A New Theory Of Numbers

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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.

A New Theory Of Numbers

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Author : Adrian de Groot
language : en
Publisher:
Release Date : 2020-07-20

A New Theory Of Numbers written by Adrian de Groot and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-20 with categories.

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?

An Illustrated Theory Of Numbers

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Author : Martin H. Weissman
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-15

An Illustrated Theory Of Numbers written by Martin H. Weissman 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 2020-09-15 with Education categories.

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.

Topics In The Theory Of Numbers

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Author : Janos Suranyi
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-14

Topics In The Theory Of Numbers written by Janos Suranyi 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 2003-01-14 with Mathematics categories.

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.

Recreations In The Theory Of Numbers

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Author : Albert H. Beiler
language : en
Publisher: Courier Corporation
Release Date : 1964-01-01

Recreations In The Theory Of Numbers written by Albert H. Beiler and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964-01-01 with Games & Activities categories.

Number theory proves to be a virtually inexhaustible source of intriguing puzzle problems. Includes divisors, perfect numbers, the congruences of Gauss, scales of notation, the Pell equation, more. Solutions to all problems.

Topics From The Theory Of Numbers

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Author : Emil Grosswald
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-23

Topics From The Theory Of Numbers written by Emil Grosswald 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 2010-02-23 with Mathematics categories.

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, including: (1) divisibility, (2) congruences, (3) the Riemann zeta function, (4) Diophantine equations and Fermat’s conjecture, (5) the theory of partitions. Comprehensive in nature, Topics from the Theory of Numbers is an ideal text for advanced undergraduates and graduate students alike.

Number Theory

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Author : Róbert Freud
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-08

Number Theory written by Róbert Freud 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 2020-10-08 with Education categories.

Number Theory is a newly translated and revised edition of the most popular introductory textbook on the subject in Hungary. The book covers the usual topics of introductory number theory: divisibility, primes, Diophantine equations, arithmetic functions, and so on. It also introduces several more advanced topics including congruences of higher degree, algebraic number theory, combinatorial number theory, primality testing, and cryptography. The development is carefully laid out with ample illustrative examples and a treasure trove of beautiful and challenging problems. The exposition is both clear and precise. The book is suitable for both graduate and undergraduate courses with enough material to fill two or more semesters and could be used as a source for independent study and capstone projects. Freud and Gyarmati are well-known mathematicians and mathematical educators in Hungary, and the Hungarian version of this book is legendary there. The authors' personal pedagogical style as a facet of the rich Hungarian tradition shines clearly through. It will inspire and exhilarate readers.

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.

A Comprehensive Course In Number Theory

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Author : Alan Baker
language : en
Publisher: Cambridge University Press
Release Date : 2012-08-23

A Comprehensive Course In Number Theory written by Alan Baker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-23 with Mathematics categories.

Developed from the author's popular text, A Concise Introduction to the Theory of Numbers, this book provides a comprehensive initiation to all the major branches of number theory. Beginning with the rudiments of the subject, the author proceeds to more advanced topics, including elements of cryptography and primality testing, an account of number fields in the classical vein including properties of their units, ideals and ideal classes, aspects of analytic number theory including studies of the Riemann zeta-function, the prime-number theorem and primes in arithmetical progressions, a description of the Hardy–Littlewood and sieve methods from respectively additive and multiplicative number theory and an exposition of the arithmetic of elliptic curves. The book includes many worked examples, exercises and further reading. Its wider coverage and versatility make this book suitable for courses extending from the elementary to beginning graduate studies.