A Brief Guide to Algebraic Number Theory

A Brief Guide to Algebraic Number Theory
Author: H. P. F. Swinnerton-Dyer
Publisher: Cambridge University Press
Total Pages: 164
Release: 2001-02-22
Genre: Mathematics
ISBN: 9780521004237

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Algorithmic Algebraic Number Theory

Algorithmic Algebraic Number Theory
Author: M. Pohst
Publisher: Cambridge University Press
Total Pages: 520
Release: 1997-09-25
Genre: Mathematics
ISBN: 9780521596695

Now in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.

Theory of Algebraic Integers

Theory of Algebraic Integers
Author: Richard Dedekind
Publisher: Cambridge University Press
Total Pages: 170
Release: 1996-09-28
Genre: Mathematics
ISBN: 0521565189

A translation of a classic work by one of the truly great figures of mathematics.

An Adventurer's Guide to Number Theory

An Adventurer's Guide to Number Theory
Author: Richard Friedberg
Publisher: Courier Corporation
Total Pages: 241
Release: 2012-07-06
Genre: Mathematics
ISBN: 0486152693

This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.

A Conversational Introduction to Algebraic Number Theory

A Conversational Introduction to Algebraic Number Theory
Author: Paul Pollack
Publisher: American Mathematical Soc.
Total Pages: 329
Release: 2017-08-01
Genre: Mathematics
ISBN: 1470436531

Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.

A Course in Computational Algebraic Number Theory

A Course in Computational Algebraic Number Theory
Author: Henri Cohen
Publisher: Springer Science & Business Media
Total Pages: 556
Release: 2013-04-17
Genre: Mathematics
ISBN: 3662029456

A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.

Classical Theory of Algebraic Numbers

Classical Theory of Algebraic Numbers
Author: Paulo Ribenboim
Publisher: Springer Science & Business Media
Total Pages: 676
Release: 2013-11-11
Genre: Mathematics
ISBN: 0387216901

The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.

Algebraic Number Theory

Algebraic Number Theory
Author: Frazer Jarvis
Publisher: Springer
Total Pages: 298
Release: 2014-06-23
Genre: Mathematics
ISBN: 3319075454

This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.

Fundamentals of Number Theory

Fundamentals of Number Theory
Author: William J. LeVeque
Publisher: Courier Corporation
Total Pages: 292
Release: 2014-01-05
Genre: Mathematics
ISBN: 0486141500

This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given — making the book self-contained in this respect. The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diophantine approximation, and more. Included are discussions of topics not always found in introductory texts: factorization and primality of large integers, p-adic numbers, algebraic number fields, Brun's theorem on twin primes, and the transcendence of e, to mention a few. Readers will find a substantial number of well-chosen problems, along with many notes and bibliographical references selected for readability and relevance. Five helpful appendixes — containing such study aids as a factor table, computer-plotted graphs, a table of indices, the Greek alphabet, and a list of symbols — and a bibliography round out this well-written text, which is directed toward undergraduate majors and beginning graduate students in mathematics. No post-calculus prerequisite is assumed. 1977 edition.

A Brief Guide to Algebraic Number Theory

A Brief Guide to Algebraic Number Theory
Author: H. P. F. Swinnerton-Dyer
Publisher: Cambridge University Press
Total Pages: 160
Release: 2001-02-22
Genre: Mathematics
ISBN: 9780521004237

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.