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Cool Math for Hot Music [electronic resource] : A First Introduction to Mathematics for Music Theorists / by Guerino Mazzola, Maria Mannone, Yan Pang.

By: Mazzola, Guerino [author.].
Contributor(s): Mannone, Maria [author.] | Pang, Yan [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Computational Music Science: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2016Description: XV, 323 p. 179 illus., 112 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319429373.Subject(s): Computer science | Music | Computer science -- Mathematics | Artificial intelligence | Application software | Mathematics | Computer Science | Computer Appl. in Arts and Humanities | Music | Mathematics in Music | Mathematics of Computing | Artificial Intelligence (incl. Robotics)Additional physical formats: Printed edition:: No titleDDC classification: 004 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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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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.

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