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Galois Theory: Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures, Number 2) (Englisch) Taschenbuch – 10. Juli 1997

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Produktinformation

  • Taschenbuch: 96 Seiten
  • Verlag: Dover Pubn Inc; Auflage: Revised. (10. Juli 1997)
  • Sprache: Englisch
  • ISBN-10: 0486623424
  • ISBN-13: 978-0486623429
  • Größe und/oder Gewicht: 14 x 0,5 x 21,6 cm
  • Durchschnittliche Kundenbewertung: 4.7 von 5 Sternen  Alle Rezensionen anzeigen (3 Kundenrezensionen)
  • Amazon Bestseller-Rang: Nr. 21.853 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)

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17 von 17 Kunden fanden die folgende Rezension hilfreich Von A MATH NERD am 20. Februar 2000
Format: Taschenbuch
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.
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5 von 5 Kunden fanden die folgende Rezension hilfreich Von M. Diether am 14. August 2006
Format: Taschenbuch
A very short introduction to Galois Theory. But for that little money you can't expect a real in-depth discussion of such a big theory. The basic theorems are very clearly written, the proofs are marvellous compared to any other book that I've seen on this topic. So, if you're looking for a little introduction, this is your book to get.

The layout of the text is a little old-school, because it's a reprint from the 1940's. There's sadly nothing like the modern TeX-style layout that you get in more recent math-books. But the quality of the text and the clarity of all the proofs make this book a definite good buy.
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10 von 13 Kunden fanden die folgende Rezension hilfreich Von Ein Kunde am 17. März 1999
Format: Taschenbuch
I'm an eighth grader at GMMS (So I guess you could say I'm advanced for my age!) but this book has such a clear, concise format that even I could understand it.
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Amazon.com: 16 Rezensionen
44 von 48 Kunden fanden die folgende Rezension hilfreich
Great even if you're not an Eighth grader 20. Februar 2000
Von A MATH NERD - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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.
13 von 13 Kunden fanden die folgende Rezension hilfreich
the source! 13. April 2004
Von another reader - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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.
13 von 14 Kunden fanden die folgende Rezension hilfreich
Succinct exposition of modern Galois theory by a pioneer. 13. November 2003
Von anon2001 - Veröffentlicht auf Amazon.com
Format: Taschenbuch
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.
6 von 6 Kunden fanden die folgende Rezension hilfreich
Artin is the man 2. März 2008
Von Salute Your Shorts - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
Any student (graduate or undergraduate) who is learning Galois theory will benefit greatly from reading this book. Artin has a very elegant style of writing and many parts of the book read like a novel. At its current price, there's no reason to not buy this book; you may actually want to buy a few extra copies as they make great gifts and/or stocking stuffers.

I would also recommend Artin's Geometric Algebra.
10 von 12 Kunden fanden die folgende Rezension hilfreich
Not a Self-Contained Book on Galois Theory 31. Mai 2008
Von Man Kam Tam - Veröffentlicht auf Amazon.com
Format: Taschenbuch Verifizierter Kauf
Galois Theory is in traditional mathematical format. The major elements of the book are definitions, lemmas, theorems, and proofs. The book introduces the major topics of Galois Theory. They are fields, extension fields, splitting fields, unique decomposition of polynomials into irreducible factors, solvable groups, permutation groups, and solution of equations by radical.

The last part of the book contains the major results of Galois Theory with proofs using the theorems from the second part of the book. They are theorem 5: The polynomial f(x) is solvable by radicals if and only if its group is solvable; theorem 4: The symmetric group G on n letters is not solvable for n > 4; theorem 6: The group of the general equation of degree n is the symmetric group on n letters. The general equation of degree n is not solvable by radicals if n > 4.

This is my second Galois Theory book. What impress me most is the involvement to prove the major results of Galois Theory such as theorem 5 and theorem 6. In order to prove the theorems, mathematicians invent many mathematical objects. They are root, group, symmetric group, solvable group, field, extension field, splitting field, Kummer field/extension, Abelian group, normal subgroup, normal extension, factor/quotient group, homomorph, fixed field, extension by radicals field, and more. Nowadays, we put all these objects under the domain of abstract algebra.

The book is certainly not self-contained because one would need an abstract algebra textbook for reference to the mathematical objects.
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