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Cool math for hot musica first intro...

Mannone, Maria.

Cool math for hot musica first introduction to mathematics for music theorists /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Cool math for hot musicby Guerino Mazzola, Maria Mannone, Yan Pang.
Reminder of title:	a first introduction to mathematics for music theorists /
Author:	Mazzola, Guerino.
other author:	Mannone, Maria.
Published:	Cham :Springer International Publishing :2016.
Description:	xv, 323 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	MusicMathematics.
Online resource:	http://dx.doi.org/10.1007/978-3-319-42937-3
ISBN:	9783319429373$q(electronic bk.)

Cool math for hot musica 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$q(electronic bk.)

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

737289
Music
--Mathematics.

LC Class. No.: ML3800

Dewey Class. No.: 780.0519

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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.
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