There is evidence that exercising your brain help you stave off Alzheimer's disease, meaning studying mathematics, learning another languages, etc. all prolong your enjoyable lifespan!

There should be several good books on the mathematics of sound encoding/compression, as well as the mathematics of music itself, but I cannot recommend anything in particular.

I'll list some other books you might find interesting however :

Another nice elementary differential equations text is Boyce and DiPrima. Ordinary Differential Equations by Garrett Birkhoff and Gian-Carlo Rota is slightly more advanced. Folland's Introduction to Partial Differential Equations is a nice light introduction to the more advanced stuff that mathematicians working in PDE worry about.

If you're curious about Stochastic Differential Equations, Baxter and Rennie's Financial Calculus: An Introduction to Derivative Pricing gives a wonderfully simple, but fairly correct treatment of the Black-Scholes pricing formula. I'm afraid it doesn't talk about the Black-Scholes PDE though, which is basically the heat equation evolving backwards in time, but the stochastic calculous is enjoyable on it's own, and fairly elementary.

Wilf's Generatingfunctionology is a wonderful introduction to Generating Functions, which anyone reading mathematics solely for enjoyment should briefly delve into. You might also be interested in Introduction to the Theory of Computation by Sipser, or even Algorithm Design by Kleinberg and Tardos.