Publication list for Rotman, Joseph

Latest Titles

  • Advanced Modern Algebra: Third Edition, Part 2
    Base Product Code Keyword List: gsm; GSM; gsm/180; GSM/180; gsm-180; GSM-180
    Print Product Code: GSM/180
    Online Product Code: GSM/180.E
    Title (HTML): Advanced Modern Algebra: Third Edition, Part 2
    Author(s) (Product display): Joseph J. Rotman
    Affiliation(s) (HTML): University of Illinois at Urbana-Champaign, Urbana, IL
    Abstract:

    This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

    Book Series Name: Graduate Studies in Mathematics
    Volume: 180
    Publication Month and Year: 2017-08-15
    Copyright Year: 2017
    Page Count: 558
    Cover Type: Hardcover
    Print ISBN-13: 978-1-4704-2311-7
    Online ISBN 13: 978-1-4704-4170-8
    Print ISSN: 1065-7339
    Online ISSN: 1065-7339
    Primary MSC: 12; 13; 14; 15; 16; 18; 20
    Textbook?: true
    Applied Math?: false
    Electronic Media?: false
    Apparel or Gift: false
    SXG Subject: AA
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/gsm-180
    Online Price 1 Label: List
    Online Price 1: 94.00
    Print Price 1 Label: List
    Print Price 1: 94.00
    Online Price 2 Label: Individual Member
    Online Price 2: 75.20
    Print Price 2 Label: Individual Member
    Print Price 2: 75.20
    Dual Price 1 Label: List
    Dual Price 1: 117.5
    Dual Price 2 Label: Individual Member
    Dual Price 2: 94
    Print Add to Cart URL: /some/url/at/AMS/GSM-180
    Electronic Add to Cart URL: /some/url/at/AMS/GSM-180.E
    Exam/Desk Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4170-8&pisbn=978-1-4704-2311-7&epc=GSM/180.E&ppc=GSM/180&title=Advanced%20Modern%20Algebra%3A%20Third%20Edition%2C%20Part%202&author=Joseph%20J.%20Rotman&type=DE
    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4170-8&pisbn=978-1-4704-2311-7&epc=GSM/180.E&ppc=GSM/180&title=Advanced%20Modern%20Algebra%3A%20Third%20Edition%2C%20Part%202&author=Joseph%20J.%20Rotman&type=R
    Sets and Parts:

    This item is also available as part of a set:

    GSM/165/180

    Readership:

    Graduate students and researchers interested in learning and teaching algebra.

    Reviews:

    This is a good book and a fitting tribute to a great mathematical expositor. I'll keep both the second edition and the two parts of the third edition on my shelf, and I'm sure I'll turn to them often in the future.

    -- Fernando Q. Gouvêa, MAA Reviews

    Related Products: Algebra Algebra: Chapter 0 Advanced Modern Algebra
    Cover Image URL: ~~FreeAttachments/gsm-180-cov.jpg
  • Advanced Modern Algebra: Third Edition, Parts 1 and 2
    Base Product Code Keyword List: gsm; GSM; gsm/165; GSM/165; gsm-165; GSM-165; gsm/165/180; GSM/165/180; gsm-165-180; GSM-165-180
    Print Product Code: GSM/165/180
    Title (HTML): Advanced Modern Algebra: Third Edition, Parts 1 and 2
    Author(s) (Product display): Joseph J. Rotman
    Affiliation(s) (HTML): University of Illinois at Urbana-Champaign, Urbana, IL
    Abstract:

    This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. The 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.

    The second part presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

    Book Series Name: Graduate Studies in Mathematics
    Publication Month and Year: 2017-08-29
    Copyright Year: 2017
    Cover Type: Hardcover
    Print ISBN-13: 978-1-4704-4174-6
    Print ISSN: 1065-7339
    Primary MSC: 12; 13; 14; 15; 16; 18; 20
    Textbook?: true
    Applied Math?: false
    Home Page?: false
    Sample?: false
    Reference?: false
    Electronic Media?: false
    Apparel or Gift: false
    SXG Subject: AA
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/gsm-165
    Print Price 1 Label: List
    Print Price 1: 174.00
    Print Price 2 Label: Individual Member
    Print Price 2: 139.20
    Print Add to Cart URL: /some/url/at/AMS/GSM-165-180
    Exam/Desk Copy: http://www.ams.org/exam-desk-review-request?&pisbn=978-1-4704-4174-6&ppc=GSM/165/180&title=Advanced%20Modern%20Algebra%3A%20Third%20Edition%2C%20Parts%201%20and%202&author=Joseph%20J.%20Rotman&type=DE
    Review Copy: http://www.ams.org/exam-desk-review-request?&pisbn=978-1-4704-4174-6&ppc=GSM/165/180&title=Advanced%20Modern%20Algebra%3A%20Third%20Edition%2C%20Parts%201%20and%202&author=Joseph%20J.%20Rotman&type=R
    Sets and Parts:

    Item(s) contained in this set are available for individual sale:

    GSM/165
    GSM/180

    Readership:

    Graduate students and researchers interested in learning and teaching algebra.

