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.