This presentation will briefly survey some of the most important links between
the fields of mathematics and music by grouping the links into four main areas:
mathematics in composition, mathematics in analysis, mathematics in acoustics,
and mathematics in synthesis. Each of these areas will suggest a certain kind
of connection that can be explored through research or applied as a tool for
the making of music or as a tool for the teaching of particular mathematical
concepts.\par Examples using probability theory, dynamical systems, set theory,
Fourier analysis and Chebychev polynomials in music composition and analysis
will be presented. These examples are included in a multidisciplinary course
"Mathematical Models in Music" developed by the authors and taught at North
Carolina State University.