Instead, the contest emphasizes problem solving skill within traditional middle-school mathematics.

Computable functions are a fundamental concept within computer science and mathematics.

Several terms used in category theory, including the term "morphism", differ from their uses within mathematics itself.

By the 1930s symbolic logic itself was adequately included within mathematics.

He backed away from sociological data, trying to remain within physics and mathematics.

The Magma system is used extensively within pure mathematics.

Applications within pure mathematics other than those found in the text are far too numerous and diverse to mention here.

As well as having applications within mathematics, they are useful in the study of music theory and visual harmony.

By the middle of the 20th century, topology had become an important area of study within mathematics.

Thus, functors are generally applicable in areas within mathematics that category theory can make an abstraction of.