Softcover ISBN:  9781470465711 
Product Code:  GSM/104.S 
List Price:  $95.00 
MAA Member Price:  $85.50 
AMS Member Price:  $76.00 
Electronic ISBN:  9781470411688 
Product Code:  GSM/104.E 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 

Book DetailsGraduate Studies in MathematicsVolume: 104; 2009; 713 ppMSC: Primary 00; Secondary 12; 13; 15; 18; 20;
Algebra: Chapter 0 is a selfcontained 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 followup 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 crossreferences.
ReadershipUndergraduate and graduate students interested in algebra.

Table of Contents

Chapters

Chapter I. Preliminaries: Set theory and categories

Chapter II. Groups, first encounter

Chapter III. Rings and modules

Chapter IV. Groups, second encounter

Chapter V. Irreducibility and factorization in integral domains

Chapter VI. Linear algebra

Chapter VII. Fields

Chapter VIII. Linear algebra, reprise

Chapter IX. Homological algebra


Additional Material

Reviews

An obvious question: why another graduate algebra book? Aren't there all but too many already? Is there anything genuinely novel to be done when it comes to educating fledgling graduate students in this subject, given such an already wellpopulated and highquality field? Well, the answer is yes. And the title of the book under review, Algebra: Chapter 0, is already a clue to what the author, Paolo Aluffi, is up to. In a perhaps Bourbakian sense, the prevailing motivation and objective is to present the subject at hand in a manner that pays proper due to relatively new foundations, making for a rather different orientation and flavor for what ensues. ...His treatment of these preliminaries is thorough as well as eminently accessible: Aluffi writes well, clearly and engagingly. This characterizes all of Algebra: Chapter 0, actually, and makes it easy to recommend the book enthusiastically even aside from the fact that I am a big fan of category theory to begin with.
MAA Online 
This selfcontained introduction is suitable for a first sequence at the beginning graduate or upper undergraduate level. A distinguishing feature of the book is the early introduction of categories, used as a unifying theme.
SciTech Book News


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Algebra: Chapter 0 is a selfcontained 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 followup 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 crossreferences.
Undergraduate and graduate students interested in algebra.

Chapters

Chapter I. Preliminaries: Set theory and categories

Chapter II. Groups, first encounter

Chapter III. Rings and modules

Chapter IV. Groups, second encounter

Chapter V. Irreducibility and factorization in integral domains

Chapter VI. Linear algebra

Chapter VII. Fields

Chapter VIII. Linear algebra, reprise

Chapter IX. Homological algebra

An obvious question: why another graduate algebra book? Aren't there all but too many already? Is there anything genuinely novel to be done when it comes to educating fledgling graduate students in this subject, given such an already wellpopulated and highquality field? Well, the answer is yes. And the title of the book under review, Algebra: Chapter 0, is already a clue to what the author, Paolo Aluffi, is up to. In a perhaps Bourbakian sense, the prevailing motivation and objective is to present the subject at hand in a manner that pays proper due to relatively new foundations, making for a rather different orientation and flavor for what ensues. ...His treatment of these preliminaries is thorough as well as eminently accessible: Aluffi writes well, clearly and engagingly. This characterizes all of Algebra: Chapter 0, actually, and makes it easy to recommend the book enthusiastically even aside from the fact that I am a big fan of category theory to begin with.
MAA Online 
This selfcontained introduction is suitable for a first sequence at the beginning graduate or upper undergraduate level. A distinguishing feature of the book is the early introduction of categories, used as a unifying theme.
SciTech Book News