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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.
I. Linear Algebra
B. Vector Spaces
C. Homogeneous Linear Equations
D. Dependence and Independence of Vectors
E. Non-homogeneous Linear Equations
II. Field Theory
A. Extension fields
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
Posted August 15, 2001
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.Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.
Posted March 24, 2009
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