# Lecture 6 - Asymptotic Analysis

Estimating the time complexity of a given function can be a tough task. Usually such reasoning is done in a casual way, which can mask errors in an analysis. When reasoning about the runtime of recursive functions, however, it turns out that we can write recurrence relations, which are mathematical equations that describe the runtime in a recursive way, and can be solved to a closed form.

We saw how we could examine SML code to obtain these recurrences, which describe the work, or runtime cost, of a function. By using a simple unrolling method, we can obtain a closed form, and then derive an asymptotic bound for a function's cost.

Next we introduced the concept of span, which is the work done by a parallel computer which can evaluate arbitrarily many expressions at the same time, and saw that we could similarly derive recurrences for estimating the span of a function.