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Algebra: Chapter 0
 
Paolo Aluffi Florida State University, Tallahassee, FL
Algebra: Chapter 0
Softcover ISBN:  978-1-4704-6571-1
Product Code:  GSM/104.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-1168-8
Product Code:  GSM/104.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-6571-1
eBook: ISBN:  978-1-4704-1168-8
Product Code:  GSM/104.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
Algebra: Chapter 0
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Algebra: Chapter 0
Paolo Aluffi Florida State University, Tallahassee, FL
Softcover ISBN:  978-1-4704-6571-1
Product Code:  GSM/104.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-1168-8
Product Code:  GSM/104.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-6571-1
eBook ISBN:  978-1-4704-1168-8
Product Code:  GSM/104.S.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1042009; 713 pp
    MSC: Primary 00; Secondary 12; 13; 15; 18; 20;

    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.

    Readership

    Undergraduate 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
  • 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 well-populated and high-quality 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 self-contained 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1042009; 713 pp
MSC: Primary 00; Secondary 12; 13; 15; 18; 20;

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.

Readership

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 well-populated and high-quality 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 self-contained 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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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