Galois Theory: Lectures Delivered at the University of Notre Dame (Notre Dame Mathematical Lectures, Number 2) / Edition 2

Galois Theory: Lectures Delivered at the University of Notre Dame (Notre Dame Mathematical Lectures, Number 2) / Edition 2

3.5 2
by Emil Artin
     
 

ISBN-10: 0486623424

ISBN-13: 9780486623429

Pub. Date: 07/10/1997

Publisher: Dover Publications

In the nineteenth century, French mathematician Evariste Galois developed the Galois theory of groups-one of the most penetrating concepts in modem mathematics. The elements of the theory are clearly presented in this second, revised edition of a volume of lectures delivered by noted mathematician Emil Artin. The book has been edited by Dr. Arthur N. Milgram, who

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Overview

In the nineteenth century, French mathematician Evariste Galois developed the Galois theory of groups-one of the most penetrating concepts in modem mathematics. The elements of the theory are clearly presented in this second, revised edition of a volume of lectures delivered by noted mathematician Emil Artin. The book has been edited by Dr. Arthur N. Milgram, who has also supplemented the work with a Section on Applications.
The first section deals with linear algebra, including fields, vector spaces, homogeneous linear equations, determinants, and other topics. A second section considers extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, Noether equations, Jummer's fields, and more.
Dr. Milgram's section on applications discusses solvable groups, permutation groups, solution of equations by radicals, and other concepts.

Product Details

ISBN-13:
9780486623429
Publisher:
Dover Publications
Publication date:
07/10/1997
Series:
Dover Books on Mathematics Series
Pages:
98
Sales rank:
776,878
Product dimensions:
5.50(w) x 8.50(h) x 0.20(d)

Table of Contents

I. Linear Algebra
  A. Fields
  B. Vector Spaces
  C. Homogeneous Linear Equations
  D. Dependence and Independence of Vectors
  E. Non-homogeneous Linear Equations
  F. Determinants
II. Field Theory
  A. Extension fields
  B. Polynomials
  C. Algebraic Elements
  D. Splitting fields
  E. Unique Decomposition of Polynomials into Irreducible Factors
  F. Group Characters
  G. Applications and Examples to Theorem 13
  H. Normal Extensions
  I. Finite Fields
  J. Roots of Unity
  K. Noether Equations
  L. Kimmer's Fields
  M. Simple Extensions
  N. Existence of a Normal Basis
  O. Theorem on natural Irrationalities
III. Applications. By A. N. Milgram
  A. Solvable Groups
  B. Permutation Groups
  C. Solution of Equations by Radicals
  D. The General Equation of Degree n
  E. Solvable Equations of Prime Degree
  F. Ruler and Compass Construction

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Galois Theory: Lectures Delivered at the University of Notre Dame (Notre Dame Mathematical Lectures, Number 2) 3.5 out of 5 based on 0 ratings. 2 reviews.
Anonymous More than 1 year ago
Guest More than 1 year ago
You don't need any algebra background to read and appreciate this book. Only the knowledge of the definitions of groups and normal subgroups is needed. You can find these in any modern algebra book. I read it as a college sophomore without much prior knowledge in this field. I was able to enjoy it pretty much. It might be a little too dense for beginners, but it is almost entirely self contained. It is written based on lecture notes, so don't expect it to be in a very organized format. The only thing I don't like is that it doesn't have an index, but it's okay since the book is very thin.