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Problems in Algebraic Number Theory

Librairie Eyrolles - Paris 5e
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Problems in Algebraic Number Theory

Problems in Algebraic Number Theory

- Collection Graduate Texts in Mathematics

352 pages, parution le 10/02/2005 (2eme édition)

Résumé

Asking how one does mathematical research is like asking how a composer creates a masterpiece. No one really knows. However, it is a recognized fact that problem solving plays an important role in training the mind of a researcher. It would not be an exaggeration to say that the ability to do mathematical research lies essentially asking "well-posed" questions. The approach taken by the authors in Problems in Algebraic Number Theory is based on the principle that questions focus and orient the mind. The book is a collection of about 500 problems in algebraic number theory, systematically arranged to reveal ideas and concepts in the evolution of the subject. While some problems are easy and straightforward, others are more difficult. For this new edition the authors added a chapter and revised several sections. The text is suitable for a first course in algebraic number theory with minimal supervision by the instructor. The exposition facilitates independent study, and students having taken a basic course in calculus, linear algebra, and abstract algebra will find these problems interesting and challenging. For the same reasons, it is ideal for non-specialists in acquiring a quick introduction to the subject.

Sommaire

  • Problems
    • Elementary Number Theory
    • Euclidean Rings
    • Algebraic Numbers and Integers
    • Integral Bases
    • Dedekind Domains
    • The Ideal Class Group
    • Quadratic Reciprocity
    • The Structure of Units
    • Higher Reciprocity Laws
    • Analytic Methods
    • Density Theorems
  • Solutions
    • Elementary Number Theory
    • Euclidean Rings
    • Algebraic Numbers and Integers
    • Integral Bases
    • Dedekind Domains
    • The Ideal Class Group
    • Quadratic Reciprocity
    • The Structure of Units
    • Higher Reciprocity Laws
    • Analytic Methods
    • Density Theorems
Voir tout
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Caractéristiques techniques du livre "Problems in Algebraic Number Theory"

  PAPIER
Éditeur(s) Springer
Auteur(s) M. Ram Murty, Jody Esmonde
Collection Graduate Texts in Mathematics
Parution 10/02/2005
Édition  2eme édition
Nb. de pages 352
Format 16 x 24
Couverture Relié
Poids 649g
Intérieur Noir et Blanc
EAN13 9780387221823
ISBN13 978-0-387-22182-3

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