Algebra Chapter 0

Author : Paolo Aluffi
Publisher : American Mathematical Soc.
ISBN 13 : 147046571X
Total Pages : 713 pages
Book Rating : 4.11/5 ( download)

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Download or read book Algebra: Chapter 0 written by Paolo Aluffi and published by American Mathematical Soc.. This book was released on 2021-11-09 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Paolo Aluffi
Publisher : American Mathematical Soc.
ISBN 13 : 0821847813
Total Pages : 713 pages
Book Rating : 4.17/5 ( download)

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Download or read book Algebra: Chapter 0 written by Paolo Aluffi and published by American Mathematical Soc.. This book was released on 2009 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Paolo Aluffi
Publisher : American Mathematical Society(RI)
ISBN 13 : 9781470411688
Total Pages : 0 pages
Book Rating : 4.87/5 ( download)

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Download or read book Algebra written by Paolo Aluffi and published by American Mathematical Society(RI). This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an introduction to the main topics of algebra. This book also offers introduction of categories used as a unifying theme in the presentation of the main topics. It includes approximately 1,000 exercises that provide practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics.

Author : Paolo Aluffi
Publisher : Cambridge University Press
ISBN 13 : 1108958230
Total Pages : 489 pages
Book Rating : 4.33/5 ( download)

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Download or read book Algebra written by Paolo Aluffi and published by Cambridge University Press. This book was released on 2021-06-03 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: A conversational introduction to abstract algebra from a modern, rings-first perspective, including a treatment of modules.

Author : Masaki Kashiwara
Publisher : Springer Science & Business Media
ISBN 13 : 3540279504
Total Pages : 498 pages
Book Rating : 4.01/5 ( download)

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Download or read book Categories and Sheaves written by Masaki Kashiwara and published by Springer Science & Business Media. This book was released on 2005-12-20 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

Author : W. Keith Nicholson
Publisher : John Wiley & Sons
ISBN 13 : 1118135350
Total Pages : 560 pages
Book Rating : 4.58/5 ( download)

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Download or read book Introduction to Abstract Algebra written by W. Keith Nicholson and published by John Wiley & Sons. This book was released on 2012-03-20 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.

Author : I. Martin Isaacs
Publisher : American Mathematical Soc.
ISBN 13 : 0821847996
Total Pages : 531 pages
Book Rating : 4.92/5 ( download)

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Download or read book Algebra written by I. Martin Isaacs and published by American Mathematical Soc.. This book was released on 2009 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: as a student." --Book Jacket.

Author : George M. Bergman
Publisher : Springer
ISBN 13 : 3319114786
Total Pages : 572 pages
Book Rating : 4.81/5 ( download)

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Download or read book An Invitation to General Algebra and Universal Constructions written by George M. Bergman and published by Springer. This book was released on 2015-02-05 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.

Author : Charles C Pinter
Publisher : Courier Corporation
ISBN 13 : 0486474178
Total Pages : 402 pages
Book Rating : 4.75/5 ( download)

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Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

Author : Serge Lang
Publisher : Springer Science & Business Media
ISBN 13 : 1475768982
Total Pages : 380 pages
Book Rating : 4.85/5 ( download)

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Download or read book Undergraduate Algebra written by Serge Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group