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Original Essays | September 15, 2014

Lois Leveen: IMG Forsooth Me Not: Shakespeare, Juliet, Her Nurse, and a Novel



There's this writer, William Shakespeare. Perhaps you've heard of him. He wrote this play, Romeo and Juliet. Maybe you've heard of it as well. It's... Continue »
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    Juliet's Nurse

    Lois Leveen 9781476757445

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Theory of Algebraic Numbers 3RD Edition

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Theory of Algebraic Numbers 3RD Edition Cover

 

Synopses & Reviews

Publisher Comments:

An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.

Book News Annotation:

A brief introduction for undergraduate students and teachers, presenting detailed proofs and explanations of the elementary components of classical algebraic number theory. Begins with divisibility and Gaussian primes, and proceeds to ideal classes and class numbers and the Fermat conjecture. A slightly revised and totally unexpurgated edition of the 1975 publication by the Mathematical Association of America. Annotation c. by Book News, Inc., Portland, OR (booknews@booknews.com)

Synopsis:

Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; more. 1975 edition.

Table of Contents

Chapter I. Divisibility

  1. Uniqueness of factorization

  2. A general problem

  3. The Gaussian integers

  Problems

Chapter II. The Gaussian Primes

  1. Rational and Gaussian primes

  2. Congruences

  3. Determination of the Gaussian primes

  4. Fermat's theorem for Gaussian primes

  Problems

Chapter III. Polynomials over a field

  1. The ring of polynomials

  2. The Eisenstein irreducibility criterion

  3. Symmetric polynomials

  Problems

Chapter IV. Algebraic Number Fields

  1. Numbers algebraic over a field

  2. Extensions of a field

  3. Algebraic and transcendental numbers

  Problems

Chapter V. Bases

  1. Bases and finite extensions

  2. Properties of finite extensions

  3. Conjugates and discriminants

  4. The cyclotomic field

  Problems

Chapter VI. Algebraic Integers and Integral Bases

  1. Algebraic integers

  2. The integers in a quadratic field

  3. Integral bases

  4. Examples of integral bases

  Problems

Chapter VII. Arithmetic in Algebraic Number Fields

  1. Units and primes

  2. Units in a quadratic field

  3. The uniqueness of factorization

  4. Ideals in an algebraic number field

  Problems

Chapter VIII. The Fundamental Theorem of Ideal Theory

  1. Basic properties of ideals

  2. The classical proof of the unique factorization theorem

  3. The modern proof

  Problems

Chapter IX. Consequences of the Fundamental Theorem

  1. The highest common factor of two ideals

  2. Unique factorization of integers

  3. The problem of ramification

  4. Congruences and norms

  5. Further properties of norms

  Problems

Chapter X. Ideal Classes and Class Numbers

  1. Ideal classes

  2. Class numbers

  Problems

Chapter XI. The Fermat Conjecture

  1. Pythagorean triples

  2. The Fermat conjecture

  3. Units in cyclotomic fields

  4. Kummer's theorem

  Problems

  References; List of symbols; Index

Product Details

ISBN:
9780486404547
Author:
Pollard, Harry
Author:
Diamond, Harold G.
Author:
Pollard
Author:
Mathematics
Author:
Diamond
Publisher:
Dover Publications
Location:
Mineola, N.Y. :
Subject:
Number Theory
Subject:
Algebraic number theory
Subject:
General Mathematics
Subject:
Mathematics-Number Theory
Edition Number:
3
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20100831
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
192
Dimensions:
8.5 x 5.38 in 0.47 lb

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Related Subjects


Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Algebra » Linear Algebra
Science and Mathematics » Mathematics » Calculus » Precalculus
Science and Mathematics » Mathematics » Number Theory

Theory of Algebraic Numbers 3RD Edition New Trade Paper
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Product details 192 pages Dover Publications - English 9780486404547 Reviews:
"Synopsis" by ,
Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; more. 1975 edition.
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