Type of Mathematics with Examples

There are many types of mathematics because quantifying the world can be broken into many categories, and, over the years, each category has developed its own branch. For example, the study of rates of change has its own branch of math called calculus. The study of circles and right triangles and how they relate is called trigonometry, and the study of all shapes is called geometry. There are many more types of math other than these three, and the types of math described below are only a part of the expansive field of mathematics.

Arithmetic

Arithmetic is the study of numbers. It can be considered the basis of all mathematics, and the field of arithmetic consists of concepts such as counting and the manipulation of counting numbers. Addition, subtraction, multiplication, division, and exponentiation are all examples of arithmetic. Arithmetic is the most commonly used form of mathematics. Arithmetic is used when balancing a checking account, paying for items, or adding up the boxes of Girl Scout Cookies sold. Arithmetic is also used in physics, chemistry, biology, business, and any other field that uses numbers.

Examples of Arithmetic

a) Add 5 and 3. b) Multiply 2 and 4.

a) Adding means taking a group of 5 and a group of 3 and combining them. In math, addition uses a + symbol so 5 plus 3 is written as 5 + 3 and 5 + 3 = 8.

b) Multiplying means adding multiple groups of a number. This example asks that 4 groups of 2 be added. Multiplication can be written using an x or an *. In this example, 2*4 = 8.

Algebra

Many times, when trying to describe the world, some quantities are known but one or more quantities are unknown. The field of algebra is dedicated to the study of unknown numbers which are called variables. Algebra is also associated with functions which are mathematic expressions that define a relationship, and functions always contain at least one unknown quantity. The function {eq}r(x, y) = \sqrt(x^2 + y^2) {/eq} relates two points, x and y, and to the radius of a circle, r. This function, depicted in Figure 1, is the algebraic way to describe a circle.

Figure 1: A visual representation of the algebraic function f(x, y) = sqrt(x^2 + y^2).

Example of Algebra

Find the value of the variable in the expression 3 - x = 10.

Conceptually, this example wants to know what number when subtracted from 3 will equal 10. To solve this expression, the goal is to get the variable alone on one side. This can be done by subtracting 3 from both sides so that the expression becomes 3 - x - 3 = 10 -3. The 3's cancel on the left, and all that is left is -x = 7. Convention says that the variable should be positive, so x = -7. When -7 is subtracted from 3 it does indeed give a final answer of 10.

Geometry

Geometry is one of the oldest forms of mathematics, and it was Archimedes who was the first to calculate the value of {eq}\pi {/eq}, a naturally occurring value that is crucial to mathematics. Geometry concerns itself with the measurement of shapes, and the concepts of area, surface area, volume, and perimeter belong to the field of geometry. Geometry is used in physics, chemistry, biophysics, engineering, and other fields that are concerned with shapes.

Example of Geometry

Find the perimeter of the square in Figure 2.