## Mathematics: Arithmetic

Mathematics is one of the most important areas of study for mankind. It has applications in almost all fields: science, technology, business, medicine, meteorology, astronomy, etc. From elementary addition and subtraction to rocket science, mathematics is present everywhere.

Mathematics is a vast area of study and has developed throughout history. It's divided into several disciplines. Let's take a look at some of the popular disciplines.

**Arithmetic** is one of the oldest disciplines of mathematics and also the most basic. It deals with numbers and elementary operators (addition, subtraction, multiplication, and division). All the basic rules of interactions of these operators with numbers are covered in arithmetic. You can say that arithmetic is everyday math, useful for handy calculations. A simple multiplication problem is:

These numbers and operators form the basic building blocks of other disciplines of mathematics.

## Algebra & Geometry

One of the most widely used disciplines of mathematics, **algebra** involves the study of mathematical variables, functions, equations, and the rules associated with them. It uses unknown quantities represented by letters or symbols. It's the most basic and essential field of study and has applications across all the disciplines. Most commonly, it's used for solving equations for unknown variables. A typical algebra problem would look like:

The equation-solving rules in algebra are often applied in other disciplines as well.

The study of shapes, sizes, distance, location, etc. is called **geometry**. It covers length, area and volume, in one-, two-, and three-dimensional planes, respectively. It has many applications in our day-to-day life, such as finding the area of a plot of land, finding volume of a gas cylinder, etc. It also has many complex applications, such as in the field of astronomy to mark locations of stars, calculating distances between two celestial bodies, etc.

## Trigonometry & Calculus

**Trigonometry** involves the study of the relationship between angles and sides of a triangle. Most commonly it is used for right-angled triangles. It has special functions, called trigonometric functions, that relate the sides and angles. In real life applications, it's used commonly for finding heights of towers, buildings, mountains, etc. Trigonometric functions are also used in study of waves and their characteristics.

**Calculus** is another vast discipline associated with the study of conditions of continuous change and its impact on functions. It has two major branches. **Differential calculus** deals with the rate of change and slope of continuous functions. For example, biologists determine the rate of growth in bacterial culture with the help of differential calculus. **Integral calculus** involves calculating accumulation of entities and areas under curves. It's often used by architects to calculate the quantity of materials required for curved surfaces.

## Statistics & Probability

**Statistics** is the study of data. It is used for analyzing data to convert it into meaningful information, such as graphs, pie charts, histograms, and calculations of average, median, etc. This field is most commonly used in business, government surveys and census analysis, meteorology, etc.

Another discipline of mathematics that's closely related to statistics is **probability**. It involves the calculation of chances of occurrence of any event. It utilizes past data and deduces the chances from that. For example, the chances of rain on a particular day can be found by historical weather data and current atmospheric conditions.

These are some of the popular disciplines of mathematics. There are other more complex and abstract disciplines of mathematics that are used for more complex studies such as games, networks, and graphs.

## Lesson Summary

In this lesson, we explored some of the popular disciplines of mathematics and their applications.

**Arithmetic** involves the study of numbers and basic mathematical operators. This forms the building block for other disciplines.
**Algebra** involves the study of mathematical variables, functions, equations, and the rules associated with them.
**Geometry** is the study of shapes, sizes, and lengths.
**Trigonometry** is the study of triangles, involving relationship between angles and sides of a triangle.
**Calculus** involves measuring the continuous changes in functions.
**Differential calculus** deals with the rate of change and slope of continuous functions.
**Integral calculus** involves calculating accumulation of entities and areas under curves.

**Statistics** is the study of data.
**Probability** involves the calculation of chances of occurrence of any event.