### Efficient Problem Solving

When one is either writing a proof or solving a problem, one must keep in mind that some proofs and some problems are quite involved and may have many little parts. The most parts it has the higher the chances that you might make a mistake. The worst is when one finally gets an answer only to find that is either wrong, or your proof has a fatal flaw.

This happens more often than not, and finding the culprit is usually a tedious and difficult task. In general one should start with the easier parts first, check your signs and symbols, then move on to the harder stuff like checking that each step is mathematically valid. The last step is usually the most tedious and time consuming and sometimes we constantly overlook any mistakes we make, therefore one should go through each step in detail and verfy it mathematicaly.

John G.