## Applying Mathematical Analysis

Mathematical analysis is the process of factoring theoretical early and late start dates and theoretical early and late finish dates for each activity within the project network diagram (PND). The early and late dates are not the expected schedule, but rather a potential schedule based on the project constraints, the likelihood of success, the availability of resources, and other constraints.

The most common approach to calculating when a project may finish is by using the critical path method. It uses a "forward" and "backward" pass to reveal which activities are considered critical. Activities on the critical path may not be delayed; otherwise, the project end date will be delayed. The critical path is the path with the longest duration to completion. Activities not on the critical path have some float (also called slack) that allows some amount of delay without delaying the project end date.

EXAM TIP The critical path is used to determine which activities have no float. You can also use the critical path to determine the earliest date for when the project may be completed. There can be more than one critical path in a project, and it's possible for the critical path to change.