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Algebraic Groups and Differential Galois Theory (Graduate Studies in Mathematics): 122
Author(s): Teresa Crespo (Author), Zbigniew Hajto (Author)
- Publisher: American Mathematical Society
- Publication Date: 1 April 2011
- Language: English
- Print length: 225 pages
- ISBN-10: 082185318X
- ISBN-13: 9780821853184
Book Description
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.
Editorial Reviews
Review
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
About the Author
Teresa Crespo, Universitat de Barcelona, Barcelona, Spain
Zbigniew Hajto, Jagiellonian University, Kraków, Poland
