60才からの数学への理解
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0217132人目の素数さん
2011/02/05(土) 09:51:55As others have said, this is not a book to begin learning algebra,
but is a necessary book for most students to have on their shelves.
Why is that? Basic topics are discussed from scratch in this book
from the most advanced possible viewpoint.
Hence few can learn them here for the first time,
but no one can graduate to professional status without eventually arriving at this perspective.
In particular the categorical point of view is simply essential to a research mathematician
to acquire at some point, and Lang uses it here from the beginning,
while Dummitt and Foote place it in appendix II, after page 800.
So Lang's goal seems not to introduce basic algebra,
but to provide essential algebraic facts not found elsewhere,
and to give them all from a professional's perspective.
This is probably a third book on algebra in today's world,
and that is assuming the student is pretty good.
The only current book I know of out there that is really aimed at students
and also written by a top professional is Artin.
If you can, begin with Artin, then read Dummitt and Foote for topics Artin omits,
then read Lang to see how you should view the same material and find things
Dummitt and Foote left out.
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