Trigonometry (from Greek , "triangle" and , "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

Algebra (from Arabic "al-jabr" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields.

The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra.

Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics.

Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.

Calculus (from Latin calculus, literally "small pebble used for counting") is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves); these two branches are related to each other by the fundamental theorem of calculus.

Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit.

Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Leibniz.

Today, calculus has widespread uses in science, engineering and economics.

Geometry (from the; "earth", "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

A mathematician who works in the field of geometry is called a geometer.

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.