Among the ways to divide the field of mathematics is by field of application. There are many books and courses in schools labeled "Engineering mathematics", "Financial mathematics", "Mathematics for social scientists", and so on. While it is perhaps easier for the reader to have the material pre-filtered according to application, this hides the fact that the underlying mathematics is really quite similar.
is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of operations that combine numbers. In common usage, it refers to the simpler properties when using the traditional operations of addition, subtraction, multiplication and division with smaller values of numbers.
While the word algebra comes from the Arabic language (الجبر al-jabr "restoration") and much of its methods from Arabic/Islamic mathematics, its roots can be traced to earlier traditions, which had a direct influence on Muhammad ibn Mūsā al-Khwārizmī (c. 780–850). He later wrote The Compendious Book on Calculation by Completion and Balancing, which established algebra as a mathematical discipline that is independent of geometry and arithmetic.
is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies
Numerical analysis continues this long tradition of practical mathematical calculations, Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st century, the life sciences and even the arts have adopted elements of scientific computations, modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice.
