| 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 |
| 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 |
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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.
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Table of Contents
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Part A. Course I
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Chapter A-1. Classical formulas
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Chapter A-2. Classical number theory
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Chapter A-3. Commutative rings
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Chapter A-4. Groups
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Chapter A-5. Galois theory
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Chapter A-6. Appendix: Set theory
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Chapter A-7. Appendix: Linear Algebra
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Part B. Course II
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Chapter B-1. Modules
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Chapter B-2. Zorn’s lemma
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Chapter B-3. Advanced linear algebra
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Chapter B-4. Categories of modules
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Chapter B-5. Multilinear algebra
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Chapter B-6. Commutative algebra II
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Chapter B-7. Appendix: Categorical limits
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Chapter B-8. Appendix: Topological spaces
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Additional Material
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Reviews
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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
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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 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
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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
