Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
To get the free app, enter your email address or mobile phone number.
Galois Theory: Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures, Number 2) Paperback – July 10, 1997
Top 20 lists in Books
View the top 20 best sellers of all time, the most reviewed books of all time and some of our editors' favorite picks. Learn more
Frequently Bought Together
Customers Who Bought This Item Also Bought
More About the Author
Top Customer Reviews
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.
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.
I would also recommend Artin's Geometric Algebra.
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.
In any case, patient reader will walk away from this book with a feeling of having built the subject from the ground up.
Nevertheless, I can't give it 5 stars because the book is very lacking in exercises. There are some applications scattered here and there (e.g. on symmetric extensions of function fields and on symmetric functions) but this is hopelessly insufficient to solidify the knowledge gained from the theorems. To properly understand Galois theory one needs to get their hands dirty by investigating splitting fields and Galois groups of all kinds of polynomials and paying close attention to the interaction of roots and group actions. In this regard the book leaves the reader completely on their own and so should be complemented by some additional source of exercices.
Most Recent Customer Reviews
Evariste Galois was the Beethoven of mathematics because he was able to "see" mathematical ideas with his entire being. Read morePublished 16 months ago by Thomas Enzor
... from [...]%20M.%20Galois%20theory%20(2ed,%20London,%201944)(86s).pdf
This is still an excellent way to learn the basics of Galois Theory on your own (assuming you've... Read more
great book but the kindle version is packed full of typos and misprints. get the latest dover edition and you're all set.Published on March 6, 2013 by anabasist
during reading this cute booklet, you can surely hear the gentle talk of an old math maven.(from the publishing date, the auther was 44 but that's my impression. Read morePublished on February 19, 2002