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 as professor in the School of Music at the College of Liberal Arts, University of Minnesota.

Maria Caterina Mannone is completing her Ph.D. in the School of Music of the University of Minnesota.

Based on authors' experience teaching mathematics to music theorists

Presents ideas in a critical manner, highlighting problems with earlier teaching approaches

Includes many illustrations and exercises with solutions

Includes supplementary material: [...]

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.