Galois Theory (Graduate Texts in Mathematics)

Rating:
Summary: Too historical, anecdotal
Review: I found this book kind of hard to read. The author tried to give topics motivation by putting them in their historical context, but I found that this muddied the treatment so that the reader is left wishing that the author would chose between a history book and a math book. I disagree with the author that the original text of Galois is the best way to learn the theory, I found it considerably less readable than Artin's book, and it placed Galois theory too much in its historical context of solution by radicals. This obscured its manifold modern uses...

Rating:
Summary: Too historical, anecdotal
Review: I found this book kind of hard to read. The author tried to give topics motivation by putting them in their historical context, but I found that this muddied the treatment so that the reader is left wishing that the author would chose between a history book and a math book. I disagree with the author that the original text of Galois is the best way to learn the theory, I found it considerably less readable than Artin's book, and it placed Galois theory too much in its historical context of solution by radicals. This obscured its manifold modern uses...

Rating:
Summary: Best treatment for the "mechanics" of Galois Theory
Review: This is the only book I have seen that "mechanically dissects" galois theory. Other books would give a succession of "theorem-proofs" that eventually proved the Galois solvability theorem but when I was finished, I still could not intuitively understand how the solvability of Galois groups to corresponds to solvability by radicals.

Instead of plodding thru theorem-proof without insight or motivation, this book actually works thru the relation between the algebra of polynomial solutions and the structure of their groups. Ultimately it shows the structure that an equation must have to be solvable (equivalently to have a solvable Galois group).

Unlike the other reader who did not get alot out of Galois' original writing, it opened a window of understanding for me.

Make no mistake, understanding the material here took considerable effort to work out the math on paper to follow the examples and the proofs. Perhaps the book could be improved by adding more detail in places, but then, this is a graduate-level text.

This is the second book I have read from Harold Edwards. I found I learn an awful lot of the low-level details of a subject that I can't find anywhere else. I believe he is one of the best authors in mathematics today. I would happily collect all his works.

Rating:
Summary: Best treatment for the "mechanics" of Galois Theory
Review: This is the only book I have seen that "mechanically dissects" galois theory. Other books would give a succession of "theorem-proofs" that eventually proved the Galois solvability theorem but when I was finished, I still could not intuitively understand how the solvability of Galois groups to corresponds to solvability by radicals.

Instead of plodding thru theorem-proof without insight or motivation, this book actually works thru the relation between the algebra of polynomial solutions and the structure of their groups. Ultimately it shows the structure that an equation must have to be solvable (equivalently to have a solvable Galois group).

Unlike the other reader who did not get alot out of Galois' original writing, it opened a window of understanding for me.

Make no mistake, understanding the material here took considerable effort to work out the math on paper to follow the examples and the proofs. Perhaps the book could be improved by adding more detail in places, but then, this is a graduate-level text.

This is the second book I have read from Harold Edwards. I found I learn an awful lot of the low-level details of a subject that I can't find anywhere else. I believe he is one of the best authors in mathematics today. I would happily collect all his works.