000			03472nam a22004695i 4500
001			978-0-387-46112-0
003			DE-He213
005			20250710084000.0
007			cr nn 008mamaa
008			100301s2007 xxu| s |||| 0|eng d
020			_a9780387461120 _a99780387461120
024	7		_a10.1007/978-0-387-46112-0 _2doi
082	0	4	_a511.6 _223
100	1		_aBeck, Matthias. _eauthor.
245	1	0	_aComputing the Continuous Discretely _h[recurso electrónico] : _bInteger-Point Enumeration in Polyhedra / _cby Matthias Beck, Sinai Robins.
264		1	_aNew York, NY : _bSpringer New York, _c2007.
300			_aXVIII, 226 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aThe Essentials of Discrete Volume Computations -- The Coin-Exchange Problem of Frobenius -- A Gallery of Discrete Volumes -- Counting Lattice Points in Polytopes:The Ehrhart Theory -- Reciprocity -- Face Numbers and the Dehn-Sommerville Relations in Ehrhartian Terms -- Magic Squares -- Beyond the Basics -- Finite Fourier Analysis -- Dedekind Sums, the Building Blocks of Lattice-point Enumeration -- The Decomposition of a Polytope into Its Cones -- Euler-Maclaurin Summation in ?d -- Solid Angles -- A Discrete Version of Green's Theorem Using Elliptic Functions.
520			_aThis much-anticipated textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. Because there is no other book that puts together all of these ideas in one place, this text is truly a service to the mathematical community. We encounter here a friendly invitation to the field of "counting integer points in polytopes," also known as Ehrhart theory, and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant, and the authors' engaging style encourages such participation. The many compelling pictures that accompany the proofs and examples add to the inviting style. For teachers, this text is ideally suited as a capstone course for undergraduate students or as a compelling text in discrete mathematical topics for beginning graduate students. For scientists, this text can be utilized as a quick tooling device, especially for those who want a self-contained, easy-to-read introduction to these topics.
650		0	_aMATHEMATICS.
650		0	_aCOMPUTER SCIENCE.
650		0	_aCOMBINATORICS.
650		0	_aDISCRETE GROUPS.
650		0	_aNUMBER THEORY.
650	1	4	_aMATHEMATICS.
650	2	4	_aCOMBINATORICS.
650	2	4	_aNUMBER THEORY.
650	2	4	_aCONVEX AND DISCRETE GEOMETRY.
650	2	4	_aCOMPUTATIONAL SCIENCE AND ENGINEERING.
700	1		_aRobins, Sinai. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387291390
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-46112-0 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c57685 _d57685