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Hardcover ISBN:  9781470415549 
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Hardcover ISBN:  9781470415549 
Product Code:  GSM/165 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Sale Price:  $87.75 
eBook ISBN:  9781470427313 
Product Code:  GSM/165.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Sale Price:  $55.25 
Hardcover ISBN:  9781470415549 
eBook ISBN:  9781470427313 
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 
Sale Price:  $143.00 $115.38 

Book DetailsGraduate Studies in MathematicsVolume: 165; 2015; 706 ppMSC: 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.
ReadershipGraduate students and researchers interested in learning and teaching algebra.

Table of Contents

Part A. Course I

Chapter A1. Classical formulas

Chapter A2. Classical number theory

Chapter A3. Commutative rings

Chapter A4. Groups

Chapter A5. Galois theory

Chapter A6. Appendix: Set theory

Chapter A7. Appendix: Linear Algebra

Part B. Course II

Chapter B1. Modules

Chapter B2. Zorn’s lemma

Chapter B3. Advanced linear algebra

Chapter B4. Categories of modules

Chapter B5. Multilinear algebra

Chapter B6. Commutative algebra II

Chapter B7. Appendix: Categorical limits

Chapter B8. Appendix: Topological spaces


Additional Material

Reviews

The organization of the text is clear and the pace is leisurely...recently I taught the second part of a firstyear 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


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 Book Details
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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.
Graduate students and researchers interested in learning and teaching algebra.

Part A. Course I

Chapter A1. Classical formulas

Chapter A2. Classical number theory

Chapter A3. Commutative rings

Chapter A4. Groups

Chapter A5. Galois theory

Chapter A6. Appendix: Set theory

Chapter A7. Appendix: Linear Algebra

Part B. Course II

Chapter B1. Modules

Chapter B2. Zorn’s lemma

Chapter B3. Advanced linear algebra

Chapter B4. Categories of modules

Chapter B5. Multilinear algebra

Chapter B6. Commutative algebra II

Chapter B7. Appendix: Categorical limits

Chapter B8. Appendix: Topological spaces

The organization of the text is clear and the pace is leisurely...recently I taught the second part of a firstyear 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