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008			161026s2016 gw | s |||| 0|eng d
020			_a9783319429373
040			_aES-MaUEC
050		4	_aML3800 _b.M399 2016
082	0	4	_a004
100	1		_aMazzola, Guerino. _914065 _0comprobar BNE19925784576
245	1	0	_aCool Math for Hot Music : _bA First Introduction to Mathematics for Music Theorists _cby Guerino Mazzola, Maria Mannone, Yan Pang
260			_aCham _bSpringer International Publishing _c2016
300			_a1 recurso en línea (XV, 323 páginas) _b179 ilustraciones, 112 ilustraciones en color
336			_aTexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
490	0		_aComputational Music Science _x1868-0305
505	0		_aPart I: Introduction and Short History -- The �Counterpoint� of Mathematics and Music -- Short History of the Relationship Between Mathematics and Music -- Part II: Sets and Functions -- The Architecture of Sets -- Functions and Relations -- Universal Properties -- Part III: Numbers -- Natural Numbers -- Recursion -- Natural Arithmetic -- Euclid and Normal Forms -- Integers -- Rationals -- Real Numbers -- Roots, Logarithms, and Normal Forms -- Complex Numbers -- Part IV: Graphs and Nerves -- Directed and Undirected Graphs -- Nerves -- Part V: Monoids and Groups -- Monoids -- Groups -- Group Actions, Subgroups, Quotients, and Products -- Permutation Groups -- The Third Torus and Counterpoint -- Coltrane�s Giant Steps -- Modulation Theory -- Part VI: Rings and Modules -- Rings and Fields -- Primes -- Matrices -- Modules -- Just Tuning -- Categories -- Part VII: Continuity and Calculus -- Continuity -- Differentiability -- Performance -- Gestures -- Part VIII: Solutions, References, Index -- Solutions of Exercises -- References -- Index.
520	3		_aThis textbook is a first introduction to mathematics for music theorists, covering basic topics such as sets and functions, universal properties, numbers and recursion, graphs, groups, rings, matrices and modules, continuity, calculus, and gestures. It approaches these abstract themes in a new way: Every concept or theorem is motivated and illustrated by examples from music theory (such as harmony, counterpoint, tuning), composition (e.g., classical combinatorics, dodecaphonic composition), and gestural performance. The book includes many illustrations, and exercises with solutions.
710	2		_aSpringerLink (Online service) _0Local _9106996
942			_2lcc _cLE
988			_aEBOOK, asignarmaterias , EBSPRINGER
650		7	_aMúsica _0comprobar BNE19900961860 _2embne _9138603
650		7	_aMatemáticas _0(OCoLC)1012163 _2embne _0 _9405008
700	1		_aMannone, Maria. _999921 _0Local
700	1		_aPang, Yan. _999922 _0Local
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://link.springer.com/book/10.1007/978-3-319-42937-3 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
901			_ai9783319429373
907			_a.b12955760 _b10-10-17 _c21-11-16
998			_am _a_alco _a_vill _b - - _cm _dz _e- _feng _ggw _h0
945			_aML3800 .M399 2016 EB _g1 _ieBOOK _j0 _lmae _o- _pEUR0.00 _q- _r- _sb _t15 _u0 _v0 _w0 _x0 _y.i11597823 _z06-04-17
999			_c86298 _d86298 _x1