Paolo Aluffi's Books

Algebra

Notes from the Underground

By: Paolo Aluffi

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Algebra

Notes from the Underground

By: Paolo Aluffi

A conversational introduction to abstract algebra from a modern, rings-first perspective, including a treatment of modules.

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Page Count

489

Publisher

Cambridge University Press

Published Date

ISBN 10

1108958230

ISBN 13

9781108958233

Algebra: Chapter 0

By: Paolo Aluffi

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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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Page Count

713

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147046571X

ISBN 13

9781470465711

Algebra: Chapter 0

By: Paolo Aluffi

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Algebra: Chapter 0

By: Paolo Aluffi

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Page Count

713

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147046571X

ISBN 13

9781470465711

Algebra

Notes from the Underground

By: Paolo Aluffi

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Algebra

Notes from the Underground

By: Paolo Aluffi

From rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules, including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition, standard topics - such as the Chinese Remainder Theorem, the Gauss Lemma, the Sylow Theorems, simplicity of alternating groups, standard results on field extensions, and the Fundamental Theorem of Galois Theory - are all treated in detail. Students will appreciate the text's conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the main text problems, and an appendix with general background on basic logic and naïve set theory.

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Page Count

490

Publisher

Cambridge University Press

Published Date

ISBN 10

1108962696

ISBN 13

9781108962698

Citizenship in the Arab World

Kin, Religion and Nation-state

By: Gianluca Paolo Parolin

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Citizenship in the Arab World

Kin, Religion and Nation-state

By: Gianluca Paolo Parolin

Subject: The book is the fruit of five years of on-site research on citizenship in the Arab world. It takes a broader legal perspective to the multifaceted reality of nationality and citizenship. The methodology employed builds on the interdisciplinary approach of comparative legal studies, and brings in theories, concepts and insights from anthropology, political science, Arab and Islamic studies, linguistics and sociology. The work relies on a broad range of Western and Arab references, and all sources and documents were directly accessed in their original languages; this is particularly relevant for Arab legislation (all in-text reference has been translated by the author, and the original has been inserted using scientific transliteration). -- Website OAPEN Library.

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Page Count

191

Publisher

Amsterdam University Press

Published Date

ISBN 10

9089640452

ISBN 13

9789089640451

Facets of Algebraic Geometry: Volume 1

A Collection in Honor of William Fulton's 80th Birthday

By: Paolo Aluffi,David Anderson,Milena Hering,Mircea Mustaţă,Sam Payne

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Facets of Algebraic Geometry: Volume 1

A Collection in Honor of William Fulton's 80th Birthday

By: Paolo Aluffi,David Anderson,Milena Hering,Mircea Mustaţă,Sam Payne

Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the first of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured topics include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.

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Page Count

418

Publisher

Cambridge University Press

Published Date

ISBN 10

1108890539

ISBN 13

9781108890533

Book's by Paolo Aluffi

Algebra

Algebra

Algebra: Chapter 0

Algebra: Chapter 0

Algebra: Chapter 0

Algebra: Chapter 0

Algebra

Algebra

Citizenship in the Arab World

Citizenship in the Arab World

Facets of Algebraic Geometry: Volume 1

Facets of Algebraic Geometry: Volume 1

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