Advanced Modern Algebra - Joseph J. Rotman

Preface

Algebra is used by virtually all mathematicians, be they analysts, combinatorists, computer

scientists, geometers, logicians, number theorists, or topologists. Nowadays, everyone

agrees that some knowledge of linear algebra, groups, and commutative rings is

necessary, and these topics are introduced in undergraduate courses. We continue their

study.

This book can be used as a text for the first year of graduate algebra, but it is much more

than that. It can also serve more advanced graduate students wishing to learn topics on

their own; while not reaching the frontiers, the book does provide a sense of the successes

and methods arising in an area. Finally, this is a reference containing many of the standard

theorems and definitions that users of algebra need to know. Thus, the book is not only an

appetizer, but a hearty meal as well.

When I was a student, Birkhoff and Mac Lane’s A Survey of Modern Algebra was the

text for my first algebra course, and van der Waerden’s Modern Algebra was the text for

my second course. Both are excellent books (I have called this book Advanced Modern

Algebra in homage to them), but times have changed since their first appearance: Birkhoff

and Mac Lane’s book first appeared in 1941, and van der Waerden’s book first appeared

in 1930. There are today major directions that either did not exist over 60 years ago, or

that were not then recognized to be so important. These new directions involve algebraic

geometry, computers, homology, and representations (A Survey of Modern Algebra has

been rewritten as Mac Lane–Birkhoff, Algebra, Macmillan, New York, 1967, and this

version introduces categorical methods; category theory emerged from algebraic topology,

but was then used by Grothendieck to revolutionize algebraic geometry).

hulkload

depositfiles

Hacene@freebooks