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

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

A Course in Algebraic Number Theory

A Course in Algebraic Number Theory
Author: Robert B. Ash
Publisher: Courier Corporation
Total Pages: 130
Release: 2010-01-01
Genre: Mathematics
ISBN: 0486477541

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This text for a graduate-level course covers the general theory of factorization of ideals in Dedekind domains as well as the number field case. It illustrates the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition.

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

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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.

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

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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.

The Math Dude's Quick and Dirty Guide to Algebra

The Math Dude's Quick and Dirty Guide to Algebra
Author: Jason Marshall
Publisher: St. Martin's Griffin
Total Pages: 496
Release: 2011-07-05
Genre: Mathematics
ISBN: 9781429983365

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Need some serious help solving equations? Totally frustrated by polynomials, parabolas and that dreaded little x? THE MATH DUDE IS HERE TO HELP! Jason Marshall, popular podcast host known to his fans as The Math Dude, understands that algebra can cause agony. But he's determined to show you that you can solve those confusing, scream-inducing math problems--and it won't be as hard as you think! Jason kicks things off with a basic-training boot camp to help you review the essential math you'll need to truly "get" algebra. The basics covered, you'll be ready to tackle the concepts that make up the core of algebra. You'll get step-by-step instructions and tutorials to help you finally understand the problems that stump you the most, including loads of tips on: - Working with fractions, decimals, exponents, radicals, functions, polynomials and more - Solving all kinds of equations, from basic linear problems to the quadratic formula and beyond - Using graphs and understanding why they make solving complex algebra problems easier Learning algebra doesn't have to be a form of torture, and with The Math Dude's Quick and Dirty Guide to Algebra, it won't be. Packed with tons of fun features including "secret agent math-libs," and "math brain games," and full of quick and dirty tips that get right to the point, this book will have even the biggest math-o-phobes basking in a-ha moments and truly understanding algebra in a way that will stick for years (and tests) to come. Whether you're a student who needs help passing algebra class, a parent who wants to help their child meet that goal, or somebody who wants to brush up on their algebra skills for a new job or maybe even just for fun, look no further. Sit back, relax, and let this guide take you on a trip through the world of algebra.

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

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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.

Number Theory and Its History

Number Theory and Its History
Author: Oystein Ore
Publisher: Courier Corporation
Total Pages: 400
Release: 2012-07-06
Genre: Mathematics
ISBN: 0486136434

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Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.

A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond Z

A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond Z
Author: Paul Pollack
Publisher: American Mathematical Soc.
Total Pages: 312
Release: 2017-08-01
Genre: Algebraic number theory
ISBN: 1470436531

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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.

Number Theory II

Number Theory II
Author: A. N. Parshin
Publisher: Springer
Total Pages: 292
Release: 1992
Genre: Mathematics
ISBN:

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Volume 62 of the Encyclopedia presents the main structures and results of algebraic number theory with emphasis on algebraic number fields and class field theory. Written for the nonspecialist, the author assumes a general understanding of modern algebra and elementary number theory. Only the general properties of algebraic number fields and relate.