This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography. The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate. --Mathematical Reviews
生活數字有秘密
本书是一本经典的数论名著,取材于作者在牛津大学,剑桥大学等大学授课的讲义.主要包括:素数理论,无理数,费马定理,同余式理论,连分数,用有理数逼近无理数,不定方程,二次域 ...
... Editor Collected Works of Witold Hurewicz 1995 3.2 Richard E. Block , Nathan Jacobson , J. Marshall Osborn , David J. Saltman , and Daniel Zelinsky , Editors A. Adrian Albert Collected Mathematical Papers : Nonassociative Algebras ...
For one-semester undergraduate courses in Elementary Number Theory This title is part of the Pearson Modern Classics series.
In addition to the instructional material, the book contains hundreds of problems ... This book is ideal for students who have mastered basic algebra, such as solving linear equations.
At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few.
The primary goal of this book is to present the essential elements of algebraic number theory, including the theory of normal extensions up through a glimpse of class field theory.
Definition 4.8: Let R be any non-associative ring, R is said to be a right alternative ring if (xy) y = x (yy) for ... by the following table: The loop ring ZL is a right alternative ring as the loop L itself a right alternative loop.
This text blends classical theory with modern applications and is notable for its comprehensive exercise sets.
Elementary Number Theory