| dc.description.abstract | As I see it, the graduate course in algebra must primarily prepare students
to handle the algebra which they will meet in all of mathematics: topology,
partial differential equations, differential geometry, algebraic geometry, analysis ,
and representation theory, not to speak of algebra itself and algebraic number
theory with all its ramifications . Hence I have inserted throughout references to
papers and books which have appeared during the last decades , to indicate some
of the directions in which the algebraic foundations provided by this book are
used ; I have accompanied these references with some motivating comments, to
explain how the topics of the present book fit into the mathematics that is to
come subsequently in various fields ; and I have also mentioned some unsolved
problems of mathematics in algebra and number theory . The abc conjecture is
perhaps the most spectacular of these.
Often when such comments and examples occur out of the logical order,
especially with examples from other branches of mathematics , of necessity some
terms may not be defined , or may be defined only later in the book . I have tried
to help the reader not only by making cross-references within the book, but also
by referring to other books or papers which I mention explicitly .
I have also added a number of exercises . On the whole, I have tried to make
the exercises complement the examples, and to give them aesthetic appeal. I
have tried to use the exercises also to drive readers toward variations and applications
of the main text , as well as toward working out special cases, and as
openings toward applications beyond this book . | en_US |
