die Fachrichtung
specialization
A specialized subfield within a larger academic discipline, course of study, or training area.
Sie studiert Medizin mit der Fachrichtung Kardiologie.
She is studying medicine with a specialization in cardiology.

specialization
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specialization
A specialized subfield within a larger academic discipline, course of study, or training area.
Sie studiert Medizin mit der Fachrichtung Kardiologie.
She is studying medicine with a specialization in cardiology.

The word is made up of 'Fach' (subject, as in an academic subject or field) and 'Richtung' (direction). So it literally describes the specific direction you take within a subject.
Innerhalb des Fachs Informatik gibt es viele verschiedene Richtungen.
Within the field of computer science, there are many different directions.
The component 'Fach-' is very productive and always refers to a specific area or expertise. Other examples are 'Fachbuch' (specialist book), 'Fachsprache' (technical language), 'Fachmann' (expert), or 'Facharzt' (medical specialist).
Für dieses Problem brauchen wir einen Fachmann.
For this problem, we need an expert.
'Fachrichtung' (specialization) is used almost exclusively in the context of education and work, especially for degree programs at universities or for vocational training occupations.
Welche Fachrichtung möchtest du in deinem Masterstudium wählen?
Which specialization would you like to choose in your master's program?
Common verbs used with 'Fachrichtung' (specialization) are 'wählen' (to choose), 'wechseln' (to change), 'studieren' (to study), or 'sich spezialisieren auf' (to specialize in).
Er hat sich entschieden, seine Fachrichtung von Maschinenbau zu Elektrotechnik zu wechseln.
He decided to change his specialization from mechanical engineering to electrical engineering.
science
'die Wissenschaft' and 'die Fachrichtung' can both have to do with an academic or professional area. 'Wissenschaft' means a larger area of knowledge and research, for example chemistry or history. 'Fachrichtung' means a more specific direction within a course of study, a training program, or a larger subject. You often use 'Fachrichtung' when someone chooses what they specialize in. The words can be confused because a 'Fachrichtung' can belong to a 'Wissenschaft'. Remember: 'Wissenschaft' is the larger area, while 'Fachrichtung' is the chosen specialization within it.

Im Studium wählt er die Fachrichtung Umwelttechnik.
In his studies, he chooses the specialization environmental engineering.
Die Biologie ist eine Wissenschaft, die sich mit Lebewesen beschäftigt.
Biology is a science that deals with living things.