國立虎尾科技大學 |

Cool math for hot music = a first introduction to mathematics for music theorists /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Cool math for hot music/ by Guerino Mazzola, Maria Mannone, Yan Pang.
其他題名:	a first introduction to mathematics for music theorists /
作者:	Mazzola, Guerino.
其他作者:	Mannone, Maria.
出版者:	Cham :Springer International Publishing : : 2016.,
面頁冊數:	xv, 323 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Music - Mathematics. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-42937-3
ISBN:	9783319429373

Cool math for hot music = a first introduction to mathematics for music theorists /
Mazzola, Guerino.

Cool math for hot musica first introduction to mathematics for music theorists /[electronic resource] :by Guerino Mazzola, Maria Mannone, Yan Pang. - Cham :Springer International Publishing :2016. - xv, 323 p. :ill., digital ;24 cm. - Computational music science,1868-0305. - Computational music science..

Part 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.

This 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.

ISBN: 9783319429373

Standard No.: 10.1007/978-3-319-42937-3doiSubjects--Topical Terms:

1102253
Music
--Mathematics.

LC Class. No.: ML3800

Dewey Class. No.: 780.0519

Cool math for hot music = a first introduction to mathematics for music theorists /
LDR:02733nam a2200349 a 4500 001 867559
003 DE-He213
005 20161026142451.0
006 m d
007 cr nn 008maaau
008 170720s2016 gw s 0 eng d
020 $a 9783319429373 $q (electronic bk.)
020 $a 9783319429359 $q (paper)
024 7 $a 10.1007/978-3-319-42937-3 $2 doi
035 $a 978-3-319-42937-3
040 $a GP $c GP
041 0 $a eng
050 4 $a ML3800
072 7 $a H $2 bicssc
072 7 $a UB $2 bicssc
072 7 $a COM018000 $2 bisacsh
072 7 $a ART000000 $2 bisacsh
082 0 4 $a 780.0519 $2 23
090 $a ML3800 $b .M477 2016
100 1 $a Mazzola, Guerino. $3 670247
245 1 0 $a Cool math for hot music $h [electronic resource] : $b a first introduction to mathematics for music theorists / $c by Guerino Mazzola, Maria Mannone, Yan Pang.
260 $a Cham : $c 2016. $b Springer International Publishing : $b Imprint: Springer,
300 $a xv, 323 p. : $b ill., digital ; $c 24 cm.
490 1 $a Computational music science, $x 1868-0305
505 0 $a Part 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 $a This 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.
650 0 $a Music $x Mathematics. $3 1102253
650 0 $a Music. $3 649088
650 0 $a Computer science $x Mathematics. $3 528496
650 0 $a Artificial intelligence. $3 559380
650 0 $a Application software. $3 528147
650 0 $a Mathematics. $3 527692
650 1 4 $a Computer Science. $3 593922
650 2 4 $a Computer Appl. in Arts and Humanities. $3 669937
650 2 4 $a Mathematics in Music. $3 885668
650 2 4 $a Mathematics of Computing. $3 669457
650 2 4 $a Artificial Intelligence (incl. Robotics) $3 593924
700 1 $a Mannone, Maria. $3 1114509
700 1 $a Pang, Yan. $3 1114510
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Computational music science. $3 1067005
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-42937-3
950 $a Computer Science (Springer-11645)