000			02960nam a22004695i 4500
001			978-0-387-26955-9
003			DE-He213
005			20250710083937.0
007			cr nn 008mamaa
008			100301s2005 xxu| s |||| 0|eng d
020			_a9780387269559 _a99780387269559
024	7		_a10.1007/b138364 _2doi
082	0	4	_a512 _223
100	1		_aChambert-Loir, Antoine. _eauthor.
245	1	2	_aA Field Guide to Algebra _h[recurso electrónico] / _cby Antoine Chambert-Loir.
264		1	_aNew York, NY : _bSpringer New York, _c2005.
300			_aX, 195 p. 12 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUndergraduate Texts in Mathematics, _x0172-6056
505	0		_aField extensions -- Roots -- Galois theory -- A bit of group theory -- Applications -- Algebraic theory of differential equations.
520			_aThis unique textbook focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of pi and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibility theorem. The reader will hear about equations, both polynomial and differential, and about the algebraic structure of their solutions. In explaining these concepts, the author also provides comments on their historical development and leads the reader along many interesting paths. In addition, there are theorems from analysis: as stated before, the transcendence of the numbers pi and e, the fact that the complex numbers form an algebraically closed field, and also Puiseux's theorem that shows how one can parametrize the roots of polynomial equations, the coefficients of which are allowed to vary. There are exercises at the end of each chapter, varying in degree from easy to difficult. To make the book more lively, the author has incorporated pictures from the history of mathematics, including scans of mathematical stamps and pictures of mathematicians. Antoine Chambert-Loir taught this book when he was Professor at École polytechnique, Palaiseau, France. He is now Professor at Université de Rennes 1.
650		0	_aMATHEMATICS.
650		0	_aALGEBRA.
650		0	_aFIELD THEORY (PHYSICS).
650		0	_aNUMBER THEORY.
650	1	4	_aMATHEMATICS.
650	2	4	_aALGEBRA.
650	2	4	_aFIELD THEORY AND POLYNOMIALS.
650	2	4	_aNUMBER THEORY.
650	2	4	_aCOMMUTATIVE RINGS AND ALGEBRAS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387214283
830		0	_aUndergraduate Texts in Mathematics, _x0172-6056
856	4	0	_uhttp://dx.doi.org/10.1007/b138364 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c56603 _d56603