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Advanced Modern Algebra: Third Edition, Part 1
 
Joseph J. Rotman University of Illinois at Urbana-Champaign, Urbana, IL
Advanced Modern Algebra
Hardcover ISBN:  978-1-4704-1554-9
Product Code:  GSM/165
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-2731-3
Product Code:  GSM/165.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-1554-9
eBook: ISBN:  978-1-4704-2731-3
Product Code:  GSM/165.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
Advanced Modern Algebra
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Advanced Modern Algebra: Third Edition, Part 1
Joseph J. Rotman University of Illinois at Urbana-Champaign, Urbana, IL
Hardcover ISBN:  978-1-4704-1554-9
Product Code:  GSM/165
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-2731-3
Product Code:  GSM/165.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-1554-9
eBook ISBN:  978-1-4704-2731-3
Product Code:  GSM/165.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1652015; 706 pp
    MSC: Primary 12; 13; 14; 15; 16; 18; 20;

    This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. This first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. Topics covered in the first course are classical formulas for solutions of cubic and quartic equations, classical number theory, commutative algebra, groups, and Galois theory. Topics in the second course are Zorn's lemma, canonical forms, inner product spaces, categories and limits, tensor products, projective, injective, and flat modules, multilinear algebra, affine varieties, and Gröbner bases.

    Readership

    Graduate students and researchers interested in learning and teaching algebra.

  • Table of Contents
     
     
    • Part A. Course I
    • Chapter A-1. Classical formulas
    • Chapter A-2. Classical number theory
    • Chapter A-3. Commutative rings
    • Chapter A-4. Groups
    • Chapter A-5. Galois theory
    • Chapter A-6. Appendix: Set theory
    • Chapter A-7. Appendix: Linear Algebra
    • Part B. Course II
    • Chapter B-1. Modules
    • Chapter B-2. Zorn’s lemma
    • Chapter B-3. Advanced linear algebra
    • Chapter B-4. Categories of modules
    • Chapter B-5. Multilinear algebra
    • Chapter B-6. Commutative algebra II
    • Chapter B-7. Appendix: Categorical limits
    • Chapter B-8. Appendix: Topological spaces
  • Reviews
     
     
    • The organization of the text is clear and the pace is leisurely...recently I taught the second part of a first-year graduate course in algebra, and in the process dipped into this book at various points. I enjoyed the presentation, and the commentary on constructions and results aimed to place them in context, and I found the numerous examples and exercises helpful. I will be using this book when teaching such courses again, if not always as the main text, certainly as a useful supplement.

      Srikanth B. Iyengar, Mathematical Reviews
    • Rotman is a wonderful expositor, and the two courses in this book strike me as well thought out and well presented.

      Fernando Q. Gouvêa, MAA
  • 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: 1652015; 706 pp
MSC: Primary 12; 13; 14; 15; 16; 18; 20;

This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. This first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. Topics covered in the first course are classical formulas for solutions of cubic and quartic equations, classical number theory, commutative algebra, groups, and Galois theory. Topics in the second course are Zorn's lemma, canonical forms, inner product spaces, categories and limits, tensor products, projective, injective, and flat modules, multilinear algebra, affine varieties, and Gröbner bases.

Readership

Graduate students and researchers interested in learning and teaching algebra.

  • Part A. Course I
  • Chapter A-1. Classical formulas
  • Chapter A-2. Classical number theory
  • Chapter A-3. Commutative rings
  • Chapter A-4. Groups
  • Chapter A-5. Galois theory
  • Chapter A-6. Appendix: Set theory
  • Chapter A-7. Appendix: Linear Algebra
  • Part B. Course II
  • Chapter B-1. Modules
  • Chapter B-2. Zorn’s lemma
  • Chapter B-3. Advanced linear algebra
  • Chapter B-4. Categories of modules
  • Chapter B-5. Multilinear algebra
  • Chapter B-6. Commutative algebra II
  • Chapter B-7. Appendix: Categorical limits
  • Chapter B-8. Appendix: Topological spaces
  • The organization of the text is clear and the pace is leisurely...recently I taught the second part of a first-year graduate course in algebra, and in the process dipped into this book at various points. I enjoyed the presentation, and the commentary on constructions and results aimed to place them in context, and I found the numerous examples and exercises helpful. I will be using this book when teaching such courses again, if not always as the main text, certainly as a useful supplement.

    Srikanth B. Iyengar, Mathematical Reviews
  • Rotman is a wonderful expositor, and the two courses in this book strike me as well thought out and well presented.

    Fernando Q. Gouvêa, MAA
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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