in the minds of the students the idea of the unity of mathematics. Elements of the Theory of Numbers is a superb summary of classical material as well as allowing the reader to take a look at the exciting role of analysis and algebra in number theory. * In-depth coverage of classical number theory * Thorough discussion of the theory of groups and rings * Includes application of Taylor polynomials * Contains more advanced material than other texts * Illustrates the results of a theorem with an example * Excellent presentation of the standard computational exercises * Nearly 1000 problems--many are proof-oriented, several others require the writing of computer programs to complete the computations * Clear and well-motivated presentation * Provides historical references noting distinguished number theory luminaries such as Euclid, de Fermat, Hilbert, Brun, and Lehmer, to name a few * Annotated bibliographies appear at the end of all of the chapters

Author : Leonard Eugene Dickson
Publisher : Legare Street Press
Page : 0 pages
File Size : 47,6 Mb
Release : 2023-07-22
Category : Electronic
ISBN : 1022888676

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History Of The Theory Of Numbers - I by Leonard Eugene Dickson Pdf

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 : Karma Dajani,Cor Kraaikamp
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 52,9 Mb
Release : 2002-12-31
Category : Mathematics
ISBN : 9780883850343

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Ergodic Theory of Numbers by Karma Dajani,Cor Kraaikamp Pdf

Ergodic Theory of Numbers looks at the interaction between two fields of mathematics: number theory and ergodic theory (as part of dynamical systems). It is an introduction to the ergodic theory behind common number expansions, like decimal expansions, continued fractions, and many others. However, its aim does not stop there. For undergraduate students with sufficient background knowledge in real analysis and graduate students interested in the area, it is also an introduction to a "dynamical way of thinking". The questions studied here are dynamical as well as number theoretical in nature, and the answers are obtained with the help of ergodic theory. Attention is focused on concepts like measure-preserving, ergodicity, natural extension, induced transformations, and entropy. These concepts are then applied to familiar expansions to obtain old and new results in an elegant and straightforward manner. What it means to be ergodic and the basic ideas behind ergodic theory will be explained along the way. The subjects covered vary from classical to recent, which makes this book appealing to researchers as well as students.

Author : Minking Eie
Publisher : World Scientific
Page : 295 pages
File Size : 46,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812835185

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Topics in Number Theory by Minking Eie Pdf

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 generalized to a more general form here.

Author : Andrew Granville
Publisher : American Mathematical Soc.
Page : 587 pages
File Size : 41,5 Mb
Release : 2019-11-22
Category : Education
ISBN : 9781470441586

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Number Theory Revealed: A Masterclass by Andrew Granville Pdf

Number Theory Revealed: A Masterclass acquaints enthusiastic students with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod p p and modern twists on traditional questions like the values represented by binary quadratic forms, the anatomy of integers, and elliptic curves. This Masterclass edition contains many additional chapters and appendices not found in Number Theory Revealed: An Introduction, highlighting beautiful developments and inspiring other subjects in mathematics (like algebra). This allows instructors to tailor a course suited to their own (and their students') interests. There are new yet accessible topics like the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, a new proof of Mordell's Theorem for congruent elliptic curves, and a discussion of the abc abc-conjecture including its proof for polynomials.