**Algebra vs Calculus**

**Algebra vs Calculus**

Mathematics has its place in our everyday life. It helps in getting our problems solved in a systematic way. Mathematics has various branches, namely Algebra, Calculus, Trigonometry, Geometry, etc. Each branch has its importance and different applications.

Algebra is a branch of mathematics that acts as the base of modern arithmetic and modern mathematics. Algebra finds the values of the variables.

Calculus is a branch that is difficult to understand and is used at advanced levels of studies. Calculus studies the rate of change of events.

The **difference between Algebra and Calculus** lies in the basis of the two. Algebra is a branch of mathematics that deals with finding the values of the unknown variable by solving linear, cubic or quadratic equations that are termed as algebraic equations whereas Calculus is a branch of mathematics that deals with the rate of change of functions.

## Comparison Table Between Algebra and Calculus (in Tabular Form)

Parameter of Comparison | Algebra | Calculus |
---|---|---|

Basic idea | Algebra deals with finding the values of unknown variables. | Calculus deals with finding the rate of change of functions. |

Origin time | Originated in ancient times, development dates back to the medieval period. | Originated during the 17th century. |

Domain of work | Operates within a known domain and obtains the result within that. | Don't have any specific domain, while solving the problem one can get to know new things and results may or may not be in the domain. |

Main operations | Solving equations. | Differentiation and Integration. |

Uses | Used in everyday life mathematics such as finding distance, displacement, the slope of the line, etc. | Used in complicated fields and advanced studies. |

## What is Algebra?

A branch of mathematics that uses letters and symbols to represent numbers working on predefined rules. These symbols or letters are termed as variables. Therefore, it can be said that Algebra is a relationship between different variables defined on operators known as algebraic equations.

In other words, Algebra is generalized arithmetic where variables represent all the possible numbers in the place. Algebra helps in the formation of correlated equations and then solving them to obtain values of the variables.

The roots of algebra were laid down by the Babylonians who are also responsible for the development of advanced arithmetic. They developed formulas to solve problems using linear or quadratic equations.

During the time of Plato, Greeks developed another tactic to deal with such problems which they termed as Geometric Algebra. A Greek mathematician, Diophantus later came to be known as the “father of algebra”. The first complete solution including zero and negative values to the algebraic equations was given by an Indian mathematician Brahmagupta in his book Brahmasphitasiddhanta.

During the 16th century, Francois Viete’s works proved to be an important step towards the development of modern algebra. In the mid 16th century, another event that marked the further development of algebra was the solution of cubic and quadratic equations.

Algebra can be broadly classified into two categories- Elementary Algebra, which mainly consists of the basic part of the algebra that is essential to any mathematical study and Abstract or Modern Algebra, that consists of advanced algebra, it is generally studied by the professional mathematicians or academicians.

Algebra is used in every field of day to day life. It has an important place in statistics, engineering, economics, computer programming, etc.

## What is Calculus?

Calculus is a branch of mathematics that deals with the change of functions that are related to each other. In other words, Calculus is the study of the rate of change of functions.

It was during the 17th century that Issac Newton and Gottfried Wilhelm Leibniz independently developed the modern Calculus. Before the invention of Calculus, one can only calculate the values of the variables but can’t deduce the rates.

The invention of Calculus became the first achievement of modern mathematics. Newton developed formulas to calculate the rates, series expansion for functions according to the Taylor series of expansion.

There are two branches of Calculus, namely- Differential Calculus, that uses derivatives to find the rate of change of slopes or curves, and Integral Calculus, that finds the quantity for which the rate of change is already known.

Calculus is of utmost importance in physical sciences, actuarial sciences, computer sciences, statistics, demography, etc.

**Main Differences Between Algebra and Calculus**

- Algebra is the branch of mathematics that helps in finding the values of unknown variables. It is the relationship between different variables. On the other hand, Calculus is the branch of mathematics that helps in finding the rate of change of entities or functions with respect to each other.
- Algebra is the branch that originated during the ancient times and was developed in medieval times whereas Calculus was invented by Issac Newton during the 17th century.
- Algebra is referred to as Old mathematics while Calculus is known as Modern mathematics.
- Algebra has a specified domain of work; it operates within it and obtains results in the same while Calculus has no domain of work one may get unexpected results after solving the problem.
- The main operation of Algebra is to solve the algebraic equations while Calculus deals with differentiation and integration.
- Algebra is known as everyday mathematics as it helps in solving related to everyday life while Calculus is used in advanced fields like statistics, actuarial sciences, computer sciences, etc.

## Conclusion

Although Algebra and Calculus are the different branches of mathematics, they are correlated. Algebra deals with variables while Calculus with rates even then they are interrelated. Both are sometimes used in sync with each other to get certain problems solved.

Algebra and Calculus have advantages in their respective fields. At the elementary school level, Algebra is easy to understand but there is no Calculus.