    Cover Image URL: ~~FreeAttachments/gsm-165-180-cov.jpg
  • Advanced Modern Algebra: Third Edition, Part 1
    Base Product Code Keyword List: gsm; GSM; gsm/165; GSM/165; gsm-165; GSM-165
    Print Product Code: GSM/165
    Online Product Code: GSM/165.E
    Title (HTML): Advanced Modern Algebra: Third Edition, Part 1
    Author(s) (Product display): Joseph J. Rotman
    Affiliation(s) (HTML): University of Illinois at Urbana-Champaign, Urbana, IL
    Abstract:

    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.

    Book Series Name: Graduate Studies in Mathematics
    Volume: 165
    Publication Month and Year: 2015-11-30
    Copyright Year: 2015
    Page Count: 706
    Cover Type: Hardcover
    Print ISBN-13: 978-1-4704-1554-9
    Online ISBN 13: 978-1-4704-2731-3
    Print ISSN: 1065-7339
    Online ISSN: 1065-7339
    Primary MSC: 12; 13; 14; 15; 16; 18; 20
    Textbook?: true
    Applied Math?: false
    Home Page?: false
    Sample?: false
    Reference?: false
    Electronic Media?: false
    Apparel or Gift: false
    SXG Subject: AA
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/gsm-165
    Online Price 1 Label: List
    Online Price 1: 89.00
    Print Price 1 Label: List
    Print Price 1: 89.00
    Online Price 2 Label: Individual Member
    Online Price 2: 71.20
    Print Price 2 Label: Individual Member
    Print Price 2: 71.20
    Dual Price 1 Label: List
    Dual Price 1: 111.25
    Dual Price 2 Label: Individual Member
    Dual Price 2: 89
    Print Add to Cart URL: /some/url/at/AMS/GSM-165
    Electronic Add to Cart URL: /some/url/at/AMS/GSM-165.E
    Exam/Desk Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2731-3&pisbn=978-1-4704-1554-9&epc=GSM/165.E&ppc=GSM/165&title=Advanced%20Modern%20Algebra%3A%20Third%20Edition%2C%20Part%201&author=Joseph%20J.%20Rotman&type=DE
    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-2731-3&pisbn=978-1-4704-1554-9&epc=GSM/165.E&ppc=GSM/165&title=Advanced%20Modern%20Algebra%3A%20Third%20Edition%2C%20Part%201&author=Joseph%20J.%20Rotman&type=R
    Sets and Parts:

    This item is also available as part of a set:

    GSM/165/180

    Readership:

    Graduate students and researchers interested in learning and teaching algebra.

    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

    Related Products: Algebra Algebra: Chapter 0
    Cover Image URL: ~~FreeAttachments/gsm-165-cov.jpg
  • Advanced Modern Algebra: Second Edition
    Base Product Code Keyword List: gsm; GSM; gsm/114; GSM/114; gsm-114; GSM-114
    Online Product Code: GSM/114.E
    Title (HTML): Advanced Modern Algebra: Second Edition
    Author(s) (Product display): Joseph J. Rotman
    Abstract:

    This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different organization than the first. It begins with a discussion of the cubic and quartic equations, which leads into permutations, group theory, and Galois theory (for finite extensions; infinite Galois theory is discussed later in the book). The study of groups continues with finite abelian groups (finitely generated groups are discussed later, in the context of module theory), Sylow theorems, simplicity of projective unimodular groups, free groups and presentations, and the Nielsen–Schreier theorem (subgroups of free groups are free).

    The study of commutative rings continues with prime and maximal ideals, unique factorization, noetherian rings, Zorn's lemma and applications, varieties, and Gröbner bases. Next, noncommutative rings and modules are discussed, treating tensor product, projective, injective, and flat modules, categories, functors, and natural transformations, categorical constructions (including direct and inverse limits), and adjoint functors. Then follow group representations: Wedderburn–Artin theorems, character theory, theorems of Burnside and Frobenius, division rings, Brauer groups, and abelian categories. Advanced linear algebra treats canonical forms for matrices and the structure of modules over PIDs, followed by multilinear algebra.

    Homology is introduced, first for simplicial complexes, then as derived functors, with applications to Ext, Tor, and cohomology of groups, crossed products, and an introduction to algebraic \(K\)-theory. Finally, the author treats localization, Dedekind rings and algebraic number theory, and homological dimensions. The book ends with the proof that regular local rings have unique factorization.

    Book Series Name: Graduate Studies in Mathematics
    Volume: 114
    Publication Month and Year: 2010-08-11
    Copyright Year: 2010
    Page Count: 1008
    Online ISBN 13: 978-1-4704-1176-3
    Online ISSN: 1065-7339
    Primary MSC: 11; 12; 13; 15; 16; 18; 19; 20
    Textbook?: true
    Applied Math?: false
    Home Page?: false
    Sample?: false
    Reference?: false
    Electronic Media?: false
    Apparel or Gift: false
    SXG Subject: AA
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/gsm-114
    Online Price 1 Label: List
    Online Price 1: 99.00
    Online Price 2 Label: Individual Member
    Online Price 2: 79.20
    Electronic Add to Cart URL: /some/url/at/AMS/GSM-114.E
    Exam/Desk Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1176-3&epc=GSM/114.E&title=Advanced%20Modern%20Algebra%3A%20Second%20Edition&author=Joseph%20J.%20Rotman&type=DE
    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-1176-3&epc=GSM/114.E&title=Advanced%20Modern%20Algebra%3A%20Second%20Edition&author=Joseph%20J.%20Rotman&type=R