Introduction to Number Theory

Richard Michael Hill

• Publisher: WSPC (EUROPE)
• Year: 2017
• eBook ISBN: 9781786344731
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

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Introduction to Number Theory is dedicated to concrete questions about integers, to place an emphasis on problem solving by students. When undertaking a first course in number theory, students enjoy actively engaging with the properties and relationships of numbers.

The book begins with introductory material, including uniqueness of factorization of integers and polynomials. Subsequent topics explore quadratic reciprocity, Hensel's Lemma, p -adic powers series such as exp(px) and log(1+px), the Euclidean property of some quadratic rings, representation of integers as norms from quadratic rings, and Pell's equation via continued fractions.

Throughout the five chapters and more than 100 exercises and solutions, readers gain the advantage of a number theory book that focuses on doing calculations. This textbook is a valuable resource for undergraduates or those with a background in university level mathematics.

--> Contents:

• About the Author
• Acknowledgments
• Introduction
• Euclid's Algorithm
• Polynomial Rings
• Congruences Modulo Prime Numbers
• p -Adic Methods in Number Theory
• Diophantine Equations and Quadratic Rings
• Solutions to Exercises
• Bibliography
• Index

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--> Readership: Students and educators in a university course on number theory. -->
Keywords:Number Theory;Mathematics;Undergraduate Textbook;Integers;FactorizationReview: Key Features:

• Development of the recognition on the mysterious magnetism is followed from ancient times to modern times, including the history of the millennium of the Middle ages which is usually disregarded or slighted
• The role magnetism had played to the development of modern concept of Newton's universal force, which the ordinary history of science has overlooked in the past is fully discussed
• The connection between natural science and natural magic in the Renaissance period and early modern times, and also the importance of the latter to the formation of the former is elucidated

Table of contents

• Cover Page
• Title
• Copyright
• About the Author
• Acknowledgments
• Contents
• Introduction
• 1 Euclid’s Algorithm
• 2 Polynomial Rings
• 3 Congruences Modulo Prime Numbers
• 4 p-Adic Methods in Number Theory
• 5 Diophantine Equations and Quadratic Rings
• Solution to Exercises
• Bibliography
• Index