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Algebraic Groups and Differential Galois Theory
 
Teresa Crespo Universitat de Barcelona, Barcelona, Spain
Zbigniew Hajto Jagiellonian University, Kraków, Poland
Front Cover for Algebraic Groups and Differential Galois Theory
Available Formats:
Hardcover ISBN: 978-0-8218-5318-4
Product Code: GSM/122
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $48.00
Electronic ISBN: 978-1-4704-1183-1
Product Code: GSM/122.E
List Price: $56.00
MAA Member Price: $50.40
AMS Member Price: $44.80
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $90.00
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  • Front Cover for Algebraic Groups and Differential Galois Theory
  • Back Cover for Algebraic Groups and Differential Galois Theory
Algebraic Groups and Differential Galois Theory
Teresa Crespo Universitat de Barcelona, Barcelona, Spain
Zbigniew Hajto Jagiellonian University, Kraków, Poland
Available Formats:
Hardcover ISBN:  978-0-8218-5318-4
Product Code:  GSM/122
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $48.00
Electronic ISBN:  978-1-4704-1183-1
Product Code:  GSM/122.E
List Price: $56.00
MAA Member Price: $50.40
AMS Member Price: $44.80
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $90.00
MAA Member Price: $81.00
AMS Member Price: $72.00
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1222011; 225 pp
    MSC: Primary 12; 13; 14; 17; 20; 34; 68;

    Differential Galois theory has seen intense research activity during the last decades in several directions: elaboration of more general theories, computational aspects, model theoretic approaches, applications to classical and quantum mechanics as well as to other mathematical areas such as number theory.

    This book intends to introduce the reader to this subject by presenting Picard-Vessiot theory, i.e. Galois theory of linear differential equations, in a self-contained way. The needed prerequisites from algebraic geometry and algebraic groups are contained in the first two parts of the book. The third part includes Picard-Vessiot extensions, the fundamental theorem of Picard-Vessiot theory, solvability by quadratures, Fuchsian equations, monodromy group and Kovacic's algorithm. Over one hundred exercises will help to assimilate the concepts and to introduce the reader to some topics beyond the scope of this book.

    This book is suitable for a graduate course in differential Galois theory. The last chapter contains several suggestions for further reading encouraging the reader to enter more deeply into different topics of differential Galois theory or related fields.

    Readership

    Graduate students and research mathematicians interested in algebraic methods in differential equations, differential Galois theory, and dynamical systems.

  • Table of Contents
     
     
    • Part 1. Algebraic geometry
    • Chapter 1. Affine and projective varieties
    • Chapter 2. Algebraic varieties
    • Part 2. Algebraic groups
    • Chapter 3. Basic notions
    • Chapter 4. Lie algebras and algebraic groups
    • Part 3. Differential Galois theory
    • Chapter 5. Picard-Vessiot extensions
    • Chapter 6. The Galois correspondence
    • Chapter 7. Differential equations over $\mathbb {C}(z)$
    • Chapter 8. Suggestions for further reading
  • Reviews
     
     
    • This well-crafted book certainly serves its intended purpose well: it is a very good self-contained introduction to Picard-Vessiot theory. ... It is a very nice book indeed.

      MAA Reviews
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Volume: 1222011; 225 pp
MSC: Primary 12; 13; 14; 17; 20; 34; 68;

Differential Galois theory has seen intense research activity during the last decades in several directions: elaboration of more general theories, computational aspects, model theoretic approaches, applications to classical and quantum mechanics as well as to other mathematical areas such as number theory.

This book intends to introduce the reader to this subject by presenting Picard-Vessiot theory, i.e. Galois theory of linear differential equations, in a self-contained way. The needed prerequisites from algebraic geometry and algebraic groups are contained in the first two parts of the book. The third part includes Picard-Vessiot extensions, the fundamental theorem of Picard-Vessiot theory, solvability by quadratures, Fuchsian equations, monodromy group and Kovacic's algorithm. Over one hundred exercises will help to assimilate the concepts and to introduce the reader to some topics beyond the scope of this book.

This book is suitable for a graduate course in differential Galois theory. The last chapter contains several suggestions for further reading encouraging the reader to enter more deeply into different topics of differential Galois theory or related fields.

Readership

Graduate students and research mathematicians interested in algebraic methods in differential equations, differential Galois theory, and dynamical systems.

  • Part 1. Algebraic geometry
  • Chapter 1. Affine and projective varieties
  • Chapter 2. Algebraic varieties
  • Part 2. Algebraic groups
  • Chapter 3. Basic notions
  • Chapter 4. Lie algebras and algebraic groups
  • Part 3. Differential Galois theory
  • Chapter 5. Picard-Vessiot extensions
  • Chapter 6. The Galois correspondence
  • Chapter 7. Differential equations over $\mathbb {C}(z)$
  • Chapter 8. Suggestions for further reading
  • This well-crafted book certainly serves its intended purpose well: it is a very good self-contained introduction to Picard-Vessiot theory. ... It is a very nice book indeed.

    MAA Reviews
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