Most of the mathematical problems that one encounters have already been solved and documented. Thus, the most important problem-solving tools are references. A reference can be anything—a book, a person, or a past experience—that aids in understanding and solving a problem. References enable one to solve problems independently when no other source of help is available.

Basic Strategies

The following are some general problem-solving strategies: break the problem into smaller parts, find a new perspective, work backward, guess. In all of these strategies, simple logic is used.

Logic. Mathematics is internally consistent. If at any point a false statement is generated, like 0 = 1, it is at once apparent that an error or a false assumption has been made. A false statement can be generated intentionally, as in a proof by contradiction.

Mutually exclusive dichotomies and trichotomies categorize the universe...