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Cool math for hot music[electronic resource] :a first introduction to mathematics for music theorists /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	780.0519
書名/作者:	Cool math for hot music : a first introduction to mathematics for music theorists // by Guerino Mazzola, Maria Mannone, Yan Pang.
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.
標題:	Music.
標題:	Computer science - Mathematics.
標題:	Artificial intelligence.
標題:	Application software.
標題:	Mathematics.
標題:	Computer Science.
標題:	Computer Appl. in Arts and Humanities.
標題:	Mathematics in Music.
標題:	Mathematics of Computing.
標題:	Artificial Intelligence (incl. Robotics)
ISBN:	9783319429373
ISBN:	9783319429359
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-42937-3

Cool math for hot music[electronic resource] :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:

652343
Music
--Mathematics.

LC Class. No.: ML3800

Dewey Class. No.: 780.0519

Cool math for hot music[electronic resource] :a first introduction to mathematics for music theorists /
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