An Invitation To Modern Number Theory
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An Invitation To Modern Number Theory
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Author : Steven J. Miller
language : en
Publisher: Princeton University Press
Release Date : 2020-08-04
An Invitation To Modern Number Theory written by Steven J. Miller 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 2020-08-04 with Mathematics categories.
In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.
Invitation To Number Theory Second Edition
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Author : Oystein Ore
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-12-29
Invitation To Number Theory Second Edition written by Oystein Ore 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 2017-12-29 with Number theory categories.
Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, … and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.
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.
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.
Invitation To Number Theory
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Author : Oystein Ore
language : en
Publisher: American Mathematical Society
Release Date : 2018-08-15
Invitation To Number Theory written by Oystein Ore and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-15 with Mathematics categories.
Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, … and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.
A Classical Introduction To Modern Number Theory
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Author : K. Ireland
language : en
Publisher:
Release Date : 2014-01-15
A Classical Introduction To Modern Number Theory written by K. Ireland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Number Theory
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Author : André Weil
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-21
Number Theory written by André Weil 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 2009-05-21 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.
A Classical Introduction To Modern Number Theory
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Author : Kenneth F. Ireland
language : en
Publisher:
Release Date : 1982
A Classical Introduction To Modern Number Theory written by Kenneth F. Ireland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Nombres, Théorie des categories.
A Modern Introduction To Classical Number Theory
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Author : Tianxin Cai
language : en
Publisher: World Scientific
Release Date : 2021-07-21
A Modern Introduction To Classical Number Theory written by Tianxin Cai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Mathematics categories.
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.
From Natural Numbers To Quaternions
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Author : Jürg Kramer
language : en
Publisher: Springer
Release Date : 2017-11-15
From Natural Numbers To Quaternions written by Jürg Kramer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-15 with Mathematics categories.
This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions. Along the way, the authors carefully develop the necessary concepts and methods from abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an appendix discussing related topics from algebra and number theory, including recent developments reflecting the relevance of the material to current research. The present volume is intended for undergraduate courses in abstract algebra or elementary number theory. The inclusion of exercises with solutions also makes it suitable for self-study and accessible to anyone with an interest in modern algebra and number theory.
Invitation To Number Theory
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Author :
language : en
Publisher:
Release Date : 1961
Invitation To Number Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with categories.