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aluffi p algebra chapter 0 2009

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Textbook in PDF format 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. About the Author: Paolo Aluffi was born in Italy, and studied mathematics in Torino under the direction of Alberto Collino, and then at Brown University, obtaining a Ph.D. with a dissertation in algebraic geometry under the supervision of William Fulton. He has held postdoctoral positions at the University of Chicago and Oklahoma State University, and joined the department of mathematics at Florida State University in 1991. He is currently professor of mathematics at FSU. Paolo Aluffi has visited many universities and mathematics institutes for extended periods of time. Among these are the Max-Planck-Institut in Bonn, Germany; Harvard University; the Institut des Mathématiques in Luminy, France; the Mittag-Leffler Institut in Stockholm, Sweden; the Mathematical Sciences Research Institute in Berkeley, California; and the California Institute of Technology

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aluffi p algebra chapter 0 2009

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