This lecture discusses the BigO Notation and Binary Search.
BigO Notation
BigO notation is used to describe the order of growth of many types of things. In CS2040S, we use it to describe time complexity of algorithms.
Note that:

$O(f(n))$ describes the upperbound of the growth of $f$, i.e. the worst casetime complexity;

$\Omega(f(n))$ describes the lowerbound of the growth of $f$, i.e. the bestcase time complexity;

$\Theta(f(n))$ describes is best approximation of the order of growth of $f$, i.e. the average time complexity.
Binary Search
Searches for an element in a sorted array in $O(log(n))$ time.