mathematics
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mathematics
The science that deals with the properties and patterns of numbers, sets, figures, and structures.
Für viele Schüler ist die Mathematik eines der schwierigsten Fächer.
For many students, mathematics is one of the most difficult subjects.
The ending '-ik' is typical of many words that refer to a science or field of study. Other examples are 'Physik' (physics), 'Musik' (music), or 'Logik' (logic).
Die Informatik ist ein Teilgebiet der Mathematik.
Computer science is a subfield of mathematics.
In everyday language, especially in a school context, 'Mathematik' (mathematics) is very often shortened to 'Mathe' (math). This short form is colloquial and very common.
Ich muss noch meine Hausaufgaben für Mathe machen.
I still have to do my homework for math.
When 'Mathematik' (mathematics) refers to a school subject or field of study, it is often used without an article. When talking about the science as a whole, it usually appears with the definite article 'die'.
Am Montag haben wir in der ersten Stunde Mathematik.
On Monday, we have mathematics in the first period.
math
'die Mathematik' and 'die Mathe' mean the same subject or field in many situations. The difference is mainly in style. 'Die Mathematik' sounds complete and fits well in formal texts, at university, or when talking about the science. 'Die Mathe' is the short, colloquial form and sounds especially natural at school and in everyday speech. In an official text, you would tend to use 'Mathematik'; in conversation, many people simply say 'Mathe'.
An der Universität beschäftigt sich Lena mit der Geschichte der Mathematik.
At university, Lena studies the history of mathematics.
Für die Mathe hat Max gestern zwei Stunden gelernt.
Max studied for math for two hours yesterday.