MARC Record from Library of Congress

LEADER: 02926cam a22004094a 4500
001 2010044378
003 DLC
005 20111104112607.0
008 101101s2011 riua b 001 0 eng
010 $a 2010044378
020 $a9780821853184 (alk. paper)
020 $a082185318X (alk. paper)
035 $a(OCoLC)ocn676922968
040 $aDLC$cDLC$dYDX$dYDXCP$dIXA$dCDX$dUBY$dDLC
042 $apcc
050 00 $aQA247.4$b.C74 2011
082 00 $a515/.354$222
084 $a12H05$a13B05$a14A10$a17B45$a20G15$a34M35$a68W30$2msc
100 1 $aCrespo, Teresa,$d1955-
245 10 $aAlgebraic groups and differential Galois theory /$cTeresa Crespo, Zbigniew Hajto.
260 $aProvidence, R.I. :$bAmerican Mathematical Society,$cc2011.
300 $axiv, 225 p. :$bill. ;$c26 cm.
490 1 $aGraduate studies in mathematics ;$vv. 122
520 $a"Differential Galois theory has seen intense research activity during the last decades in several directions: elaboration of more general theories, computational aspects, model theoretic approaches, applications to classical and quantum mechanics as well as to other mathematical areas such as number theory. This book intends to introduce the reader to this subject by presenting Picard-Vessiot theory, i.e. Galois theory of linear differential equations, in a self-contained way. The needed prerequisites from algebraic geometry and algebraic groups are contained in the first two parts of the book. The third part includes Picard-Vessiot extensions, the fundamental theorem of Picard-Vessiot theory, solvability by quadratures, Fuchsian equations, monodromy group and Kovacic's algorithm. Over one hundred exercises will help to assimilate the concepts and to introduce the reader to some topics beyond the scope of this book."--$cProvided by publisher.
504 $aIncludes bibliographical references and index.
650 0 $aDifferential algebraic groups.
650 0 $aGalois theory.
650 0 $aMorphisms (Mathematics)
650 7 $aField theory and polynomials -- Differential and difference algebra -- Differential algebra.$2msc
650 7 $aCommutative algebra -- Ring extensions and related topics -- Galois theory.$2msc
650 7 $aAlgebraic geometry -- Foundations -- Varieties and morphisms.$2msc
650 7 $aNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Lie algebras of linear algebraic groups.$2msc
650 7 $aGroup theory and generalizations -- Linear algebraic groups and related topics -- Linear algebraic groups over arbitrary fields.$2msc
650 7 $aOrdinary differential equations -- Differential equations in the complex domain -- Singularities, monodromy, local behavior of solutions, normal forms.$2msc
650 7 $aComputer science -- Algorithms -- Symbolic computation and algebraic computation.$2msc
700 1 $aHajto, Zbigniew.
830 0 $aGraduate studies in mathematics ;$vv. 122.