Cool Math For Hot Music: A First Introduction To Mathematics For Music Theorists by Guerino MazzolaCool Math For Hot Music: A First Introduction To Mathematics For Music Theorists by Guerino Mazzola

Cool Math For Hot Music: A First Introduction To Mathematics For Music Theorists

byGuerino Mazzola, Maria Mannone, Yan Pang

Hardcover | November 8, 2016

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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.

Prof. Dr. Guerino Mazzola earned his Ph.D. in Mathematics from Zurich University. He wrote the groundbreaking book The Topos of Music in 2002, its formal language and models are used by leading researchers in Europe, India, Japan, and North America and have become a foundation of music software design. Prof. Mazzola has an appointment ...
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Title:Cool Math For Hot Music: A First Introduction To Mathematics For Music TheoristsFormat:HardcoverDimensions:323 pagesPublished:November 8, 2016Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319429353

ISBN - 13:9783319429359

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Table of 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.

Editorial Reviews

"This textbook in mathematics for music theorists introduces topics such as sets and functions, algebraic structures including groups, rings, matrices and modules, and more. The book includes many illustrations, online sample music files, and exercises with solutions. . Concepts are motivated and supported by examples from composition music theory." (Tom Schulte, MAA Reviews, maa.org, February, 2017)