Fakultät

Fakultät is a German term with two principal meanings. In higher education, it refers to a major organizational unit within a university, grouping together related subjects, disciplines, and academic programs. A Fakultät typically has its own administration, including a dean, and is responsible for curricula, examinations, and degree programs within its field. Examples include the Fakultät für Rechtswissenschaft (law), die Fakultät für Medizin (medicine), and die Fakultät für Naturwissenschaften (natural sciences). The structure and naming of faculties can vary between institutions and countries, with some universities using departments or schools as the primary divisions.

In mathematics, Fakultät denotes the factorial function, written with an exclamation mark as n!, and defined for nonnegative integers n as the product of all positive integers up to n (n! = 1 × 2 × ... × n). The factorial grows rapidly and is fundamental in combinatorics, probability, and algebra, for example in counting permutations or in binomial coefficients. For n = 5, 5! equals 120, and by convention 0! is defined as 1. The factorial concept extends beyond integers through the gamma function, which generalizes the idea to real and complex numbers.

Etymologically, Fakultät comes from Latin facultas meaning “ability” and was transmitted into German via French faculté. In university contexts, the term conveys both a field-based organizational unit and, in older or specialized texts, the sense of a faculty capable of judging or granting degrees.