Galois Theory: Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures, Number 2) [Paperback]

Emil Artin (Author), Arthur N. Milgram (Editor)

Book Description

Publication Date: July 10, 1997

Clearly presented elements of one of the most penetrating concepts in modern mathematics include discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.

Product Details

• Paperback: 86 pages
• Publisher: Dover Publications (July 10, 1997)
• Language: English
• ISBN-10: 0486623424
• ISBN-13: 978-0486623429
• Product Dimensions: 8.4 x 5.3 x 0.2 inches
• Shipping Weight: 4.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (11 customer reviews)
• Amazon Best Sellers Rank: #451,147 in Books (See Top 100 in Books)

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39 of 42 people found the following review helpful:

5.0 out of 5 stars Great even if you're not an Eighth grader, February 19, 2000

By 

A MATH NERD - See all my reviews

This review is from: Galois Theory: Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures, Number 2) (Paperback)

This book is one of the very best that Dover has out there. In my opinion, it is the ultimate book on Galois theory. All treatments written since this one were based on it, and do not add anything fundamentally new. There are only two things about this book which one could potentially complain about: 1) The awful cover. 2) There are no exercises because the book is just based on lecture notes. But that's forgivable, because there is no other exposition this good of Galois theory.

One wonderful thing about this book is that it is entirely self-contained. It starts by proving the few basic results from linear algebra it needs, and then builds from there in a beautiful way until the fundamental theorems of Galois theory have been proven in a most transparent way. Then, in the appendix, not by Artin, a few results from group theory are proven, just enough for the classical applications to the solvability of the quintic.

Every proof in this book is very clear and I cannot imagine how one could improve on any of them.

ET Bell claimed in one of his books that anyone who knew high school algebra could easily understand Galois's proof of the unsolvability of the quintic. I didn't believe that until I saw this book, which proves that ET Bell was absolutely correct.

11 of 11 people found the following review helpful:

4.0 out of 5 stars the source!, April 12, 2004

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another reader - See all my reviews

This review is from: Galois Theory: Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures, Number 2) (Paperback)

This is modern Galois Theory, straight from the horse's mouth! Galois Theory is taught today using field extensions rather than by actually solving polynomials, students also learn to view a field extension as a vector space over the smaller field; both of these things were pioneered by Artin. The book also has short, clear proofs of all the main theorems. The only problem is that there are no problems to work on, so I have to say this is only a good reference for Galois Theory.

10 of 11 people found the following review helpful:

5.0 out of 5 stars Succinct exposition of modern Galois theory by a pioneer., November 13, 2003

By 

anon2001 "anon2001" (Kinross, Western Australia AUSTRALIA) - See all my reviews

This review is from: Galois Theory: Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures, Number 2) (Paperback)

Emil Artin's short book gets a mention in most texts on
Galois theory. It is very short - only 60 odd pages. Yet
it is a very clear, complete and readable account of the
essential elements of modern Galois theory. It is based
on lectures he gave over 50 years ago but you might think
it was written only yesterday and is comprehensible to
anyone familiar with current abstract algebra terminology.
And the price makes it a bargain. There are no worked
examples, exercises or index here.