Algebra: Chapter 0 is a self-contained introduction to the main
topics of algebra, suitable for a first sequence on the subject at
the beginning graduate or upper undergraduate level. The primary
distinguishing feature of the book, compared to standard textbooks
in algebra, is the early introduction of categories, used as a
unifying theme in the presentation of the main topics. A second
feature consists of an emphasis on homological algebra: basic
notions on complexes are presented as soon as modules have been
introduced, and an extensive last chapter on homological algebra
can form the basis for a follow-up introductory course on the
subject. Approximately 1,000 exercises both provide adequate
practice to consolidate the understanding of the main body of the
text and offer the opportunity to explore many other topics,
including applications to number theory and algebraic geometry.
This will allow instructors to adapt the textbook to their specific
choice of topics and provide the independent reader with a richer
exposure to algebra. Many exercises include substantial hints, and
navigation of the topics is facilitated by an extensive index and
by hundreds of cross-references.
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