Mathematics includes many different subjects. So the term 'mathematics' is usually hard to define. But here is a definition that fits most of the mathematics taught in school or college:
MATHEMATICS is the study of quantities and relations through the use of numbers and symbols.
ARITHMETIC deals with quantities expressed by numbers.
ALGEBRA uses quantities and relations expressed by symbols.
GEOMETRY involves quantities associated with figures in space, such as length and area, and the relationships between figures in space.
TRIGONOMETRY is concerned with the measurement of angles and with the relationships of angles.
ANALYTIC GEOMETRY applies algebra to geometric studies.
CALCULUS works with pairs of associated quantities and the way one quantity changes in relation to the other.
SCIENCE depends on mathematics for exact descriptions and formulas of observations and experiments. In fact, there is no legitimate science without mathematics.