000			03200nam a22004575i 4500
001			978-3-319-00888-2
003			DE-He213
005			20140220082839.0
007			cr nn 008mamaa
008			130718s2013 gw | s |||| 0|eng d
020			_a9783319008882 _9978-3-319-00888-2
024	7		_a10.1007/978-3-319-00888-2 _2doi
050		4	_aQA241-247.5
072		7	_aPBH _2bicssc
072		7	_aMAT022000 _2bisacsh
082	0	4	_a512.7 _223
100	1		_aAigner, Martin. _eauthor.
245	1	0	_aMarkov's Theorem and 100 Years of the Uniqueness Conjecture _h[electronic resource] : _bA Mathematical Journey from Irrational Numbers to Perfect Matchings / _cby Martin Aigner.
264		1	_aHeidelberg : _bSpringer International Publishing : _bImprint: Springer, _c2013.
300			_aX, 257 p. 72 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aApproximation of Irrational Numbers -- Markov's Theorem and the Uniqueness Conjecture -- The Markov Tree -- The Cohn Tree -- The Modular Group SL(2,Z) -- The Free Group F2 -- Christoffel Words -- Sturmian Words -- Proof of Markov's Theorem -- The Uniqueness Conjecture.  .
520			_aThis book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov’s theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov’s theorem. What makes the Markov theme so attractive is that it appears in an astounding variety of different fields, from number theory to combinatorics, from classical groups and geometry to the world of graphs and words. On the way, there are also introductory forays into some fascinating topics that do not belong to the standard curriculum, such as Farey fractions, modular and free groups, hyperbolic planes, and algebraic words. The book closes with a discussion of the current state of knowledge about the uniqueness conjecture, which remains an open challenge to this day. All the material should be accessible to upper-level undergraduates with some background in number theory, and anything beyond this level is fully explained in the text. This is not a monograph in the usual sense concentrating on a specific topic. Instead, it narrates in five parts – Numbers, Trees, Groups, Words, Finale – the story of a discovery in one field and its many manifestations in others, as a tribute to a great mathematical achievement and as an intellectual pleasure, contemplating the marvellous unity of all mathematics.
650		0	_aMathematics.
650		0	_aGroup theory.
650		0	_aCombinatorics.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aNumber Theory.
650	2	4	_aGroup Theory and Generalizations.
650	2	4	_aCombinatorics.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783319008875
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-319-00888-2
912			_aZDB-2-SMA
999			_c96490 _d96490