Adding to this, it's very worthwhile exercise for any curious programmer to work out the IV of a stock based on options pricing and compare it to other measure of volatility (for example historic volatility, or even your own beliefs about volatility based on what you think future returns might be).

Black-Scholes/Merton makes a lot more sense once you work it all out yourself in code.

I'd actually suggest doing this through modeling the underlying geometric Brownian motion and ensuring that your simulated results match up to the analytic formula.