Processing ......
Links to Free Computer, Mathematics, Technical Books all over the World
A Course in Algebraic Number Theory
Top Free Computer Networking Books 🌠 - 100% Free or Open Source!
  • Title A Course in Algebraic Number Theory
  • Author(s) Robert B. Ash
  • Publisher: Dover Publications (June 17, 2010)
  • Hardcover/Paperback 128 pages
  • eBook: PDF Files
  • Language: English
  • ISBN-10: 0486477541
  • ISBN-13: 978-0486477541
  • Share This:  

Book Description

This graduate-level text provides coverage for a one-semester course in Algebraic Number Theory. It explores the general theory of factorization of ideals in Dedekind domains as well as the number field case. Detailed calculations illustrate the use of Kummer's theorem on lifting of prime ideals in extension fields.

The author provides sufficient details for students to navigate the intricate proofs of the Dirichlet unit theorem and the Minkowski bounds on element and ideal norms. Additional topics include the factorization of prime ideals in Galois extensions and local as well as global fields, including the Artin-Whaples approximation theorem and Hensel's lemma. The text concludes with three helpful appendixes. Geared toward mathematics majors, this course requires a background in graduate-level algebra and a familiarity with integral extensions and localization.

About the Authors
  • Robert B. Ash (1935-2015) is Professor Emeritus of Mathematics in the Department of Mathematics at the University of Illinois.
Reviews, Ratings, and Recommendations: Related Book Categories: Read and Download Links: Similar Books:
  • Number Fields (Frans Keune)

    This is a textbook for Algebraic Number Theory, focuses on the abstract theory and contains many examples and exercises. It is self-contained in the sense that it uses only mathematics of a bachelor level, including some Galois theory.

  • Number Theory: In Context and Interactive (Karl-Dieter Crisman)

    This is a textbook for an upper-level number theory course, with a clear vision to expose students to the connections to all areas of mathematics, and nearly every concept can be visualized or experimented with using the mathematics software SageMath.

  • Elementary Number Theory: Primes, Congruences, and Secrets

    This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. Many numerical examples are given throughout the book using the SageMath mathematical software.

  • An Introduction to the Theory of Numbers (Leo Moser)

    This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory.

  • Number Theory and Its Applications (Cheon Seoung Ryoo)

    Number theory plays a fundamental and important role in mathematics and applied mathematics. This book is based on recent results in all areas related to number theory and its applications.

  • An Introductory Course in Elementary Number Theory (Wissam Raji)

    This book contains a useful introduction to important topics that need to be addressed in a course in number theory. Proofs of basic theorems are presented in an interesting and comprehensive way that can be read and understood even by non-majors.

  • Yet Another Introductory Number Theory Textbook (J. A. Poritz)

    This introductory number theory textbook has a particular emphasis on connections to cryptology. It broaches the subject of these cryptologic algorithms to develop connections to the topic of number theory.

  • Topology of Numbers (Allen Hatcher)

    A textbook on elementary number theory from a geometric point of view, as opposed to the usual strictly algebraic approach. A fair amount of the book is devoted to studying Conway's topographs associated to quadratic forms in two variables.

  • Magic Squares and Cubes (William Symes Andrews)

    This book cover topics such as magic squares, magic cubes, the Franklin squares, magics and Pythagorean numbers, the theory of reversions, magic circles, spheres, and stars, and magic octahedroids, among other things.

  • A Computational Introduction to Number Theory and Algebra

    This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The coverage includes the basics of number theory, abstract algebra and discrete probability theory.

  • Algorithmic Number Theory: Lattices, Curves, and Cryptography

    This text provides a comprehensive introduction to algorithmic number theory for beginning graduate students, written by the leading experts in the field. It includes several articles that cover the essential topics in this area.

Book Categories
Other Categories
Resources and Links