This project examines not so much which functions can be computed, or which problems can be 'effectively' solved, as what is the cost of performing this computation or solution in terms of the number of steps taken. This is a major field in theoretical computer science.
The project may include some account of space and time complexity, measures of rate of growth of functions using O- and o-notations, some account of the P=NP problem (one of the millennium problems), with careful definitions of explanations of what these terms mean, and may also discuss algorithms for addition and multiplication of integers, or matrices, sorting and searching, or algorithms for solving problems in graph theory.