Mathematics and Computer Science Computer programming requires that the exact sequence of steps to perform a task must be specified completely and precisely . This is difficult, and requires careful reasoning about abstract entities and operations . Mathematics has developed over thousands of years as a method of abstract reasoning. Mathematical Objects and Operations Sets are collections of other objects, such as the set of all students in this room, or the set of all prime numbers less than 100,000. Operations on graphs include finding paths, cycles, and components.
Trees are diagrams of hierarchical relationships, such as family trees or corporate hierarchies.
Problem Solving Methods Recursion is a problem solving method in which the solution to a large problem is obtained by combining solutions to smaller instances of the same kind of problem. For example, to find all the descendents of x , concatenate the lists of descendents of each of x 's children. Induction is a reasoning method in which large objects are shown to have some property by combining proofs that smaller subobjects have the property. For example, to show that every even integer n is divisible by 2, use the fact that the previous even integer n -2 is divisible by 2. The primary operation in logic is inference , testing whether a statement is true.